## 2020

Wednesday December 9: **Francesca Arici** (University of Leiden) **[Slides]**

*Title:* A non-commutative approach to the topology of circle and sphere bundles

The theory of C*–algebras offers an elegant setting for many problems in mathematics and physics. In view of Gel’fand duality, their study is often referred to as non-commutative topology: general noncommutative C*–algebras are interpreted as non-commutative spaces. Many classical geometric and topological concepts can be translated into operator algebraic terms, leading to the so-called noncommutative geometry (NCG) dictionary. In this talk, I will describe how circle and sphere bundles, central objects in the development of algebraic topology, can be realised in terms of modules over operator algebras.

Wednesday November 25, Speaker: **Botond Szabo** (VU)

*Title:* On theoretical guarantees for variational Bayes method

I will start by giving a brief introduction to Bayesian statistics, talk about its theoretical analysis and introduce variational methods to make the computations feasible. Variational Bayes is very popular and frequently used in practice, however, so far it was considered as a black box procedure. Theoretical results started to emerge only in the last 1-2 years, but we still have a rather limited fundamental understanding about the limitations and guarantees of this procedure. In the end of the talk I will provide theoretical and empirical guarantees for variational Bayes in context of the popular high-dimensional linear and logistic regression models.

Based on a joint work with Kolyan Ray and Gabriel Clara.

Wednesday October 28, Speaker: **Eni Muska** (UvA), Zoom meeting **[Slides] **

**Reference: **Amico, M. and Van Keilegom, I. (2018) Cure models in survival analysis. Annual Review of Statistics and Its Application, 5(1).

*Title:* Statistical methods for survival data: accounting for cured patients

Survival analysis is a branch of statistics that analyzes time-to-event data, where the variable of interest is the time it takes for a certain event to happen. It helps us answer questions like: -What percentage of cancer patients will survive more than 4 years? or -Which factors affect the survival time of cancer patients? Even though the main motivation comes from the medical setting, survival analysis is used in a variety of fields as any event of interest can be considered. In this talk, I will introduce the basics of survival analysis and some issues related to conventional methods that are still subject of ongoing research. In particular, I will focus on cure rate models which offer an alternative modelling approach that accounts for the presence of 'cure' (the possibility that the event never happens). Cure models can provide additional insights with respect to the traditional methods and are of particular interest in studies of some cancer types for which advances in medical treatments have led to increased chances of long-term-survival.

Wednesday October 7, Speaker: **Martijn Caspers** (VU Amsterdam), Zoom meeting **[Slides] **

*Title:* Perturbations of commutators

The mathematical physicists M.G. Krein posed in 1964 the question whether the norm of a commutator can be estimated after it is perturbed (for instance by noise or a chance of variables, to be made precise in the talk). We provide a solution to Krein's problem that is moreover sharp. The proof relies - surprisingly - almost entirely on harmonic analysis. The solution has important consequences, for instance for the existence of non-commutative Taylor series.

Wednesday September 23, Speaker: **Paulo Serra** (VU Amsterdam), Zoom meeting **[Slides]**

*Title:* Short tour through Mathematical Statistics

In this talk I will be taking you through some fundamental ideas in Mathematical Statistics. I will use the regression model to illustrate those ideas, as well as some common approaches to inference, and I will make a connection with some concrete problems that I am currently working on. I will close by presenting some recent ork. Technical aspects will be kept to a minimum so that everyone can follow.

Wednesday September 9, Speaker: **Joost Berkhout** (VU Amsterdam), Zoom meeting **[Slides]**

*Title:* Production Scheduling in an Industry 4.0 Era

In this talk, a modern industrial plant is considered that produces a large variety of composite biomaterials. Incoming orders are processed in real-time and slotted into a production schedule to meet the required delivery deadline. The scheduling problem is complicated because of numerous constraints, chief among them the limited storage capacity for intermediate or finished products and avoiding contamination between product runs. To tackle this scheduling problem, an algorithm is presented that combines a state-of-the-art model-based evolutionary algorithm (called Gene-pool Optimal Mixing Evolutionary Algorithm) with a mixed integer linear programming. Results from numerical experiments will be presented to demonstrate the effectiveness of the algorithm.

Wednesday June 17, Speaker: **Wioletta Ruszel** (UUtrecht), Zoom meeting

*Title:* Emergence of interfaces from sandpile models

Interfaces separating two phases (e.g. water and ice) are created in phase coexistence situations such as at 0 degree Celsius. Random interface models (in continuum space) are the Gaussian free field or fractional Gaussian fields. In this talk we would like to explain how Gaussian interface models emerge from divisible sandpiles. A divisible sandpile models is defined as follows: Given a graph, assign a (real-valued) hight s(x) to each vertex of G. A positive value s(x)>0 is interpreted as mass and a negative one as a hole. At every time step do the following: If the mass s(x)>1, then keep mass 1 and redistribute the excess among the neighbours. Under some conditions, the sandpile configuration will stabilise, meaning that all the heights will be lower or equal to 1. The odometer function u(x) collects the amount of mass emitted from x during stabilisation. It turns out that, depending on the initial configuration and redistribution rule, the odometer interface (u(x))_(x in G) will scale to a Gaussian field. The results presented in this talk are in collaboration with A. Cipriani (TU Delft), L. Chiarini (TU Delft/IMPA), J. de Graaff (TU Delft), R. Hazra (ISI Kolkata) and M. Jara (IMPA).

Wednesday April 8, Speaker: **Johannes Schmidt-Hieber** (University of Twente), Zoom Meeting

*Title:* Towards a statistical foundation of deep learning

Recently a lot of progress has been made in the theoretical understanding of deep learning. One of the very promising directions is the statistical approach, which interprets deep learning as a statistical method and builds on existing techniques in mathematical statistics to derive theoretical error bounds. The talk surveys this field and describes future challenges.

Wednesday February 26, Speaker: **Nicolas Garcia Trillos** (Assistant Professor, University of Wisconsin-Madison)

*Title: * From clustering with graph cuts to isoperimetric inequalities: quantitative convergence rates of Cheeger cuts on data clouds

Graph cuts have been studied for decades in the mathematics and computer science communities, and in modern applications in machine learning have been used to formulate optimization problems for data clustering. A canonical example with historical motivation is the so called Cheeger cut problem. This problem is on the one hand intuitively motivated, but on the other, is highly non-convex with a pessimistic NP hard label stamped on it (at least in a worst case scenario setting). Despite this, in the past decade or so, several algorithmic improvements made the minimization of Cheeger cuts more feasible, and at the same time there was a renewed interest in studying statistical properties of Cheeger cuts. New analytical ideas have provided new tools to attack problems that were elusive using classical approaches from statistics and statistical learning theory. Despite the advances, several questions remain unanswered. The purpose of this talk is to present some of these theoretical developments, with emphasis on new results where, for the first time, high probability converge rates of Cheeger cuts of proximity graphs over data clouds are deduced. These quantitative convergence rates are obtained by building bridges between the original clustering problem and another field within the mathematical analysis community that has seen enormous advancements in the past few years: quantitative isoperimetric inequalities. This connection serves as a metaphor for how the mathematical analyst may be able to contribute to answer theoretical questions in machine learning, and how one may be able to deduce statistical properties of solutions to learning optimization problems that have a continuum counterpart.

Wednesday February 12, 2020: **Daniele Avitabile** (VU), 16:00-17:00 in MathLab (NU-09A46)

*Title:* This is not a bump

This talk discusses patterns in a well-known spatially-extended, deterministic network of synaptically-coupled spiking neurons, which supports coherent structures commonly referred to as “bump” and “wandering bump”, respectively. Patterns of this type are observable in a variety of cortical recordings, and determining their existence and stability properties is a key question in mathematical neuroscience. Cortical bumps have been studied intensively in neural fields (that is, coarse-grained models), but a dynamical system treatment for the case of spiking networks is more elusive. I will present a novel approach to analyse these coherent structures in spiking networks, leading to the following conclusions: The model under consideration does not support a stationary, localised, heterogeneous steady state, therefore the coherent structure referred to as “bump" is not a bump in the usual sense. In a wide region of parameter space, the model supports countably many coexisting travelling waves. These waves are linearly unstable, have a spatially localised profile, and a vanishingly small speed. I will show numerical evidence that the structures known as “bump” and “wandering bump” are a peculiar form of spatio-temporal chaos, and their existence is underpinned by the bifurcation structure of the travelling waves mentioned above.

**Flavien Léger**, Room WN-S664, 16:00-17:00

*Title:* The Schrödinger bridge problem

The Schrödinger bridge problem (SBP) nowadays plays a vital role in the physics, mathematics, engineering, information geometry and machine learning communities. It was first introduced by Schrödinger in 1931 and is closely related to, but different from the famous Schrödinger equation. The SBP searches for the minimal kinetic energy density path for drift-diffusion processes with fixed initial and final distributions. In physics, the SBP is related to the Schrödinger equation via Nelson’s stochastic mechanics. For numerical purposes, the SBP can be seen as an entropic regularisation of optimal transport; its numerical solvers include the Sinkhorn algorithm and Fisher information regularisation method. In information geometry and machine learning, the SBP has been studied as a statistical divergence function. In modelling, the SBP minimising path, via Hopf–Cole transformation, shares similar structures with Nash equilibria in mean field games.

## 2019

Wed 18 December: **Senja Barthel** (VU), Room **WN-P631**, 16:00-17:00

*Title:* Shapes in Chemistry

*Abstract:* Many properties in chemistry are related to shapes. These shapes can be found in the bond-network of a molecule, or be the shapes of electronic densities, the pore shapes of nanoporous materials, the shapes of configuration landscapes whose minimal energy paths give catalytic pathways, etc. Chemist often have a good intuition on how to think about shape and its impact, but often lack the language and tools to translate and quantify their intuition. In this talk, I exemplify the wide range of modelling of chemical intuitions by translating them into mathematical concepts that lead to computable quantities: We will see how to distinguish and classify surfaces formed from carbons that mimic triply periodic minimal surfaces. We also see how pure mathematical questions are motivated by applications, for example in spatial graph theory.

Wed 03 December: **Hiroki Takahasi** (Keio University, Yokohama, Japan), Room WN-M655, 16:00-17:00

*Title:***Peculiar asymptotic behaviors of arithmetic mean of digits in the backward continued fraction expansion**

*Abstract:* Khinchine proved that the arithmetic mean of digits in the regular continued fraction expansion of typical irrational numbers diverges to infinity. On the other hand, the asymptotic behavior of the arithmetic mean of digits in the backward continued fraction expansion is counter-intuitive. After introducing results of Aaronson, Aaronson and Nakada on typical behaviors, I will talk about a recent joint work with Johannes Jaerisch (Nagoya University) on the Hausdorff dimension of exceptional sets. Although our main tool is ergodic theory and thermodynamic formalism for dynamical systems, no prior knowledge in this field is assumed in this talk.

Wed 20 November: **Alessandro Zocca** (VU), Room WN-M655, 16.00-17.00

*Title:* Rare Events in Stochastic Networks: Theory and Applications to Power Systems

*Abstract:* I will give an overview of my current research, which aims to develop new mathematical tools to analyze complex networks and their performance in the presence of uncertainty. In this talk, I will focus in particular on rare events analysis and large deviations techniques, which in many instances are crucial to correctly assess the network performance and the risk of failures. The main application area for the purpose of this talk will be power systems with high penetration of renewables. More specifically, I will present some novel insights into the interplay between renewable energy sources and power grid reliability: rare stochastic fluctuations of the power injections, amplified by correlations and network effects, can cause failures and possibly blackouts. I will discuss various solutions we devised to mitigate their impact and non-local propagation, using mathematical methods ranging from applied probability to optimization, including new ad-hoc MCMC methods for rare events and novel clustering techniques

Wed 06 November: **Harry van Zanten** (VU), Room WN-M655, 16:00-17:00

*Title:***Performance of distributed methods for high-dimensional statistical problems**

*Abstract:* For several reasons, computer scientists and statisticians are increasingly using distributed methods to handle and analyse data. In its basic form, the idea is simply to split up the data and distribute it among multiple local servers or cores. Computations can then be done locally, parallel to each other. Typically the local machines transmit the outcomes of their computations to a central server which aggregates the local results into a global one. In the literature various methods were proposed for distributed computational methods with seemingly good practical performance, but with limited theoretical underpinning. In our work we investigate several existing distributed methods in a standard, nonparametric “benchmark” model and compare their theoretical performance. For instance, in the case of Bayesian methods, we compare posterior contraction rates and coverage probabilities of credible sets. This analysis shows that some of the methods that have been proposed have better performance than others. Next we ask what is fundamentally possible in the distributed setting. To make this precise we add certain communication restrictions and prove minimax lower bounds for distributed procedures under such restrictions. Moreover, we exhibit distributed procedure attaining the bounds. Finally, we address the issue of adaptive distributed estimation. Based on joint work with Botond Szabo (Leiden).

Wed 09 October: **Joris Bierkens** (VU), Room M-664, 16:00-17:00

*Title:* Monte Carlo in Continuous Time

*Abstract:* Markov Chain Monte Carlo (MCMC) is an essential computational tool in quantitative fields such as Bayesian statistics, statistical physics and machine learning. The goal of MCMC is to perform computations with respect to a probability distribution of interest, which is often only implicitly specified in terms of an unnormalized density and which furthermore often cannot be approached by numeric integration techniques due to a curse of dimensionality. In recent years piecewise deterministic Markov processes (PDMPs) have emerged as a promising alternative to classical MCMC algorithms. One of the attractive features of this approach is the possibility of `exact subsampling' of the data. In this talk PDMP based algorithms will be introduced and recent progress in our understanding of the underlying processes will be presented.

Wed 25 September: **Álvaro del Pino Gomez **(UU), Room WN-M664, 16:00-17:00

*Title:***A control-theoretic version of convex integration**

*Abstract:* Convex integration is a powerful technique for solving partial differential relations. It was developed by M. Gromov, based on the earlier work of J. Nash on the C^1 isometric embedding problem. One dimensional convex integration was developed independently within the Control Theory community, where it is better known as the Filippov relaxation theorem. The latter can be thought as a first order version of the Chow-Rashevskii theorem on the controllability of bracket-generating motion systems. In this talk I will explain all these ideas starting from the very basics and using a historical perspective. At the very end I will explain how one may define a scheme that generalises convex integration by using ideas from the Chow-Rashevskii theorem. This is work in progress joint with F.J. Martínez-Aguinaga.

Wed 11 September: **Augusto Gerolin** (VU), Room WN-M655, 16:00-17:00

*Title:***Optimal Transport Theory: from Monge to Scientific Computing
**

*Abstract:* In the last 20 years, the theory of Optimal Transportation (OT) has emerged as a fertile field of inquiry, and a diverse tool for exploring applications within and beyond mathematics, in such diverse fields as economics, meteorology, geometry, statistics, fluid mechanics, design problems and engineering. More recently, due to unexpected connections, as for instance with Data Sciences and Quantum Chemistry, computational aspects of OT has receive substantial attention of both theorists and practitioners. The plan of the talk is to give a gentle introduction of theoretical and computational aspects of Optimal Transport Theory, from the classical Monge problem to more recent developments in the field. The talk have few prerequisites and no contraindications - therefore Ph.D. and/or advanced master students are highly encouraged to attend the seminar.

Wed 01 May: **Magdalena Kedziorek** (UU), Room WN-S623, 16:00-17:00

*Title:* How to understand rational G-cohomology theories?

*Abstract:* One of the themes of algebraic topology aims at capturing geometry of objects with symmetries by finding algebraic invariants which take this symmetries into account. One class of such invariants are rational G-cohomology theories. By extracting essential structural information from rational G-cohomology theories we are able to provide a much easier, algebraic description of them in many cases. Such a description is called ``an algebraic model’’. The ultimate aim is to do it for any compact Lie group G. In this talk I will give a gentle introduction to rational G-cohomology theories and present algebraic models for several groups G. This is joint work with David Barnes and John Greenlees.

Wed 17 April: **Fahimeh Moktari** (VU), Room WN-S623, 16:00-17:00

*Title:* Algebraic structure study of vector fields near the triple-zero bifurcation point.

*Abstract:*In this talk, a practical method is described for computing the classical normal form of vector fields near the bifurcation point. Some necessary formulas are derived and applied to the anharmonic oscillator, the Bogdanov-Takens bifurcation, the 3D nilpotent problem, and elastic pipe conveying fluid, to demonstrate the applicability of the theoretical resultsThen, a review will be given of the developments in the last decade concerning the classification of unique normal forms in 3D nilpotent problems.This work generalizes the work on the Bogdanov-Takens bifurcation and its unique normal form, which took off with the papers of Baider and Sanders (1991-92). Here the application of the Jacobson-Morozov theorem led to a systematic approach to computing the unique normal form in a number of cases. Some of the subcases of the 2D double-zero bifurcation analysis are still open.One can imagine that the complications of analyzing the 3D triple-zero bifurcation are rather challenging. Nevertheless, progress has been made in the last decade and it is time to list what has been done and what still needs to be done.We apply the Jacobson–Morozov theorem to embed this class of three dimensional vector fields into an sl_2-triple. Three irreducible families are produced this way.The first task is to find the structure constants of these families. In this talk, we also show how the Clebsch-Gordan formula is employed to find explicit formulas for the structure constants. We demonstrate that these families can generate some Lie sub-algebras with respect to the triple-zero bifurcation point, thereby creating smaller subproblems that can be studied independently in their own right (like the Hamiltonian case in the 2D analysis).Further, we discuss possible generalizations toward a general n-dimensional theory.

Wed 20 March: **Bernard Geurts** (UTwente), Room WN-P647, 16:00-17:00

*Title:* Mathematics for Turbulence

*Abstract:* Turbulent flow arises in a wide variety of natural and technological situations. While the full richness of turbulence is appreciated qualitatively, a quantitatively accurate prediction is often outside the scope of numerical computations. As an alternative, filtered flow descriptions, such as large-eddy simulation (LES), have been proposed and studied intensively, promising a combination of accuracy and computational feasibility. A brief review of mathematical cornerstones for LES is given. Many heuristic closure models for small-scale turbulence have been put forward to represent dynamic small scale effects on the large-scale characteristics of a flow. While these models are often effective in reducing the dynamic complexity of the LES approach, accuracy limitations of LES are a matter of ongoing discussion.In this presentation, mathematical regularization for turbulence, pioneered already by Leray in the 1930s, is explored. Following the regularization approach for the nonlinear convective terms, the closure model is uniquely connected to the underlying regularization principle, thereby by-passing heuristic closure modeling that is characteristic of the filtering approach to LES. A number of regularization models will be reviewed and their performance in turbulence will be discussed. It will be shown that regularization methods can be accurate at strongly reduced computational costs.

Wed 06 March: **Ronald Meester** (VU Amsterdam), room WN-P647, 16:00-17:00

**Title**:**The DNA Database Controversy 2.0**

*Abstract:*** ** What is the evidential value of a unique match of a DNA profile in database? Although the probabilistic analysis of this problem is in principle not difficult, it was the subject of a heated debate in the literature around 15 years ago, to which today's speaker also contributed. Very recently, to my surprise, the debate was re-opened by the publication of a paper by Wixted, Christenfeld and Rouder, in which a new element to the discussion was introduced. In this lecture I will first review the problem, together with the principal solution. Then I will explain what has recently been proposed as a new element in the analysis, and also explain why this new ingredient does not add anything, and only obscures the picture. The fact that not everybody agrees with us will be illustrated by some interesting quotes from the recent literature, which might be a nice subject for discussion during the drinks in the Basket afterwards. If you thought that mathematics could not be polemic you should certainly come and listen. (Joint work with Klaas Slooten.)

Wed 20 February: **Nick Lindemulder** (TU Delft), Room WN-S607, 16:00-17:00

*Title:* A randomized difference norm for vector-valued fractional Sobelev spaces
*Abstract:* Sobolev spaces of Banach space-valued distributions and variants with fractional smoothness play an important role in the $L_{p}$-approach to evolution equations. In this talk we discuss several (equivalent) ways how to define a suitable scale of fractional Sobolev spaces. In particular, we discuss the well known Fourier analytic definition by means of the Bessel potential operator and the less well known classical characterization of the latter by means of differences due to Strichartz from the scalar-valued setting. The main aim is to discuss extensions of the classical scalar-valued setting to the Banach space-valued setting, where the concept of randomization comes into play.

Wed 06 February: **Sophia B. Coban** (CWI), 16:00-17:00

*Title:***Things your radiologist would not tell you about
**

*Abstract:* Computed tomography is the perfect example of a large-scale, mildly ill-conditioned inverse problem, and one that is highly important to accurately solve in many real world applications. In today's talk, I will be introducing the basics of computed tomography, in particular X-ray CT; discuss some of the building blocks and novel trends of image reconstruction, and finish with the state-of-the-art methods developed within the Computational Imaging group at Centrum Wiskunde & Informatica.

## 2018

Wed 12 December: **Floske Spieksma** (LU), Room WN-P663, 16:00-17:00

*Title:* Alternative formula for the Deviation Matrix

*Abstract:* In Markov process theory, the deviation matrix measures the total deviation over time of the marginal distributions from stationarity. As such, it plays a central role in the determination of average optimal policies in Markov decision processes. In finite state space, the deviation matrix is minus the generalised inverse of the generator or rate matrix of a continuous time Markov process. However, the generalised inverse is not simply computable. In countable space, if it exists at all, it may even not be unique. The importance of the deviation matrix is not restricted to Markov process theory, but e.g. it plays an important role in network robustness of undirected graphs. This motivates the study of alternative computations methods. In my talk I will discuss this, as well as some applications.

Wed 28 November: **Max Welling** (UvA), Room WN-M639, 16:00-17:00

*Title:* Combining Deep Learning with External and Expert Knowledge

*Abstract:* Deep learning is a typical 'black box’ technique: create lots of labeled examples between input and output and train a general purpose map between the two. This works great when you can create a very large annotated dataset but has it limitations when the dataset is not so large, or poorly annotated. In the latter case we should try to inject our inductive biases or expert knowledge into the model. We will discuss two new directions to achieve this. 1) extend the translational equivariance of traditional convolutional neural networks to larger groups of symmetries, such as rotations and reflections, and 2) to incorporate bits and pieces of the (known) generative process of the data into the NN. We will illustrate both examples in the medical imaging domain: using group convolutions to improve performance in pathology slide analysis and using generative knowledge to speed up MRI reconstruction. Reversely, or more generally, one could ask the question, how can deep learning integrate with rich data sources such as knowledge graphs. A successful integration could lead to improved high level reasoning and systems that have a deeper understanding of the world they operate in. We will discuss a method called graph convolutions which allows us to embed rational data into a semantic space from which reasoning becomes easier.

Wed 14 November: ** Stéphanie van der Pas** (LU), Room WN-S623, 16:00-17:00

**Title:****Posterior concentration for Bayesian regression trees and their ensembles**

*Abstract:* Since their inception in the 1980's, regression trees have been one of the more widely used nonparametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to terminal nodes of recursive partitioning. Trees are powerful, yet susceptible to overfitting. Strategies against overfitting have traditionally relied on pruning greedily grown trees. The Bayesian framework offers an alternative remedy against overfitting through priors. Roughly speaking, a good prior charges smaller trees where overfitting does not occur. In this paper, we take a step towards understanding why/when do Bayesian trees and their ensembles not overfit. We study the speed at which the posterior concentrates around the true smooth regression function. We propose a spike-and-tree variant of the popular Bayesian CART prior and establish new theoretical results showing that regression trees (and their ensembles) (a) are capable of recovering smooth regression surfaces, achieving optimal rates up to a log factor, (b) can adapt to the unknown level of smoothness and (c) can perform effective dimension reduction. These results provide a piece of missing theoretical evidence explaining why Bayesian trees (and additive variants thereof) have worked so well in practice.

Wed 31 October: **Magnus Botnan** (VU), Room WN-P633, 16:00-17:00

**Title:****From Clustering to Quiver Representations**

*Abstract:* Clustering analysis is a statistical method for uncovering structure in large and complicated data. In this talk I will show how the desire for a parameter-free, stable, and density sensitive hierarchical clustering method inspired research in the field of representation theory of quivers.

Wed 17 October: **Viresh Patel** (UvA), Room WN-F123, 16:00-17:00

*Title:* Quasi Ramsey problems*Abstract:* Ramsey theory is currently one of the most active areas of research in combinatorics. The seminal question in the area, raised by Ramsey in 1930 can be formulated as follows: how large does n have to be to guarantee that in any room with n people we can find a set S of k people such that either every pair in S is acquainted or every pair in S is not acquainted. It is not immediately clear that such an n exists, although it is not hard to show. On the other hand the known bounds for n as a function of k are quite poor. I will discuss the Ramsey problem as well as variants of it. In particular I will discuss a relaxation of the problem above for which we are able to give quite precise bounds. This is based on joint work with Janos Pach, Ross Kang, Eoin Long and Guus Regts.

Wed 03 October: **Ben Moonen** (RU Nijmegen), Room WN-S655, 16:00-17:00

*Title:* Curves, Jacobians and CM points

*Abstract:* I will tell a story of two moduli spaces: the moduli space M_g of curves of genus g, and the moduli space A_g of abelian varieties of dimension g. To a curve C of genus g (or if you prefer: a compact Riemann surface of genus g) we can associate its Jacobian J(C), an abelian variety of dimension g. This gives a map t: M_g --> A_g that is known to be injective. As I will explain in my talk, though M_g and A_g have been studied extensively and much is known about them, there are many basic questions to which we don't know the answer. I will illustrate this by discussing a conjecture of Coleman about curves whose Jacobian is of CM-type (which, informally, means that it is 'maximally symmetrical'). Along the way I will review some important developments of the last three decades, notably the André-Oort conjecture, which has now been proved using a rather spectacular variety of techniques.

*On October 3 we cannot go to the Basket. Instead, we will meet in De Tegenstelling (D103, WN gebouw) after the talk!
*

Wed 19 September: **Jan Bouwe van den Berg** (VU), Room WN-S623, 16:00-17:00

*Title:* Computer-assisted theorems in dynamics

*Abstract:* In nonlinear analysis we often simulate dynamics on a computer, or calculate a numerical solution to a partial differential equation. This gives very detailed, stimulating information. However, it would be even better if we can be sure that what we see on the screen genuinely represents a solution of the problem. In particular, rigorous validation of the computations would allow such objects to be used as ingredients of theorems. In this talk we explore an approach based on a Newton-Kantorovich type argument in a suitable neighborhood of a numerically computed candidate. This method has been applied successfully for various problems in ordinary differential equations, delay differential equations and partial differential equations. We will illustrate the general setup using an example stemming from the Navier-Stokes equations in two dimensions. The latter is joint work in progress with Maxime Breden, Jean-Philippe Lessard and Lennaert van Veen.

Wed 13 Juni: **Paola Gori-Giorgi** (VU), Room WN-M143, 16:00-17:00

*Title:* Multi-marginal Optimal Transport and Density Functional Theory: A mathematical setting for physical ideas

*Abstract:* Electronic structure calculations are at the very heart of predictive computational materials science, chemistry and biochemistry. Their goal is to solve, in a reliable and computationally affordable way, the many-electron problem, a complex combination of quantum-mechanical and many-body effects. The most widely used approach, which achieves a reasonable compromise between accuracy and computational cost, is Kohn-Sham (KS) density-functional theory (DFT). Although exact in principle, practical implementations of KS-DFT must heavily rely on approximations for the so-called exchange-correlation (XC) functional. Empirical approximations (e.g., fitted on several data sets) are successful in normal cases, but typically lack predictive power for systems outside the training set. For this reason, exact mathematical conditions and rigorous guiding principles to build the XC functional have always played a key role in the field. In the recent years, it has been shown that there is a special semiclassical limit of the XC functional, relevant for the most challenging cases in KS DFT, which can be reformulated as a multi-marginal optimal transport problem, linking two rather distant research fields. In this talk I will review this reformulation, providing an overview of the key results from the optimal transport community, and discussing some of the open questions and conjectures that still need a rigorous proof.

Wed 30 Mei: **Michiel Bertsch** (University of Rome Tor Vergata), Room WN-M143, 16:00-17:00

*Title:***Mathematical modelling of Alzheimer's disease**

*Abstract:* Up to now there is no effective cure for Alzheimer's disease (AD). One of the major reasons is its complexity. Although the biomedical knowledge about AD is rapidly increasing, there is not yet a clear picture available about the major causes and the evolution of the disease. In such circumstances, can mathematical modelling be useful at all? In the colloquium I propose a modelling approach which, in a certain sense, is characterized by flexibility. I present a "toy model", which deliberately takes into account only a very limited amount of aspects of the disease (in this case the role of beta-amyloid and the existence of different time scales). The toy model seems to be flexible enough to include other aspects (such as the role of the tau protein) or novel biomedical insight. Surprisingly, the toy model itself suggests the possible importance of a very specific biomedical process, which is also discussed in the biomedical literature.BA

**Viresh Patel**(UvA), Room WN-M143, 16:00-17:00

*Title:* Quasi Ramsey problems

*Abstract:* Ramsey theory is currently one of the most active areas of research in combinatorics. The seminal question in the area, raised by Ramsey in 1930 can be formulated as follows: how large does n have to be to guarantee that in any room with n people we can find a set S of k people such that either every pair in S is acquainted or every pair in S is not acquainted. It is not immediately clear that such an n exists, although it is not hard to show. On the other hand the known bounds for n as a function of k are quite poor. I will discuss the Ramsey problem as well as variants of it. In particular I will discuss a relaxation of the problem above for which we are able to give quite precise bounds. This is based on joint work with Janos Pach, Ross Kang, Eoin Long and Guus Regts.

Wed 02 Mei: **Joris Mooij** (UvA), Room WN-M143, 16:00-17:00

*Title:* Joint Causal Inference from Observational and Experimental Data

*Abstract:*The standard method to discover causal relations is by using experimentation. Over the last decades, alternative methods have been proposed: constraint-based causal discovery methods can sometimes infer causal relations from certain statistical patterns in purely observational data. We introduce Joint Causal Inference (JCI), a novel constraint-based approach to causal discovery from multiple data sets that elegantly unifies both approaches. Compared with existing constraint-based approaches for causal discovery from multiple data sets, JCI offers several advantages: it deals with several different types of interventions in a unified fashion, it can learn intervention targets, it systematically pools data across different datasets which improves the statistical power of independence tests, and most importantly, it improves on the accuracy and identifiability of the predicted causal relations.

Wed 18 April: **Sjoerd Verduyn Lunel** (UU), Room WN-M143, 16:00-17:00

*Title:* Transfer operators, Hausdorff dimension and the spectral theory of positive operators

*Abstract:* In this talk we present a new approach to compute the Hausdorff dimension of conformally self-similar invariant sets using an elementary direct spectral analysis of a transfer operator associated with the problem. We start from scratch, introduce the notion of transfer operator and combine ideas from the theory of positive operators and from the theory of trace class operators and their determinants. Our approach is illustrated with examples from dynamical systems and number theory via Diophantine approximations.

Wed 21 Maart: **Peter Grunwald** (CWI, Leiden), Room WN-M143, 16:00-17:00

*Title:* Safe Testing

*Abstract:*A large fraction (some claim > 1/2) of published research in top journals in applied sciences such as medicine and psychology is irreproduceable. In light of this 'replicability crisis', standard p-value based hypothesis testing has come under intense scrutiny. One of its many problems is the following: if our test result is promising but nonconclusive (say, p = 0.07) we cannot simply decide to gather a few more data points. While this practice is ubiquitous in science, it invalidates p-values and error guarantees. Here we propose an alternative hypothesis testing methodology based on supermartingales - it has both a gambling and a data compression interpretation. This method allows us to consider additional data and freely combine results from different tests by multiplication (which would be a mortal sin for p-values!), and avoids many other pitfalls of traditional testing as well. If the null hypothesis is simple (a singleton), it also has a Bayesian interpretation, and essentially coincides with a proposal by Vovk (1993). We work out the case of composite null hypotheses, which allows us to formulate safe, nonasymptotic versions of the most popular tests such as the t-test and the chi square tests. Safe tests for composite H0 are not always Bayesian, but rather based on the 'reverse information projection', an elegant concept with roots in information theory rather than statistics.

Wed 07 Maart: **Nelly Litvak**, Room WN-M143, 16:00-17:00

*Title:* Power-law hypothesis for PageRank

*Abstract:* PageRank is a well-known algorithm, which has been proposed by Google for ranking pages in the World-Wide Web. PageRank can be interpreted as a stationary distribution of a random walk of a user that hops from one web page to another. Beyond the web search, PageRank has many applications in network of different kinds, for example, discovering communities in social networks, or finding endangered species in ecological networks. Most of these real-life networks have so-called power-law degree distribution: if a network is represented as a graph, then the fraction of vertices with degree k is approximately proportional to a negative power of k. Moreover, many empirical studies confirm that PageRank also has a power law distribution, with the same negative power as in-degree. In this talk I will discuss to which extend we can formalize this empirical observations analytically. Formally, we will model networks as random graphs and investigate the limiting behavior of PageRank as the graph size goes to infinity. I will present results for some specific random graph models, and very recent general limiting results for a large class of random graphs. This talk is based on joint works with Remco van der Hofstand and Alessandro Garavaglia (Eindhoven University of Technology) and Mariana Olvera-Cravioto (Univerity of California at Berkley).

Wed 21 Februari: **Gijs Heuts** (UU), Room WN-M143, 16:00-17:00

*Title:* Lie algebras and periodicity in homotopy theory

*Abstract:* Homotopy theory is the study of continuous deformations of spaces. The general problem of classifying such deformations is notoriously hard. However, if one is only interested in rational invariants of spaces then there are good algebraic tools available: Quillen constructed for every space a Lie algebra from which such invariants can be calculated, whereas Sullivan built a commutative algebra (much like the algebra of differential forms on a manifold) that retains essentially the same information. I will discuss a modern viewpoint of homotopy theory called the "chromatic perspective": much like a ray of white light is broken into different colours through a prism, a space can be decomposed into pieces corresponding to various "frequencies". The rational invariants correspond to one of these pieces. It turns out that Lie algebras may also be used to give models for the others.

Wed 07 Februari: **Damaris Schindler** (UU), Room WN-M143, 16:00-17:00

*Title:***Systems of quadratic forms
**

*Abstract:*In this talk we discuss some aspects concerning the arithmetic of systems of quadratic forms. Our focus will be on the local-global principle for the existence of rational or integral solutions and we will discuss some failures of this principle.

## 2017

Wed 13 December 2017: ** Jaap Storm** (VU), Room P-647, 16:00-16:15

*Title:* Stability of stochastic systems.

*Abstract:* Stochastic dynamical systems are widely used nowadays in modeling real life phenomena, especially Markov processes. The applications are numerous and include the modelling of the dynamics of financial processes, populations, traffic networks and communication networks. The analysis of these models allows us to predict behavior of these systems and also allows for control on the dynamics, however for a lot of the analysis one typically uses the ergodic properties of the Markov process. For the Markov process to be ergodic we require the Markov process to be stable. Stability of Markovian systems will be the topic of my talk and during the talk I hope to give some intuition to what we mean by stability and how we can prove it.

Wed 13 December 2017: ** Wouter Hetebrij** (VU), Room P-647, 16:20-16:35

*Title:* The parameterization method for center manifolds

*Abstract:* For a hyperbolic fixed point of a dynamical system, we can topologically conjugate the dynamics with the linearization of the dynamical system. Furthermore, under some mild conditions, there exists a smooth parameterization of the (un)stable manifold which conjugates the dynamical system to a linear system on the (un)stable manifold and describes the manifold. However, for center manifolds, we can only describe the center manifold as a graph over the center subspace. In my talk, I will give a short introduction to (un)stable and center manifolds, as well as the parameterization method. Also, I will sketch how we can generalize the parameterization method to center manifolds.

Wed 13 December 2017: **Joey van Langen** (VU), Room P-647, 16:45-17:00

*Title:* The modular method for Diophantine equations

*Abstract:* In 1994 Andrew Wiles proved the famous problem known as Fermat's Last Theorem. In the years that followed number theorists have used the same ideas to solve more general Diophantine equations, such as the generalized Fermat equation, i.e. x^p + y^q = z^r , for p, q and r not necessarily the same. This general method became known as the modular method and has since been used to solve many different Diophantine equations. In this talk I want to give a broad overview of the modular method, describing the different fields of mathematics it uses and the links between them. Fermat's Last Theorem will feature as an 'easy' example in this overview. If time allows I will also highlight the areas of current research involving the modular method, including my own research.

Wed 29 November 2017: **Rikkert Hindriks** (VU), Room P-647, 16:00-17:00

*Title:* Propagation of spontaneous hemodynamic fluctuations in the human brain

*Abstract:* In the absence of explicit cognitive tasks, the brain consumes about 20% of the body's energy budget, even though its weight is only 2% of the total body weight. Since perceptual and cognitive processing only add a tiny fraction to this energy consumption, this poses the question what the brain is doing during the resting-state. Functional magnetic resonance imaging (fMRI) has brought about a paradigm shift in our thinking about brain function, by demonstrating that, during the resting-state, brain activity is organized into the same functional networks as those engaged during a variety of cognitive and perceptual tasks. Although resting-state networks provide a framework to understand functional segregation, it is unclear how information is integrated across networks. I this talk I will discuss preliminary results that suggest that resting-state networks do not behave independently, but occur in reproducible temporal progressions that reflect propagating waves of neural activity. I will also discuss several methodological issues that come up in the analysis.

Wed 15 November 2017: **Eddie Nijholt** (VU), Room P-647, 16:00-17:00

*Title:***Transversality in Dynamical Systems with Generalised Symmetry**

*Abstract:* In bifurcation theory, an important role is played by the spectrum of the linearised system. For example, a steady state bifurcation is ruled out by the implicit function theorem, unless the linearisation has a non-trivial kernel. Likewise, a Hopf bifurcation is associated with a pair of complex eigenvalues crossing the imaginary axis. When the dynamical system has a symmetry, i.e., commutes with the linear action of a compact Lie-group, spaces such as the kernel and center subspace become invariant under this action. Consequently, they may be written as the direct sum of so-called irreducible subrepresentations. These spaces are characterised by the property that they do not contain any non-trivial invariant spaces, and they come in three types: real, complex and quaternionic. A classical result from equivariant dynamics says that in the case of compact Lie-group symmetry, a one-parameter bifurcation occurs generically along one irreducible subrepresentation of real type. We generalise this result to the case where the linear action is given by a monoid (i.e a group without inverses), without any further assumptions such as finiteness or compactness. More-precisely, we describe the generic structure of the generalised kernel in the case of a k-parameter monoid-equivariant bifurcation, and likewise for the center subspace (for any natural number k). This question arose from the study of network dynamical systems, where more exotic types of symmetry occur naturally.

**Thu** 09 November 2017: **Hein Putter** (Leiden UMC), Room **HG-15A37**, **13:30-14:30**

*Title:* Non-parametric estimation of transition probabilities in non-Markov multi-state models: the landmark Aalen-Johansen estimator

*Abstract:* The topic non-parametric estimation of transition probabilities in non-Markov multi-state models has seen a remarkable surge of activity recently. Two recent papers have used the idea of subsampling in this context. The first paper, by de Uña Álvarez and Meira-Machado, uses a procedure based on (differences between) Kaplan–Meier estimators derived from a subset of the data consisting of all subjects observed to be in the given state at the given time. The second, by Titman, derived estimators of transition probabilities that are consistent in general non-Markov multi-state models. Here, we show that the same idea of subsampling, used in both these papers, combined with the Aalen–Johansen estimate of the state occupation probabilities derived from that subset, can also be used to obtain a relatively simple and intuitive procedure which we term landmark Aalen–Johansen. We show that the landmark Aalen–Johansen estimator yields a consistent estimator of the transition probabilities in general non-Markov multi-state models under the same conditions as needed for consistency of the Aalen–Johansen estimator of the state occupation probabilities. Simulation studies show that the landmark Aalen–Johansen estimator has good small sample properties and is slightly more efficient than the other estimators.

Wed 01 November 2017: **Henk Don** (RU), Room P-647, 16:00-17:00

*Title:* Bounding the length of synchronizing words.

*Abstract:* In 1964, Cerny conjectured that every n-state synchronizing deterministic finite automaton (DFA) has a synchronizing word of length at most (n-1)^2. In this talk I will explain this conjecture and discuss upper and lower bounds for the length of the shortest synchronizing word. If we randomize the input word, we can still ask if a DFA synchronizes and how long the corresponding random word will be. For this setting I will give bounds on the expected length of the random synchronizing word. Based on joint works with Michiel de Bondt, Vladimir Gusev and Hans Zantema.

Wed 18 October 2017: **Assia Mahboubi** (Inria and U Nantes), Room P-647, 16:00-17:00

*Title:* Machine-checked proofs

*Abstract:* Proof assistants belong to the large collection of tools available today for "doing mathematics with a computer". These systems allow their users to check with the highest degree of certainty the validity of the proofs they have carefully described to the machine. Formalized mathematics refers to the digitized mathematical data (definitions, theorems, and proofs) amenable to computer processing, and checking. Formalized mathematics provides a very high correctness guarantee, and can be used to verify proofs based on large-scale

computations. But it can also lead to the discovery of new constructions and proofs, and helps to organize mathematical knowledge with the help of a computer. In this talk, we will give a glimpse of the variety of research areas and methodologies involved in the area of machine-checked proofs, from the meta-mathematical properties of the underlying logical language, to the design and features of the proof assistant. We will try to illustrate what formalizing mathematics looks like on the concrete example of the formal verification of a

computer-algebra based proof of the irrationality of ζ(3). The latter example is a joint work with Frédéric Chyzak (Inria) and Thomas Sibut-Pinote (Microsoft Research).

Wed 04 October 2017: **Wadim Zudilin** (RU), Room P-647, 16:00-17:00

*Title:* Variations on One over Pi

*Abstract:* The number $\pi=3.1415926\dots$ is recognised as the bestselling mathematical constant of all the time. One hundred years ago, well before the era of the computer, the Indian prodigy Srinivasa Ramanujan found a remarkable list of formulae for $1/\pi$, which can be used to compute the quantity to several thousand places. Today, Ramanujan's equations are still in use. The last few decades have witnessed an exploding development of new methods and generalisations of these formulae, bringing together topics from analysis, combinatorics, algebraic geometry, differential equations and number theory. At the same time, we lack understanding about the structure of such generalisations. In my talk, I will surf on the waves of the story of $1/\pi$.

Wed 20 September 2017: **Rob van der Mei** and **Martin van Buuren** (VU), Room P-647, 16:00-16:30

*Title:* Applied Mathematics in Practice: How to Save Lives with Maths?

*Abstract:* In this talk, we will talk about (1) stochastic models for how to reduce emergency response times by smart proactive relocations of ambulance vehicles, and (2) how these models work in real-life.

Wed 17 Mei 2017: **Elenna Dugundji**, Room P-647, 16:00-17:00

*Title:* Social and spatial interactions in transportation mode choice.*Abstract:* To what extent are consumers influenced in their choice of mode of transport by their neighbors’ choices? Or the choices made by peers in their social circle? These are important questions to understand for both policy makers and private sector parties interested in promoting particular modes of transport, but they have only recently attracted attention of transportation researchers. We discuss a socio-dynamic variant of a classic approach to predictions in this context, from both theoretical and empirical points of view, including an application to mobility in Amsterdam.

Wed 03 Mei 2017: **Bernard Zweers**, Room P-647, 16:00-16:15

*Title:* Minimizing the cost for inland container transportation

*Abstract:* A real-life operational planning problem for a logistic service provider is considered. A number of containers have to be shipped from multiple deep sea terminals to a single inland terminal. On may choose the day of transportation and the mode: truck or barge. The goal is to find an assignment for the containers that minimizes the total costs without visiting too many terminals with one barge. For this purpose an integer linear program is formulated that can solve practical instances in reasonable time.

Wed 03 Mei 2017: **Jan-David Salchow**, Room P-647, 16:20-16:35

*Title:* Function spaces on manifolds*Abstract:* The foundation for existence and regularity of solution spaces of PDE is the theory of function spaces. While historically most interest was directed towards PDE on subspaces of R^n, there is a growing demand for function spaces on Riemannian manifolds. In my talk

I will report on recent progress in the theory of Sobolev spaces on manifolds.

Wed 03 Mei 2017: **Chris Groothedde**, Room P-647, 16:40-16:55

*Title:* Instability in Dynamical Systems with Delayed Feedback*Abstract:* Many mathematical models describe systems with feedback loops. When this feedback is not instantaneous the behaviour and analysis of such a system becomes much more complex. In this talk we will look at equilibrium solutions of such Delay Dynamical systems and the instability that occurs near equilibrium solutions. The set of unstable solutions originating in an equilibrium can be described as a manifold: the Unstable manifold. In particular I will explain some of the basic functional analytic setup behind the study of Delay Dynamical Systems and their Equilibria and how to describe and visualise the Unstable Manifolds.

Wed 19 April 2017: **Mark Veraar** (TUD), Room P-647, 16:00-17:00

*Title:* Fourier multiplier theory: old and new results*Abstract:* Using Fourier multiplier theory one can prove the L^p-boundedness of many singular integrals. The first Fourier multipliers theorem has been proved by Marcinkiewicz in 1939. His main motivation was the application to elliptic PDEs. Since his work there have been many results on multiplier theory, among which the results of Mihlin and H\"ormander. During the last 20 years, multiplier theory was extensively studied in the weighted setting and in the vector-valued setting. The weighted setting is motivated by complex and geometric analysis and has led to several famous results. The vector-valued setting is important in the operator theoretic approach to PDE. In the talk I will present a survey of some of the recent results and their applications

Wed 05 April 2017: **Sandjai Bhulai** (VU), Room P-647, 16:00-17:00

*Title:* Value Function Discovery In Markov Decision Processes.*Abstract:* In this talk, we introduce a novel method for discovery of value functions for Markov Decision Processes (MDPs). This method is based on ideas from the evolutionary algorithm field. Its key feature is that it discovers descriptions of value functions that are algebraic in nature. This feature is unique, because the descriptions include the model parameters of the MDP. The algebraic expression can be used in several scenarios, e.g., conversion to a policy, control of systems with time-varying parameters. We illustrate its application on an example MDP.

Wed 22 Maart 2017: **Bart de Smit** (RUL), Room P-647, 16:00-17:00

*Title:* On the abelian coverings of curves over finite fields.*Abstract:* The main result of this talk identifies when two curves over finite fields have equivalent categories of (possibly ramified) abelian coverings. We will also sketch where this result fits in the wider context of number theoretic analogs of Kac's famous question: "Can you hear the shape of a drum?".

Wed 08 Maart 2017: **Daan Crommelin** (UvA and CWI), Room P-647, 16:00-17:00

*Title:* Stochastic models for multiscale dynamical systems
*Abstract:* Modeling and simulation of multiscale dynamical systems such as the climate system is challenging due to the wide range of spatiotemporal scales that need to be taken into account. A promising avenue to tackle this multiscale challenge is to use stochastic methods to represent dynamical processes at the small/fast scales. The feedback from microscopic (small-scale) processes is represented by a network of Markov processes conditioned on macroscopic model variables. I will discuss some of the work from this research direction. A systematic derivation of appropriate stochastic processes from first principles is often difficult, and statistical inference from suitable datasets can provide an interesting alternative.

Wed 22 Februari 2017: **Jens Rademacher** (Bremen), Room P-647, 16:00-17:00

*Title:* Nonlinear waves: gems in evolution equations.*Abstract:* While the overall dynamics of an evolution equation can be complicated and even inaccessible to an analysis, there are often subsystems that allow for more. A prominent case are nonlinear waves in parabolic partial differential equations with an extended spatial direction. The simplest such solutions have constant shape up to translation. Examples are solitons, excitation waves and periodic patterns. The identification of such objects is not only much easier than the task to understand the dynamics of the overall problem. These nonlinear waves often form building blocks for more complex behaviour, and, last but not least, often shape the phenomena that are of most interest in applications. In this talk some prominent examples will be present, combined with a brief introduction to analytic tools for existence and stability analysis.

Wed 08 Februari 2017: **Richard J. Boucherie** (Twente), Room P-647, 16:00-17:00

*Title:* Operations research solutions to improve the quality of healthcare

*Abstract:* Healthcare expenditures are increasing in many countries. Delivering adequate quality of healthcare requires efficient utilization of resources. Operations Research allows us to maintain or increase the current quality of healthcare for a growing number of patients without increasing the required work force. In this talk, I will describe a series of mathematical results obtained in the Center for Healthcare Operations Improvement and Research of the University of Twente, and I will indicate how these results were implemented in Dutch hospitals.

Efficient planning of operating theatres will reduce the wasted hours of staff, balancing the number of patients in wards will reduce peaks and therefore increases the efficiency of nursing care, efficient rostering of staff allows for more work to be done by the same number of people. While employing operations research techniques seems to be dedicated to improving efficiency, at the same time improved efficiency leads to increased job satisfaction as experienced workload is often dominated by those moments at which the work pressure is very high, and it also improves patient safety since errors due to peak work load will be avoided.

## 2016

Wed 14 December 2016: **Sanne ter Horst** (NWU, South Africa), Room S-655, 16:00-17:00

Title: **Operator relations arising from the coupling method**

*Abstract*: The coupling method was developed in the 1980s as a tool to analyse integral operators. One of the main techniques involves showing that the integral operator is matricially coupled (MC) to an operator on a finite dimensional space, from which one deduces the two operators also satisfy other operator relations such as equivalence after extension (EAE) and Schur coupling (SC). This in turn enables one to determine the Fredholm properties of the integral operator. In the 1990s the question was raised whether these three operator relations may coincide for general Banach space operators and it was shown that MC and EAE indeed coincide and that these operator relations are implied by SC. The remaining implication, whether in general EAE=MC implies SC, remained open. Recently, the question was answered affirmatively for the case of Hilbert space operators and surprising new results about the Banach space case were obtained as well. In this talk we discuss some of these recent developments.

Wed 30 November 2016: **Robin de Jong** (RUL), Room **S-655**, 16:00-17:00

Title: **Asymptotic behavior of Faltings's delta-invariant***Abstract:* In 1983 Gerd Faltings discovered the so-called delta-invariant of a compact Riemann surface X. He did this while working on his proof of the so-called Mordell Conjecture, that earned him the Fields Medal in 1986. The delta-invariant of X should more or less be seen as the minus logarithm of the distance from X to the boundary of the classifying space of all compact Riemann surfaces. Faltings has asked whether his delta-invariant has a certain (precisely formulated) "good" asymptotic behavior near the boundary of the classifying space. Although some partial positive results were obtained in this direction in the early 1990s, Faltings's question was recently answered in the negative. We shall explain what is going on. Of course we will explain basic examples of compact Riemann surfaces, and of their classifying spaces, along the way.

Wed 16 November 2016: **Raf Bocklandt** (UvA), Room **S-655**, 16:00-17:00

Title: **From the freezer to the tropics**

*Abstract:* In this talk I will explain a connection between dynamical systems and algebraic geometry inspired by Mirror Symmetry. Starting from a bipartite graph on a torus, we can define an integrable dynamical system and look at its behaviour for different temperatures. The same bipartite graph can also be used to resolve singularities. I will show how these two become related if we go to the absolute zero temperature in the dynamical system and to the tropical limit of the resolution.

Wed 02 November 2016: **Bob Planque** (VU), Room **S-655**, 16:00-17:00

Title: **How do bacteria optimise growth? Maintaining high growth rates in dynamic environments**

*Abstract:* Microorganisms such as bacteria are the masters of growth and replication. Their internal structure is completely geared to minimise the duplication time. Their metabolism is extraordinarily well controlled, and bacteria are able selectively to turn on or off reactions to synthesise compounds, or to grow only on the best of several available substrates. In this talk, we will try to find out how bacteria must control gene expression to solve two tasks: maximising fluxes through metabolic pathways, and maximising their growth rate. Both tasks need to be solved in changing environments, so adapt to changes which are essentially unknown to the cell's interior. As I hope to convince you, there is much mathematical fun to be had in this problem: it contains a lot of different parts of mathematical analysis, including convex optimisation, local and global stability of dynamical systems, differential-algebraic systems, and more.

Wed 19 October 2016: **Bob Rink** (VU), Room S-623, 16:00-17:00

Title: **From graph fibrations to synchrony breaking in network dynamical systems***Abstract:* Networks of coupled nonlinear dynamical systems often display unexpected phenomena. They may for example synchronise. This form of collective behaviour occurs when the agents of the network behave in unison. An example is the simultaneous firing of neurons. It has also been observed that network synchrony often emerges or breaks through quite unusual bifurcation scenarios. In this talk I will show how these phenomena can be understood with the help of the notion of a graph fibration, and with representation theory. The long term aim is a classification of synchrony breaking bifurcations in networks. This is joint work with Jan Sanders and Eddie Nijholt.

**Fri 30 September 2016:** **Hansjörg Geiges** (Cologne), Room **M-143**, **15:30-16:15**

Title: **Geometry of the Kepler problem in celestial mechanics**

*Abstract*: In this colloquium talk I shall discuss some elementary geometric aspects of the Kepler problem. In particular, I want to show how Kepler's first law of planetary motion can be derived from a surprising (and surprisingly obscure) duality of force laws involving conformal transformations of the complex plane. In its basic form, this duality was known to Newton; a more general version was found by Bohlin and Kasner some 100 years ago; its modern interpretation in terms of Maupertuis's principle is due to Arnold.

This talk was part of the Mini-Workshop on Symplectic Geometry.

Wed 21 September 2016: **Danny Beckers** (VU), Room S-623, 16:00-17:00

Title: **Hans Freudenthal (1905-1990): mathematician**

*Abstract:* Freudenthal is widely recognized, both for his work as a mathematician, and for his contributions in mathematics education. In this talk I will show that, contrary to present-day historiography, the latter career took off only in the late 1960s. This raises the question where the view of Freudenthal as a didactician of mathematics originates.

Wed 22 June 2016: **Joost Hulshof** (VU), Room S-655, 16:00-17:00

Title: **Finding nonzero zero's from Newton to Nash**

*Abstract:* I will try to demystify the Hard Implicit Function Theorem as formulated by Jacob T. Schwartz in his Nonlinear Functional Analysis lectures notes expanding on a remark by Nash in his paper on isometric embeddings .

Wed 08 June 2016: **Ronald van Luijk** (RUL), Room S-655, 16:00-17:00

Title: **Geometry dictates arithmetic**

*Abstract:* The arithmetic of an algebraic variety over the rational numbers concerns the distribution of its rational points. For curves, a result of Gerd Faltings states that there are only finitely many rational points when the genus, a geometric invariant, is at least two. In this way, the geometry of a curve dictates its arithmetic. I will give an overview of some results and conjectures about how the geometry of higher-dimensional varieties dictates their arithmetic.

Wed 25 May 2016: **Guus Regts** (UvA), Room S-655, 16:00-17:00

Title: **Approximation algorithms for graph polynomials and partition functions of edge- and vertex-coloring models**

*Abstract:* Starting with a breakthrough result of Weitz in 2006, who developed an efficient deterministic approximation algorithm for counting independent sets in sparse graphs, a lot of work has been done on designing approximation algorithms for several types of partition functions. Most of these algorithms are based on the method of correlation decay, which originates in statistical physics. In this talk I will briefly sketch the idea behind this approach. After that I will describe an alternative approach, which is based on zeros of polynomials, for designing efficient deterministic approximation algorithms for certain graph polynomials and partition functions of edge- and vertex-coloring models.

Wed 11 May 2016: **Michel Mandjes** (UvA), Room S-655, 16:00-17:00

Title: **Scaling Limits for Stochastic Networks**

*Abstract:* In this talk I will sketch recent results obtained in the context of a stochastic network of dependently operating resources. These could be thought of to represent real-life networks of all sorts, such as traffic or communication networks, but I’ll point out that this setup is also highly relevant in economic and biological applications. For such large networks, one would typically like to describe their dynamic behavior, and to devise procedures that can deal with various undesired events (link failures, sudden overload, etc.). As an example, I'll demonstrate how these models can be used to develop routing strategies. Under specific parameter scalings, explicit limiting results can be obtained.

Wed 13 April 2016: **Klaas Pieter Hart** (TUD), Room S-655, 16:00-17:00

Title: **The Katowice problem**

*Abstract:* An elementary exercise: assume there is a bijection between two sets X and Y, construct a bijection between their power sets. Another elementary exercise: assume there is a bijection between the power sets of the sets X and Y , construct a bijection between the sets themselves.

The first exercise is easy; the second is really, really hard, impossible even. This will be explained. The second exercise becomes doable if one assumes the bijection is an isomorphism with respect to the partial order of inclusion. The Katowice Problem takes this one step further. Take two infinite sets X and Y and their power sets P(X) and P(Y); these are Boolean rings under the operations of symmetric difference and intersection. Now assume the quotient rings P(X)/fin and P(Y)/fin, by the ideal of finite sets, are isomorphic. Must there be a bijection between X and Y ? This problem is solved for all but one pair of infinite sets. The solution and the attacks on the remaining pair involve non-trivial set theory and I will discuss the current state of affairs and also how this problem can be formulated functional-analytically and topologically.

Wed 30 March 2016: **Jasper Stokman** (UvA), Room S-655, 16:00-17:00

Title: **Skein theory and loop models.**

*Abstract:* The combinatorial approach to the construction of knot invariants has led to skein theory on planar surfaces. The combinatorial construction of the Jones polynomial, a well known invariant of oriented knots, follows for instance from skein theory on the Riemann sphere. On the other hand, skein theory on an annulus captures the hidden symmetries of a particular class of percolation models, called loop models. This turns out to be a powerful insight, since the hidden symmetries of the loop model are expected to lead to exact predictability of the behaviour of the model. I will introduce skein theory on an annulus and explain how it captures the hidden symmetries of loop models. If time permits I will explain how the skein theory allows to compare loop models of different system sizes (based on joint work with Bernard Nienhuis and Kayed AlQasemi).

Wed 16 March 2016: **Jan van Neerven** (TUD), Room S-655, 16:00-17:00

Title: **Stochastic maximal regularity**

*Abstract:* The notion of maximal regularity plays an important role in the theory of parabolic evolution equation. The aim of this talk is to introduce a similar notion for parabolic stochastic evolution equations, called stochastic maximal regularity. Extending earlier results of Krylov, in joint work with Mark Veraar and Lutz Weis,stochastic maximal regularity has been proved recently for a large class of problems. We will present an overview of these results and discuss some applications.

Wed 17 February 2016: **Marius van der Put** (RUG), Room S-655, 16:00-17:00

Title: **New and Old on Painlevé equations**

*Abstract:* A non linear ordinary complex differential equation can have `moving' singularities, i.e., the place of the singularity depends on the initial value. The basic example is y':=dy/dz=y^3. A (complex, ordinary) differential equation is said to have the Painlevé property (PP) if the only moving singularities are poles. For first order equations the classification of PP was almost complete in the 19th century. The six Painlevé equations y''=f(y',y,z) are supposed to be the answer for explicit order two equations. In 1980, after a silence on the topic for 50 years, Jimbo and Miwa toke up the subject in connection with physics. Nowadays the literature is enormous and for a big part in Japanese hands. The main issue is now isomonodromy and moduli spaces. I will try to explain these themes for one the Painlevé equations.

Wed 03 February 2016: **Klaas Slooten** (NFI, VU), Room S-655, 16:00-17:00

Title: **Forensic genetics**

*Abstract:* In light of my recent appointment as endowed professor in forensic genetics, I will sketch an overview of this field. I will first describe what DNA profiling at forensic laboratories such as the Netherlands Forensic Institute (NFI) consists of, and then go into the statistics and probability needed for the interpretation and reporting of the obtained results. I will discuss several applications, such as the resolution of mixed DNA traces (containing DNA of several individuals), the investigation of relatedness of individuals, and database searches. Along the way I will point out what my own research interests are and also discuss some legal aspects.

## 2015

Wed 25 February: **Sonja Cox** (UvA), Room F-630, 16:00-17:00

Title: **Numerical simulations for stochastic PDEs**

*Abstract:* Various models arising from finance and natural sciences involve stochastic partial differential equations (SPDEs). As the solutions to an SPDE generally cannot be given explicitly, numerical simulations are used to gain insight in their behaviour. In my talk I will explain the challenges encountered here. In particular, I will explain why generally one cannot expect large convergence rates and why non-linear equations pose difficulties that do not occur with deterministic PDEs. Finally, I will explain my recent results concerning approximations to non-linear S(P)DEs.

Wed 11 March: **Marcel de Jeu** (Leiden), Room S-655, 16:00-17:00

Title: **Positive representations**

*Abstract:* Many spaces in analysis are ordered (real) Banach spaces, or even Banach lattices, with groups acting as positive operators on them. One can even argue that such positive representations of groups are not less natural than unitary representations in Hilbert spaces, but contrary to the latter they have hardly been studied. The same holds for representations of ordered Banach algebras where a positive element acts as a positive operator. Whereas there is an elaborate theory of representations of C*algebras, hardly anything is known about positive representations of ordered Banach algebras, or even Banach lattices algebras.

Wed 25 March: **Paola Gori-Giorgi** (VU), Room: S-655, 16:00-17:00

Title: **Optimal transport meets electronic density functional theory**

*Abstract:* Electronic structure calculations are at the heart of predictive material science, chemistry and biochemistry. Their goals is to solve, in a reliable and computationally affordable way, the many-electron problem, a complex combination of quantum mechanical and many-body effects. The most widely used approach, which achieves a reasonable compromise between accuracy and computational cost, is Kohn-Sham (KS) density functional theory (DFT), for which Walter Kohn was awarded the Nobel Prize in Chemistry in 1998. Although exact in principle, practical implementaitons of KS-DFT must heavily rely on approximations for the so-called exchange-correlation functional. After a basic introduction on the electronic structure problem and KS-DFT, I will show that an important piece of exact information can be formulated as an optimal transport problem with cost function given by the Coulomb repulsive potential. The implications for physics and chemistry will be illustrated with simple examples.

Wed 8 April: **Kristiaan Glorie** (VU), Room: S-655, 16:00-17:00

Title: **Robust market design**

*Abstract*: Many decision problems in science, engineering, and economics are affected by uncertainty in the underlying data and parameters. Robust optimization theory addresses these problems and seeks to develop methodology to provide a measure of robustness against the uncertainty. After introducing the concept of robust optimization, I will focus in this talk on designing robust centralized markets. In particular, I consider the clearing of barter exchange / swap markets in which proposed transactions must be verified before they can proceed. Proposed transactions may fail to go forward if verification fails or if a participant withdraws. The clearing problem for these markets is a combinatorial optimization problem that can be modelled as a vertex-disjoint cycle packing problem in an unreliable digraph. The arcs and nodes of this graph are subject to failure. This research finds a natural application in kidney exchange markets, which aim to enable transplants between incompatible donor-patient pairs. A set of pairs must be chosen in such a way that each selected patient can receive a kidney from a compatible donor from another pair in the set. The pairs are then notified and crossmatch tests must be performed to ensure the success of the transplants. I will present novel models and solution techniques based on the problem structure in these markets.

Wed 22 April: **Mingmin Chen** (UvA), Room: S-655, 16:00-17:00

Title: **The Chow ring of hyperkahler varieties**

*Abstract:* Hyperkahler varieties are very special objects in algebraic geometry. They also naturally arise in differential geometry and mathematical physics. Beauville conjectured that the Chow ring of a hyperkahler variety has a decomposition, as in the case of abelian varieties, that respects the intersection product. In the talk, we discuss the decomposition in explicit examples (variety of lines on a cubic fourfold and Hilbert scheme of a K3 surface). We also explain what is expected in general.

Wed 6 May: **James Cussens** (University of York), Room: S-655, 16:00-17:00

Title: **Leibniz's new kind of Logic**

*Abstract:* In this talk I will analyse Leibniz's "new kind of Logic" which aimed to use probabilities to guide human reasoning. I will discuss what Leibniz thought probabilities were and how he thought we could derive them. Amongst the topics to be discussed will be: possible worlds, statistical inference and the connections between subjective and objective probabilities.

Wed 20 May: **Lenny Taelman** (UvA), Room S-655, 16:00-17:00

Title: **The Kummer-Vandiver conjecture**

*Abstract*: The Kummer-Vandiver conjecture is a 150 year old open problem in number theory that was born out of attempts to prove Fermat's Last Theorem. If true, it has profound consequences in algebraic number theory as well as in algebraic topology. It is however far from universally believed. In this introductory talk, which is aimed at a non-expert audience, I will explain the history and statement of the conjecture, and sketch some arguments both for and against the conjecture.

Wed 02 September: **Cor Kraaijkamp** (TU Delft), Room S-655, 16:00-17:00

Title: **Natural extensions and Nakada's alpha-expansions**

*Abstract:* In 1981, Nakada introduced and studied a large class of continued fraction transformations, which are now known as alpha-expansions. For alpha between 1/2 and 1 he obtained the so-called "natural extension" the underlying dynamical systems underlying these continued fraction algorithms. His work played a fundamental role in the solution of the Doeblin-Lenstra conjecture by Bosma, Jager and Wiedijk in 1983. Later, Marmi, Moussa and Yoccoz found the natural extension for alpha's between square root of 2 minus 1, and 1/2. Only recently, due to work by Marmi and his student Luzzi, alpha-expansions are intensely studied for values of alpha between 0 and square root of 2 minus 1. In this talk I will explain why this case is so much more difficult than the case of alpha between square root of 2 minus 1 and 1.

Wed 16 September: **Joost Batenburg** (UL), Room S-655, 16:00-17:00

Title: **Recent Trends in Tomography**

*Abstract**:* Tomography deals with the reconstruction of 3D objects from their projections, taken from a range of angles. Mathematically, tomography fits within the broad category of linear inverse problems. In recent years, the mathematics of tomography has developed strongly with breakthroughs in image reconstruction from limited data. At the same time, experimental imaging setups have become increasingly complex and diverse, leading to new classes of image reconstruction problems that are not addressed in current mathematical and computational models. An interdisciplinary approach, combining mathematical insights with advanced computational tools and understanding of the underlying physics, is called for. In this lecture, I will sketch recent trends and challenges in the interdisciplinary field of tomography, linking theoretical results to modern imaging practice.

Wed 30 September: **Ronald Meester** (VU), Room S-655, 16:00-17:00

Title: **Assessing evidence beyond probability**

*Abstract:* There are many situations in legal or forensic context in which modeling with classical probability is inappropriate for assessing the strength of evidence. We first identify some of these situations. Then we introduce belief functions, which generalize classical probability distributions, and which were originally introduced in the seventies of the previous century. We develop a calculus for these belief functions. Then we show that their flexibility allows them to be used in legal settings where the classical theory fails, by actually computing a number of examples and compare the answers to the classical ones. We believe that our theory should replace the classical Bayes' rule in many situations. Joint work with Timber Kerkvliet.

Wed 07 October: **Leonid Polterovich** (Tel Aviv), Room **HG-10A20 (Hoofdgebouw), 15:30-16:15**

Title: **Geometry of symplectic transformations: 25 years after**

*Abstract:* In 1990 Helmut Hofer introduced a bi-invariant metric on symplectomorphism groups which nowadays plays an important role in symplectic topology and Hamiltonian dynamics. I will review some old, new and yet unproved results in this direction. (This talk is part of the Mini-Workshop on Symplectic Geometry)

Wed 14 October: **Bram Gorissen** (Harvard, VU), Room S-655, 16:00-17:00

Title: **Solving Robust Nonlinear Optimization Problems via the Dual**

*Abstract:* We show how to solve a robust nonlinear (convex-concave) optimization problem by explicitly deriving its dual. Given an optimal solution of this dual, we show how to recover the primal optimal solution. The fascinating and appealing property of our approach is that any convex uncertainty set can be used. We obtain computationally tractable robust counterparts for many new robust nonlinear optimization problems, including problems with robust quadratic constraints, second order cone constraints, and SOS-convex polynomials.

Wed 28 October: **Martijn Kool** (UU), Room S-655, 16:00-17:00

Title: **Enumerative geometry: from Ancient Greeks to Modern Physicists**

*Abstract:* Apollonius of Perga asked: how many circles are tangent to 3 given circles in the plane? This is a typical problem of enumerative geometry. The subject saw great advances in the 19th century under the influence of Schubert, but certain problems remained unsolved, such as the determination of the number of rational curves of degree d through 3d-1 general points in the plane for arbitrary d. In the 20th century, new invariants of algebraic varieties were discovered such as Gromov-Witten invariants, which play a role in string theory. Kontsevich used these invariants to solve this longstanding problem. I will give a *non-technical* overview of some of the history of enumerative geometry with an eye towards recent developments. Links with topology are discussed.

Wed 11 November: **Gert Heckman** (RU), Room S-655, 16:00-17:00

Title: **Moduli of real genus 3 curves**

*Abstract:* We discuss the PhD work of my former student Sander Rieken, about reality questions for the Kondo period map from the moduli space of genus 3 curves to a certain ball quotient of dimension 6 over Gauss integers. The analysis of the maximal real component (quartic curves with 4 ovals) is particularly nice, and leads to an odd presentation of the Weyl group of type E_7, analogous to a presentation of the bimonster group, due to Ivanov, Norton, Conway and Simons. (This talk is intended also for non-experts in the audience.)

Wed 25 November: **Lex Schrijver** (CWI), Room S-655, 16:00-17:00

Title: **Graph invariants and invariant theory**

*Abstract:* Several graph invariants can be described as `partition functions' (in the sense of de la Harpe and Jones), and their duals based on edge colouring. We present characterizations of such invariants, and of related invariants for knots and chord diagrams, where Lie algebras come in. The talk will be introductory and does not assume any specific knowledge in this area.

Wed 09 December 2015: **Martijn van Otterlo** (Feweb VU), Room S-655, 16:00-17:00

Title: **From adaptive computational logic to optimization of customer journeys**

*Abstract:* As a brand new researcher in the Amsterdam Center for Business Analytics

(ACBA), affiliated with the Amsterdam-wide AAA programme on "data

science", I have a home base at FEWEB (business and economics) but I am

partially affiliated with mathematics (operations research) and computer

science (high-performance computing). In this talk I will very briefly

outline my past artificial intelligence research and highlight my main

interests: reinforcement learning and computational logic, but I might

also briefly touch upon the ethics of algorithms. My main expertise is

the optimization of behavior, and the modeling of such

decision-theoretic optimization processes in high-level knowledge

representation languages, topics on which I published two books. I will

use this talk further to introduce several projects I have just started

at the VU, among which is a data science brick-and-mortar library

project. I will discuss some of my plans, reaching out, and looking out

for possible collaborations.

## 2014

- Wed. 3 December:
**Thomas Rot**(University of Cologne), Room C-623, 16:00-17:00

Title:**TBA** - Wed. 5 November:
**Eric Cator**(RU), Room C-623, 16:00-17:00

Title**:****Ergodic theory of stochastic Burgers equation in non-compact setting**

Abstract: In this talk I will explain recent results about the existence of a one-force-one-solution principle for the stochastic Burgers equation in a non-compact (but homogeneous) setting. In recent years several results were proved for stochastically forced Burgers equation in (essentially) compact settings, showing that there exists global solutions that act as attractors for large classes of initial conditions. However, extending these results to truly non-compact settings was not possible using the same methods, and it was even conjectured by Sinai that the results would not hold in that case. Using results from First and Last Passage Percolation, first developed by Newman et al., we were able to prove the one-force-one-solution principle for a Poisson forcing on the real line.

This is joint work with Yuri Bakhtin and Konstantin Khanin. - Wed. 22 October:
**Sander Dahmen**(VU), Room F-123, 16:00-17:00

Title**:****Elliptic curves, modular forms, and Diophantine problems**

Abstract: Since the proof of Fermat's Last Theorem, many Diophantine problems have been solved using deep results about elliptic curves, modular forms, and associated Galois representations. The purpose of this talk is to discuss some of these results and explain how they can be applied to explicitly solve certain Diophantine problems. - Wed. 24 September:
**Oliver Fabert**(VU), Room C-623, 16:00-17:00

Title**: From superstring theory to classical mechanics**

Abstract: Hamiltonian mechanics is a mathematical framework in order to study problems in classical mechanics. In my talk I will present a surprising link between Hamiltonian dynamics and algebraic geometry originating from superstring theory of physics. Among other things, it provides a direct correspondence between periodic solutions and holomorphic functions. - Wed. 24 September:
**Ben de Pagter**(TUD), Room C-623, 16:00-17:00

Title:**Translation invariant Banach function spaces**

Abstract: In this talk we will discuss some properties of so-called translation invariant Banach function spaces on compact abelian groups. This class of Banach function spaces includes all rearrangement invariant spaces on such groups, but is much larger and exhibits different features. Translation invariant Banach function spaces arise naturally in the study of Fourier multiplier operators. The talk is based on joint work with Werner Ricker. - Wed. 10 September:
**Mike Keane**(TUD) , Room: C-623, 16:00-17:00

Title:**Dynamical Classification of Primitive Constant Length Substitutions**

Abstract: Substitutions arise frequently in analysis, topology, probability,and computer science (where they are usually called morphisms). Their dynamical (that is, long-term behavioural) properties are surprisingly complex, given their simplicity and intrinsically finite nature. Primitive substitutions give rise to unique minimal dynamical systems, and isomorphisms between such systems are simply given by finite data in the form of a sliding block code. For primitive substitutions having the same constant length (but possibly different alphabets), we have developed an algorithm deciding whether they are isomorphic or not; in addition, we can for a given such substitution make a list of all isomorphic substitutions of the same length in an algorithmic manner. For example, for the Toeplitz substitution

0 → 01

1 → 00

the list contains (when counted properly) two other substitutions, one on a two-symbol alphabet and one on a three-symbol alphabet, and the Thue-Morse substitution

0 → 01

1 → 10

list contains exactly twelve members, including two on a six-symbol alphabet. Moreover, for any primitive constant length substitution the list is finite and in principle can be generated by a machine.

In this lecture I hope to give an account of the above starting from the beginning, with emphasis on understanding the simple definitions and the two or three key ideas behind the results. I would very much like to explain a similar theory for primitive substitutions of nonconstant length, but up until now we have not met with success. For instance, we know nothing about the class of the Fibonacci substitution

0 → 01

1 → 0. - Wed. 14 May: Jason Frank (UU)

Title:**Application of Thermostats to Discretized Fluid Models.**Abstract: In meteorology and climate science, fluid models are simulated on time scales very long compared to the characteristic Lyapunov time of chaotic growth, with the goal of generating a data set suitable for statistical analysis. The choice of a numerical discretization scheme for a problem carries with it a certain bias in the statistical data generated in long simulations. In this talk I will discuss recent research on the use of thermostat techniques, commonly used in molecular dynamics, to control the invariant measure of a discretized model, with the goals of correcting bias or effecting a statistically consistent model reduction. These will be illustrated for a point-vortex gas and a Burgers/KdV equation. I will also discuss challenges to extending the approach to the Euler equations. - Wed. 2 April: Frank Redig (TU Delft) , Room: S-623, 16:00-17:00

Title:**Large deviations and thermodynamic formalism for multiple ergodic averages: first steps**Abstract: Let X_i be a sequence of real-valued independent random variables with finite exponential moment generating function.

Classical large deviation theory predicts that

P(1/n \sum_{i=1}^n X_i ~ x) ~ e^{-n I(x)} (*)

with I(x), the large deviation rate function, the Legendre transform of the log-moment generating function.

The simplest example of a multiple ergodic average is

S^2n/n= 1/n \sum_{i=1}^n X_{i} X_{2i}

and more generally

S^(k)_n/n =(1/n) \sum_{i=1}^n X_{i} X_{2i}... X_{ki}

The ergodic theory of such averages along arithmetic progressions plays an important role in Furstenberg's proof of Szemeredi's theorem.

Only recently, other probabilistic fluctuation properties such as central limit theorem and large deviations have been studied by Kifer and Varadhan.

We will look at the analogue of (*) for such averages. We take a statistical mechanics approach and show how this gives rise naturally to

a thermodynamic formalism with multiplication invariant Gibbs interactions, and corresponding Gibbs measures.

Based on joint work with J.R. Chazottes (Paris). - Wed. 19 March: Eduard Belitser (VU) , Room: C-147, 16:00-17:00

Title:**On coverage of credible sets**Abstract: For a general statistical model we consider the problem of constructing confidence sets for an unknown (possibly infinite dimensional) parameter, as a credible set based on

a random data dependent measure. Typical example of such a measure is the posterior distribution with respect to some prior on the parameter. We are concerned with the

optimality of such credible sets, which is basically a trade-off between the ``size'' of the set and its coverage probability. In general it is impossible to construct

optimal (fully) adaptive confidence set in the minimax sense, only some limited amount of adaptivity can be achieved. We discuss some approaches.

- Wed. 5 March: Jan Draisma (TU/e) , Room: C-147, 16:00-17:00

Title:**The algebra of symmetric high-dimensional data**

Abstract: In this age of high-dimensional data, many challenging questions take the following shape: can you check whether the data has a certain desired property by checking that property for many, but low-dimensional data fragments? In recent years, such questions have inspired new, exciting research in algebra, especially relevant when the property is highly symmetric and expressible through systems of polynomial equations.

I will discuss three concrete questions of this kind that we have settled in the affirmative: Gaussian factor analysis from an algebraic perspective, high-dimensional tensors of bounded rank, and higher secant varieties of Grassmannians. The theory developed for these examples deals with group actions on infinite-dimensional algebraic varieties, and applies to problems from many areas. In particular, I will sketch its (potential) relation to the fantastic Matroid Minor Theorem. - Wed. 5 February: Mark van de Wiel (VU) , Room: F-612, 16:00-17:00

Title:**Bayesian analysis of genomics data with application to network reconstruction**

Abstract:

Genomics data are high-dimensional data, meaning that we have more variables (genes) than observations (individuals, typically). From a practical perspective Bayesian statistics is attractive, because for complex models the inferential frame work is conceptually much more straightforward than in the classical (`p-value-based') setting.

I will start by shortly reviewing elementary Bayesian statistics. Next, I discuss exact and numerical methods to obtain posterior densities, which is the conditional density of a parameter given the data. Posterior densities play a central role in Bayesian inference. Then, I will demonstrate how, in high-dimensional setting, a crucial quantity in Bayesian statistics, the prior, can be estimated rather than be assumed. This solves, to a large extent, a much heard criticism on Bayesian statistics about objectivity of the analysis.

Finally, I will focus on application of the methodology to gene network reconstruction by use of a structural equation model. For this application, additional methodological work was needed for obtaining fast approximations of posteriors (variational Bayes). Also, new criteria for selecting edges in a network, which correspond to parameters in the model, were formulated.

This is joint work with Gwenael Leday, and others.

## 2013

- Wed. 30 October: Sergey Shadrin (UvA) , Room: S-607, 16:00-17:00

Title:**Hurwitz numbers, moduli spaces, and integrable systems**

Abstract: I am going to discuss three absolutely classical topics going back to the 19th century:

1. Hurwitz problem related to the combinatorics of the symmetric group.

2. The spaces parametrizing possible complex structures on surfaces.

3. The non-linear PDE's coming from hydrodynamics, KP and KdV equations.

Until recently all these topics were studied absolutely independently and seemed to have nothing in common at all. But in the last 25 years it has appeared that all these three topics are actually closely related to each other. I'll try to make a short introduction to each of them and explain the way they interplay.

- Wed. 16 October: Fabian Ziltener (UU) , Room: S-655, 16:00-17:00

Title:**Coisotropic Submanifolds of Symplectic Manifolds, Leafwise Fixed Points, and a Discontinuous Capacity**

Abstract: Consider a symplectic manifold (M,ω), a coisotropic submanifold N of M, and a selfmap φ of M. A leafwise fixed point of φ is a point in N, which under φ is mapped to the isotropic leaf through itself. Symplectic manifolds naturally generalize phase space of classical mechanics. In this setting coisotropic submanifolds arise as energy level sets. Let φ be the time-one flow of a time-dependent perturbation of a given Hamiltonian function on M. Then a leafwise fixed point of φ is a point on a given energy level set whose trajectory is changed only by a phase shift, under the perturbation. I will discuss lower bounds on the number of leafwise fixed points of φ. As an application one obtains a symplectic capacity by considering the minimal actions of regular closed coisotropic submanifolds of a given symplectic manifold. A variant of this capacity is discontinuous.

- Wed. 2 October: Iris Loeb (VU) , Room: S-655, 16:00-17:00

Title:**An introduction to constructive (reverse) analysis**

Abstract: Intuitionism, founded by L.E.J. Brouwer in the early 20th century, is based on the idea that mathematics deals with languageless constructions. As a consequence Brouwer dismissed the use of proof by contradiction, and accepted certain controversial theorems, like the one stating that every (total) real function is continuous. Constructive mathematics can roughly be characterised as that part of intuitionistic mathematics that does not conflict with the classical understanding of mathematics. In this talk I will give an introduction to intuitionism, to intuitionistic and constructive analysis, and to the search for the weakest principles that are necessary to prove certain theorems of (intuitionistic/classical) analysis.

- Wed. 18 September: Bartek Knapik (VU) , Room: S-655, 16:00-17:00

Title:**Bayesian asymptotics in nonparametric inverse problems**

Abstract: In my talk I will first introduce basic notions of Bayesian asymptotics, namely posterior consistency and contraction rates. Studies of these properties of Bayesian inference for ill-posed inverse problems have emerged only recently, and I will briefly elaborate on this issue. I will discuss several results in the white noise model with Gaussian priors, in mildly and severely ill-posed settings. In both cases priors can be rate-adaptive, i.e., the knowledge of the regularity of the truth is not required for optimal inference based on the posterior. Later, I will present more recent results that enable studies of frequentist properties of Bayesian approach to inverse problems beyond the white noise model and conjugate settings. Based on joint works with Botond Szabó (Eindhoven), Harry van Zanten (UvA), Aad van der Vaart (Leiden), and J-B Salomond (Paris-Dauphine and ENSAE-CREST)

- Wed. 15 May: Klaas Landsman (RU) , Room S-655, 16:00-17:00

Title:**Asymptotic emergence**Abstract: Opponents of a reductionist view of science (some of whom have a religious agenda) claim that certain (macroscopic) properties or and/or laws may "emerge" all of a sudden in some limiting regime of a given (microscopic) theory. One of their strongest cases is what physicists call spontaneous symmetry breaking, which according to official mathematical physics indeed cannot exist in finite quantum systems and hence seems to be an "emergent" property of physics in the infinite-volume limit. We explain this example, which has brought reductionists (like the speaker) to despair, but we also show that due to a very subtle mechanism in spectral theory this threat to reductionism can be neutralized. To understand this talk all you need to know is elementary Hilbert space theory and popular-science level quantum physics. - Wed. 1 May: Christoph Temmel (VU), Room S-655, 16:00-17:00

Title:**The Lovasz Local Lemma and the hardcore lattice gas**Abstract: The Lovasz Local Lemma (LLL) is a classic tool in the probabilistic method in combinatorics. It is a sufficient condition to show the existence, and even construct, combinatorial objects fulfilling properties with sparse enough dependency graph. I will give several examples. Among the distributions fulfilling the LLL, there is a uniform worst case, discovered by Shearer. It drives all calculations and is strongly related to the independent set polynomial of the dependency graph. The latter relation links Shearer's measure and the LLL with the hardcore lattice gas model on a graph. - Wed. 17 Apr: Gil Cavalcanti (UU), Room S-655, 16:00-17:00

Title:**Formality beyond****Kähler geometry**Abstract: I will review the notion of formality for manifolds and recall a result of Deligne, Griffiths, Morgan and Sullivan stating that Kähler manifolds are formal. Then we will move on to study the question "what else is formal?" Different extensions of the Kähler condtion are complex and symplectic manifolds, generalized complex manifolds and manifolds with special holonomy and each of these extensions leads to something interesting. - Wed. 20 Mar: Jeff Williams (SFU, British Columbia), Room S-655, 16:00-17:00

Title:**Adaptive numerical methods based on optimal transportation.**Abstract: The solution of many differential equations in science and technology requires the use of a careful selection of the computational grid. This talk will discuss one strategy for doing this based on ideas from optimal transportation. I will present some of the theoretical results available for such methods as well as applications to PDEs with blow-up and examples from meteorology. - Wed. 6 Mar: Odo Diekmann (UU), Room S-655, 16:00-17:00

Title:**Delay Equations**Abstract: A delay equation is a rule for extending a function of time towards the future, on the basis of the known past. Renewal Equations prescribe the current value, while Delay Differential Equations prescribe the derivative of the current value. With a delay equation one can associate a dynamical system by translation along the extended function. I will illustrate by way of examples how such equations arise in the description of the dynamics of structured populations and sketch the available theory, while noting the need for numerical bifurcation tools. The lecture is based on joint work with Mats Gyllenberg, Hans Metz and many others. - Wed. 20 Feb: Bas Edixhoven (UL), Room S-655, 16:00-17:00

Title:**Fast computation of the numbers of vectors of given length in a lattice**Abstract: The question is how one can compute the number of ways in which an integer m can be written as a sum of n squares of integers, fast. I will explain how recent progress in computation of 2-dimensional Galois representations makes it possible to compute this number, for n even and m given with its factorisation in prime numbers, in time at most a power of n.log(m) (assuming the Riemann hypothesis for number fields). This is an application of a generalisation by Peter Bruin of joint work of the speaker with Jean-Marc Couveignes, Robin de Jong and Franz Merkl. - Wed. 6 Feb: Rob van der Mei (VU), Room S-655, 16:00-17:00

Title:**Towards a unifying theory on polling models: new results and challenges**Abstract: Polling systems are multi-queue systems in which a single server visits the queues in some order to serve the customers waiting at the queues, typically incurring some amount of switch-over time to proceed from one queue to the next. Polling models find a wide variety of applications in areas like computer-communication systems, logistics, flexible manufacturing systems, production systems and maintenance systems. In this talk I will (1) give a brief overview of my research activities, and (2) discuss a number of interesting fundamental properties of polling models, and discuss recent progress in an attempt to develop a unifying theory on polling models under heavy-load circumstances.

## 2012

- Wed. 8 Feb: Bob Planque (VU), Room C-147, 16:00-17:00

Title:Abstract: Ant colonies spanning a million or more are among nature's greatest wonders. Some raid the tropical forest floor in huge armies, others rely on agriculture invented millions of years ago. Just how such insect city states work and indeed are initially founded is largely unknown. Especially for those species whose colonies start as single fertilized queens, we may still only marvel how a colony's organization changes as numbers change over six orders of magnitude. In this talk, I will focus on the role of diversity in recruitment mechanisms to harvest food, using differential equation models, The main question will be to understand how some of the most efficient such mechanisms, usually employed by large numbers of ants, may be employed in small colonies.**Building giant ant colonies from single queens** - Wed. 22 Feb: Hansjoerg Geiges (Koeln), Room C-147, 16:00-17:00

Title:**How to visualise manifolds up to dimension 5**

Abstract: We usually think of 2-dimensional manifolds as surfaces embedded in Euclidean 3-space. Since most humans, including the speaker, cannot visualise Euclidean spaces of higher dimensions, it appears to be impossible to give pictorial representations of higher-dimensional manifolds. However, one can in fact draw 1-dimensional pictures truly representing the topology of surfaces. By analogy, one can draw 2-dimensional pictures of 3- manifolds (Heegaard diagrams), and 3-dimensional pictures of 4-manifolds (Kirby diagrams). With a little trick, one can even draw 2-dimensional (sic!) pictures of at least some 5-manifolds. In this talk I shall explain how to draw such pictures and how to use them for answering topological and geometric questions. The work on 5-manifolds is joint with Fan Ding and Otto van Koert.

- Wed. 7 March: Michael McAssey (VU), Room C-147, 16:00-17:00

Title:Abstract: Identifying clusters among data is a common goal of exploratory data analysis. Spectral clustering has become a popular technique that extracts cluster information from the spectrum of the graph Laplacian associated with a graph whose vertices are the data points. However, its effectiveness is limited when, for example, the clusters are non-convex, or their intra-cluster scales are heterogeneous. We present a regulated random walk on the graph by which we obtain a similarity measure based on an intuitive definition of a cluster. From this similarity measure we obtain a graph Laplacian that extends the effectiveness of spectral clustering to a much wider variety of data settings. We illustrate this method on both simulated and real data sets.**Spectral data clustering using a regulated random walk.** - Wed. 21 March: Rob van der Vorst (VU), Room C-147, 16:00-17:00

Title:Abstract: Closed integral curves of 1-periodic Hamiltonian vector fields on the 2-disc may be regarded as braids. If the Braid Floer homology of associated proper relative braid classes is non-trivial, then additional closed integral curves of the Hamiltonian equations are forced via a Morse type theory. In this talk we explain that certain information contained in the braid Floer homology - the Euler-Floer characteristic - also forces closed integral curves and periodic points of arbitrary vector fields and diffeomorphisms and leads to a Poincare-Hopf type Theorem. The Euler-Floer characteristic for any proper relative braid class can be computed via a finite cube complex that serves as a model for the given braid class. The results are restricted to the 2-disc, but can be extend to two-dimensional surfaces(with or without boundary).**The Poincare-Hopf Theorem and Braids** - Wed. 4 April: Speaker: Bob Rink (VU), Room M-623, 16:00-17:00

Title:Abstract: A classical result of Aubry and Mather states that Hamiltonian twist maps have orbits of all rotation numbers. Analogously, one can show that certain ferromagnetic crystal models admit ground states of every possible mean lattice spacing. In this talk, I will show that these ground states generically form Cantor sets, if their mean lattice spacing is an irrational number that is easy to approximate by rational numbers.**Ferromagnetic crystals and the destruction of minimal foliations** - Wed. 18 April: Paulien Koeleman (VU) and Pia Kempker (VU), Room M-623, 16:00-17:00

Titles: (Pia)Abstracts: Coordinated linear systems are a particular class of distributed dynamical systems, characterized by conditional independence and invariance properties of the underlying linear spaces. The motivation behind studying these systems is that some global control objectives can be achieved via local controllers: For example, global stabilizability reduces to local stabilizability of all subsystems. In this talk, coordinated linear systems will be introduced, and some aspects of the construction and control of this class of systems will be discussed.**Coordination control of linear systems** Speakers: - Wed. 2 May: Marcel van de Vel (VU), Room M-623, 16:00-17:00

Title:Abstract: Random number generators (RNGs) are vulnerable in a cryptograph environment.**Applicable Math from Scratch: $n$-permutron**

One of the simplest effective proposals to remedy such defects was made by Donald Knuth

in his "Art of Computer Programming". Our research on $n$-permutrons originated

as an attempt to eliminate a potential weakness of this proposal. An $n$-permutron is an $n \times n$ array of digits $0,1, ..,n-1$, each occurring $n$ times. (Latin squares are a special case of this.) It is operated by "shuffling" and "indirection". The main result is that (for suitable dimensions $n$, including 16 and 32) any input sequence can be turned into any output sequence provided two shuffles are allowed before each indirection. We will take some time out to explain the basic ideas behind the proof: optimising a set of $n$ positions in an $n$-permutron, a "crumbling spaghetti effect" on $n$-sets, and finding a "distance partition" in a regular $n$-gon. Some steps require computer assistance. If time permits, we will give some details on how a hexadecimal ($n=16$) and a duotrigesimal ($n=32$) permutron can be implemented. The physical model of an $n$-permutron is a torus with, for each of its two main directions, a system of $n$ rotating rings. Thinking of digits as colors, we obtain a relative of Rubik's cube with a programmable solution of the generic "restoration problem". - Wed. 16 May: Frank Bruggeman (VU), Room M-623, 16:00-17:00

Title:Abstract: In the last decades, biology has made great advances. The dynamic and molecular basis of life can at present be measured at high detail. What those experiments indicate is that the system properties of organisms are emergent properties of large molecular networks. These networks are highly dynamic and give rise to spatial organization and stochastic behavior. To understand how molecular interactions give rise to cell behavior is the main aim of systems biology; from a fundamental as well as an applied perspective. Considering the complexity of this task, systems biology undoubtedly has to rely heavily on mathematics. In this talk, I will present a number of mathematical challenges in systems biology that I identify in my own work. These examples will show you that systems biology has the potential to become a major application field of new mathematics in the next decades.**Mathematics for Systems Biology** - Wed. 30 May: Ronald Meester (VU), Room C-147, 16:00-17:00

Title:Abstract: In fractal percolation, we study connectivity properties of randomly generated fractal sets. In this lecture, I will discuss some background, notably the existence of a so called phase transition when the underlying retention parameter p varies from 0 to 1. Then I will explain how recent developments in scaling theory lead to a new and fruitful way of looking at the random fractal sets. For instance, this leads to the conclusion that the connected components essentially consist of holder-continuous arcs, all with the same exponent.**Recent developments in fractal percolation** - Wed. 19 Sept: Jaap Top, Room S-655, 16:00-17:00

Title:Abstract: On Saturday May 27th, 1893, the Groningen geometer Pieter Hendrik Schoute presented three string models of discriminant surfaces during the monthly science meeting of the KNAW (Royal Dutch Academy of Sciences). Why he did this, and how discriminants since J.J. Sylvester were used in a geometric way, is the subject of this talk.**Schoute's discriminant surfaces** - Wed. 3 Oct: Remco van der Hofstad, Room S-655, 16:00-17:00

Title:Abstract: A branching process is a simple population model where individuals have a random number of children, independently of one another. Branching processes have a phase transition. Indeed, when the mean offspring is at most 1, the branching process dies out almost surely, while for mean offspring larger than one, the branching process survives with positive probability. Branching processes with mean offspring equal to one are called critical. In this talk we extend classical results by Kolmogorov and Yaglom on branching processes to high-dimensional statistical physical models. Models to which our results apply are oriented percolation above 4+1 dimensions, the contact process above 4+1 dimensions, and lattice trees above 8 dimensions. We give general conditions to show that Kolmogorov's and Yaglom's theorems hold. In the case of oriented percolation, this reproves a result with den Hollander and Slade (that was proved using a 100 page lace expansion argument), at the cost of losing explicit error estimates. [This is joint work with Mark Holmes, building on work with Gordon Slade, Frank den Hollander and Akira Sakai.]*The survival probability and r-point functions in high dimensions* - Wed. 17 Oct: Marco Streng (VU) , Room S-655, 16:00-17:00

Title:Abstract: Some lattices inside the plane are mapped into themselves by a combination of scaling and rotating. This is called complex multiplication, and turns out to have (through analysis, geometry, and algebra) applications in both pure number theory, and daily life.**Elliptic curves: complex multiplication, application, and generalization** - Wed. 31 Oct: Martijn Zaal (VU) & Simone Munao (VU), Room S-655, 16:00-17:00

Title Martijn:s**Gradient flows in metric and non-metric spaces and applications to parabolic free boundary problem**Abstracts: In this talk, a very simple model for cell swelling by osmosis will be studied. The problem consists of diffusion in a free domain. The boundary moves by surface tension and osmotic force. A variational formulation for this problem will be introduced, and it will be shown that the osmotic force can be thought of as a Lagrange multiplier. Finally, it appears that the concept of gradient flow can be stretched a bit further than metric spaces, and that this generalization is useful to study the variational structure of the mean curvature flow. Title Simone:Abstract: The Poincare'-Bendixson Theorem is a classical theorem for flows in the plane. The proof of the Theorem relies on properties of \R^2, and there are counterexamples already in dimension 3. We show that surprisingly the Theorem holds in an infinite dimensional setting i.e. for flow lines of the non-linear Cauchy-Riemann equations.**The Poincare'-Bendixson Theorem and the non-linear Cauchy-Riemann equations.** - Wed. 14 Nov: Jan van de Craats (UvA), Room S-655, 16:00-17:00

Title:**Aansluitingsproblemen wiskunde vwo-universiteit: is er al verbetering merkbaar?**Abstract: In de nasleep van de studentenactie "Lieve Maria" werd in 2006 op initiatief van de Tweede Kamer een Resonansgroep Wiskunde ingesteld die tot taak had aanbevelingen te doen om de aansluiting van de wiskunde op havo en vwo met het hbo en de universiteit te verbeteren. De voorstellen van de Resonansgroep werden in 2008 vrijwel ongewijzigd door staatssecretaris Marja van Bijsterveldt van OCW met instemming van de HBO-raad en de VSNU tot beleidsbeslissingen verheven. We zijn inmiddels 4 jaar later en het is tijd voor een tussenbalans. Wat is er van die besluiten in de praktijk gerealiseerd, en in hoeverre is deaansluiting daadwerkelijk verbeterd? - Wed. 28 Nov:
**Teun Koetsier**(VU), Room S-655, 16:00-17:00

Title:e**Stevin and the Rise of Archimedean Mechanics in the Renaissanc**Abstract: In 2008 in an interesting paper in the renowned Archive for History of Exact Science Palmieri discussed the emergence of Archimedean mechanics during the late Renaissance. In his paper he does not mention Simon Stevin (1546-1620). In the talk I will discuss Archimedes, the rise of mechanics in the Renaissance and the position of Stevin's work in this development. I will argue that if we have to point at the first true successor of Archimedes in the Renaissance it is Stevin and not one of the Italians mentioned by Palmieri. - Wed. 12 Dec: Martijn Pistorius (UvA/Imperial College), Room S-655, 16:00-17:00

Title:**On consistent valuation under uncertain drift and jump-rates**Abstract: This talk is concerned with the problem of an agent that seeks to value financial claims in a multinomial random walk model in a time-consistent way reflecting her uncertainty over the value of the true transition probabilities of the random walk. To take into account this uncertainty, a valuation operator is proposed that is defined in terms of distorted transition probability measures with respect to a given concave distortion Psi and a given filtration G. We show that under a suitable scaling there is convergence to a particular continuous-time non-linear expectation operator. We will give an explicit description of this operator and derive various properties of interest.

- Wed. 8 Feb: Bob Planque (VU), Room C-147, 16:00-17:00

## 2011

- Wed. 2 Feb: Stephan van Gils (Twente), Room M623, 16:00-17:00

Title:**Detailed and population models for a microcolumn of the cortex**

Abstract: We present two models developed to study neuronal activity during normal and pathological state. A detailed model describes a microcolumn of the neocortex. It contains many parameters, whose values are based on experimental data. Depending on global parameters (the total network excitation and inhibition), the model exhibits different types of behavior like saturated desynchronized activity, irregular bursts, fast oscillations and burst suppression. The second model is a lumped population model. It describes the activity of two interacting excitatory populations in terms of a system of delay differential equations with two point delays. In this model we analyze steady states and we perform bifurcation analysis in two parameters. Finally, the behavior of the two completely different models is compared. These different states are compared with the stable states in a delay differential population model for the activity of neuronal populations. - Wed. 16 Feb: Arjeh Cohen (Eindhoven), Room M623, 16:00-17:00

Title:*Algebraic models for some Hurwitz surfaces*

Abstract: Compact Riemann surfaces are equivalent mathematical objects to smooth complex projective algebraic curves. But finding the curve corresponding to a given Riemann surface is not easy. For five Hurwitz surfaces, instances of Riemann surfaces with relatively large automorphisms, Maxim Hendriks and I were able to compute the curve. Two of these are known; one of these is the classic Klein quartic. In my talk, I will provide an introduction to the basic theory, show nice pictures of the Riemann surfaces by Jack van Wijk, and describe the method of construction. - Wed. 2 March: Han Peters (UvA), Room M623, 16:00-17:00

Title:Abstract: In complex dynamical systems we study the orbits under the iteration of holomorphic maps. Roughly said, an initial value is said to lie in the Fatou set if the orbits of all nearby initial values are similarly. In other words, the dynamical system behaves orderly (not chaotically) near the initial value. Connected components of the Fatou set are called Fatou components, and these components play an important role in our understanding of complex dynamical systems. Since 1985 the Fatou components that can occur for rational functions in the Riemann sphere are completely described. I will review these classical one-dimensional results, and discuss what is known (and not known) in two complex dimensions.**Fatou Theory in two complex dimensions** - Wed. 16 March: Tobias Mueller (CWI), Room M623, 16:00-17:00

Title:Abstract: If we pick n points at random from d-dimensional space (i.i.d. according to some probability measure) and fix an r > 0, then we obtain a random geometric graph by joining two points by an edge whenever their distance is at most r. I will give a brief overview of some of the main results on random geometric graphs and then describe my own work on Hamilton cycles and the chromatic number of random geometric graphs.**Random geometric graphs** - Wed. 30 March: Rommert Dekker (Rotterdam), Room M623, 16:00-17:00

Title:Abstract: Real-time railway operations are subject to stochastic disturbances. Thus a timetable should be designed in such a way that it can cope with these disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. Traditionally the Dutch Railways uses a time supplement of 7% for all connections over the country, yet there is no clear explanation of the choice of that percentage. This presentation studies the aspects of timetable robustness. We first consider a single line and derive some results which resemble results from hospital appointment planning. Next we consider a deterministic model for cyclic railway timetables. We adapt it into a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called ‘‘Zaanlijn”. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable. If time allows we will also consider the extension to liner shipping schedules.**In search of a reliable timetable for the Dutch Railways** - Wed. 13 April: Roberto Fernandez (Utrecht), Room M623, 16:00-17:00

Title:Abstract: Gibbs measures are the main characters of equilibrium statistical mechanics. They enjoy a fully developed theory that has lead to their widespread application well beyond their original field. Nevertheless, examples show us that Gibbsianness can not be taken for granted, because it can be destroyed by simple transformations and even during spin-flip simulations. The talk will review the notion of Gibbsianness and will present examples of loss of Gibsianness illustrating the mechanisms behind the Gibbs-nonGibbs transitions.**Gibbsianness and the transformations that destroy it** - Wed. 27 April: Steven Wepster (Utrecht), Room M623, 16:00-17:00

Title:**Preparing a translation of Ludolph van Ceulen's "Vanden Circkel"**

Abstract: Currently we are working on a translation into English, plus commentary, of Ludolph van Ceulen's book "Vanden Circkel" ("On the circle"), originally published in 1596. Through a number of examples I will show why such a translation is of interest to a modern mathematician and/or historian of mathematics: partly because the book falls in with the tradition of mathematical practice at the time, partly because it contributes to reshaping that tradition, and partly because it contains some very advanced results (to 16th century standards). There is even a kind of "open problem": in specific instances we still do not know the computational methods that Van Ceulen applied. - Wed. 11 May: Wieb Bosma (Nijmegen), Room M623, 16:00-17:00

Title:Abstract: For ages, continued fractions have been known to provide alternative representations of real numbers (instead of decimal or binary expansions). They have advantages, particularly for the approximation by rational numbers, but also severe disadvantages, for real arithmetic, for example, because the digits can be arbitrarily large, for instance. In this talk some aspects of continued fractions with bounded partial quotients (digits) will be discussed. By elementary geometric and topological means some results on such representations can be found, and a surprising recent result for complex continued fraction will be derived: the existence of algebraic numbers of arbitrary degree with bounded complex partial quotients.**Some intriguing problems on continued fractions** - Wed. 25 May: Pierre Nolin (NYU), Room M143, 16:00-17:00

Title:**Universality of some random interfaces: inhomogeneity and SLE(6)**

Abstract: We present classical lattice models of statistical mechanics, particularly percolation and the Ising model. In two dimensions, these two models feature a sharp change of behavior - a phase transition - at a certain value of the macroscopic parameter (density, temperature), and for this specific critical value, they both possess a conformal invariance property, as proved by Smirnov (2001, 2007). This strong property has important consequences for the models considered, at and near their critical point. In particular, we discuss the formation of "universal" random shapes, observed in various concrete situations (chemical etching, erosion...): fractal interfaces with dimension 7/4, coming from density fluctuations, arise spontaneously. - Wed. 7 Sept: Bert Zwart (CWI/VU), Room M-639, 16:00-17:00

Title:**Using probability to develop rules of thumb**

Abstract: I will discuss several research problems I have been involved with which are mathematically challenging and at the same time have a story our grandmothers would be able to understand. These all relate to measuring the performance of and/or designing systems that operate in a random environment. Examples are call centers, computer systems, and communication networks. Although the focus will be on explaining the physical intuition behind the results, I will indicate the mathematical challenges as well. - Wed. 21 Sept: Michael Levin (Ben Gurion), Room M-639, 16:00-17:00

Title:**Revisiting two classical results of Dimension Theory**

Abstract: The talk is focused on the following classical results of Dimension Theory: the Menger-Urysohn formula and the Hurewicz theorem on dimension lowering maps. We will examine ways of strengthening these results by means of Cohomological Dimension and Extension Theory. - Wed. 5 Oct: Ale Jan Homburg (UvA/VU), Room M-639, 16:00-17:00

Title:**From iterated function systems to partially hyperbolic dynamics**

Abstract: I'll provide an overview of topics in chaotic dynamical systems I've been working on, and discuss their relations. I'll proceed from iterated function systems to forced circle diffeomorphisms to partially hyperbolic dynamics on the 3-torus. A common theme will be the search for dynamical properties that occur robustly (that persist when perturbing the system), such as the robust occurrence of dense orbits. - Wed. 19 Oct: Jan Hogendijk (Utrecht), Room M-639, 16:00-17:00

Title:**Aspects of mathematics in medieval Islamic civilization**

Abstract: I will discuss some characteristic aspects of mathematics in medieval Islamic civilization, on the basis of the works of the mathematician and astronomer Abu Rayhan Biruni (973-1046). My examples will include applications such as the astrolabe and an instrument for finding the direction of Mecca (the qibla). - Wed. 2 Nov: Anish Sarkar (Delhi), Room M-639, 16:00-17:00

Title:**Some models of random oriented trees**

Abstract: Random oriented trees originate in many physical models. In many river

network models such as Howards model, Scheidegger model etc.,

random oriented trees can be found. In this talk, I will describe some

of these above models and also describe models from other fields. I will state some

of the results and describe a few open problems.

Scaling limits of these models are also of interest, which brings out

the connection of Brownian web with these models. If time permits, I

will discuss this connection briefly. - Wed. 16 Nov: Speaker: Aner Shalev (Jerusalem), Room M-639, 16:00-17:00

Title:**Words and Waring type problems**

Abstract: Non-commutative analogues of Waring problem in number theory were studied extensively in recent years, where the goal is to express group elements as short products of special elements; these may be powers, commutators, values of a general word w, or elements of a given conjugacy class, or of certain subgroups or subsets. Such problems arise naturally in profinite groups, finite groups, and finite simple groups in particular. I will describe background, recent results (with various coauthors), and relations to representations, geometry, and growth. I will conclude with some applications and conjectures. The talk will be accessible for a wide audience. - Wed. 30 Nov: Speaker: Shota Gugushvili (VU), Room M-639, 16:00-17:00

Title:**Parametric inference for stochastic differential equations: a smooth and match approach**

Abstract: In this talk we will consider a parameter estimation problem for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. In the first, less technical part of the talk we will supply some remarks on the history of discovery and study of a physical phenomenon known under the name of Brownian motion and the impact it had on the development of probability theory. In particular, we will show how explanation of the Brownian motion phenomenon led to writing down the first ever stochastic differential equation by Langevin in 1908 (even prior to formulation of a rigorous mathematical theory of stochastic differential equations). Next, after some basic information on the modern theory of stochastic differential equations, in the second, more technical part of the talk we will turn to the parameter estimation problem itself. For construction of our estimator of the parameter of interest we will propose a specific two-step procedure with steps being referred to as a smoothing step and a matching step. We will highlight computational advantages furnished by our procedure and will discuss the asymptotic behaviour of the estimator. Our main result is that under suitable assumptions our procedure leads to an estimator with an optimal, square root of n convergence rate. Finally, we will also discuss a further improvement of our estimator through a one-step Newton-Raphson type procedure. The talk is based on a joint work with Peter Spreij. - Wed. 14 Dec: Speaker Gunther Cornelissen (Utrecht), Room M-639, 16:00-17:00

Title:**Number theory and physics, an eternal rusty braid**

Abstract: I will describe joint work with Matilde Marcolli in which we apply ideas from quantum statistical mechanics and dynamical systems to solve the number theoretical analogue of the problem "how to hear the shape of a drum".

## 2010

- Wed. 27 Jan: Colloquium in memory of
**Israel Gohberg.**Room M-129, 15:00-17:00. Click here to see a more detailed program. Main speaker:**Albrecht Böttcher**(Chemnitz).*Title: Two projections: from Paul Halmos to Israel Gohberg*

Abstract: The two projections theorem by Paul Halmos provides us with a canonical representation of two selfadjoint projections that can be used to solve several problems in geometry and operator theory in Hilbert space. Singular integral or Toeplitz operators with discontinuous symbols lead to Banach algebras generated by two idempotents which are usually not selfadjoint. Motivated by these applications, Roch, Silbermann, Gohberg, and Krupnik established an invertibility criterion for Banach algebras generated by two idempotents, which is one of the most spectacular achievements in the field since Halmos. The talk gives an introduction to the subject and also embarks on the fascinating history of the topic. - Wed. 24 Feb: Speaker:
**Spencer Bloch**(Chicago), Room HG-04A05, 16:00-17:00*Note: This colloquium is part of a dedicated afternoon on the occasion of Prof. Bloch's Stieltjes-professorship in Spring 2010.**Title: An algebraic geometer looks at renormalization in physics*

Abstract: Algebraic geometry has some powerful tools to deal with divergent integrals. I will outline one approach in elementary terms and sketch how it can be applied to integrals arising in physics. - Wed. 10 Mar: Speaker:
**Marius Crainic**(Utrecht), Room M-623, 16:00-17:00*Title: Stability of leaves*

Abstract: In this talk I will discuss stability phenomena (and criteria) for leaves/orbits of geometric structures. I will start with the classical cases of vector fields/foliations (and the known "Reeb-Thurston stability'') and group actions on manifolds ("Hirsch-Stowe stability'') and then, depending on the time left, I will explain similar recent results in Poisson geometry (joint work with R.L. Fernandes). - Wed. 24 Mar: Speaker:
**Erik van den Ban**(Utrecht) -**cancelled***We are deeply sad to hear that last weekend Hans Duistermaat passed away.*.

We offer our condolences to his family, friends and colleagues.

This week's general mathematics colloquium is cancelled - Wed. 7 Apr: Speaker:
**Kirsten Valkenburg**(VU), Room M-623, 16:00-17:00*Title: On nonseparable Erdős type spaces*

Abstract: Erdős space is the subspace of Hilbert space consisting of vectors that have all coordinates rational. For complete Erdős space one takes coordinates in a convergent sequence instead of the rationals. Erdős showed that both are one-dimensional and homeomorphic to their own squares. Therefore, they are important examples in dimension theory. Nevertheless, complete Erdős space has surfaced in complex dynamics, functional analysis and descriptive set theory as well. Note that both spaces are basically the intersection of a countable product of zero-dimensional subsets of the reals and an l^{p}-space. We investigate Erdős type spaces that are uncountable products of zero-dimensional subsets of the reals in a nonseparable l^{p}-space. Spaces of this kind that are one-dimensional and topologically complete can be classified as products of complete Erdős space with a countable product of discrete spaces, depending on two cardinal invariants of the Erdős type space. There is a similar classification that links certain one-dimensional Erdős type spaces and products of Erdős space with a countable product of discrete spaces. - Wed. 21 Apr: Speaker:
**Markus Heydenreich**(VU), Room M-623, 16:00-17:00**Title: Mean-field behaviour in percolation**

Abstract: Various random spatial models show 'mean-field behaviour' above a certain upper critical dimension d_{c}. In this talk I shall explain what is meant by mean-field behaviour, and why it holds for percolation on the high-dimensional (Euclidean) lattice. Furthermore, I will discuss why it holds for a percolation model on the hyperbolic disc. - Wed. 5 May: No colloquium (liberation day)
- Wed. 19 May: Speaker:
**Bernd Heidergott**(VU), Room M-623, 16:00-17:00Abstract: Starting point of our presentation will be a simple and easy to prove relation for Markov operators. As we will explain, this relation is a versatile tool for the analysis of Markov processes. On the one hand, it leads to gradient estimation and Taylor series expansions of stationary Markov processes. On the other hand, it can be made fruitful for numerical approximations. The latter application is of particular interest as it provides a new approach to Markov decision processes (independent of value iteration or policy iteration). Time permitting, we will also address applications to the numerical analysis of general Markov operators.**Title: A Swiss Army knife formula for Markov processes** - Wed. 2 Jun: Speaker:
**Geert Geeven**(VU), Room M-623, 16:00-17:00**Title**Abstract: Condition-specific and time-dependent transcriptional regulatory networks underlie the coordinated expression of genes involved in all biological processes. Insight into these networks is crucial for the understanding of biological systems under normal and pathological conditions. In this talk I will discuss how statistical models can be used to infer relationships between DNA binding proteins and target genes by analyzing experimental gene expression and DNA sequence data. We developed an algorithm called GEMULA (Gene Expression Modeling Using LASSO) and applied it to real experimental data to identify transcription factors that are crucial regulators of the transcriptional network underlying neuronal outgrowth.*: Computational statistics for the identification of transcription factor gene interactions* - Wed. 16 Jun: Speaker:
**Eric Opdam**(UvA), Room M-623, 16:00-17:00Abstract: The local Langlands conjecture asserts that the Fourier dual of a real or p-adic reductive group G has a description in terms of algebraic data, so-called Langlands parameters. This would imply that the Shahidi-Langlands local L-functions attached to those representations of G relevant for the Fourier analysis on G are holomorphic in the right half plane. Recently we could prove this property of L-functions in general (joint work with Volker Heiermann).**Title: The local L-function conjecture** - Wed. 29 Sept: Speaker:
**Laurent Stolovitch**(Nice), Room F-123, 16:00-17:00Abstract: In this talk, we'll give an overview of recent progress that was made in the study of vector fields (or systems of ODEs) in a neighbourhood of a fixed point. We shall focus on the notion of normal form. The latter is supposed to be a "simple" model to which the vector field can be transformed. We shall show some dynamical and geometric properties that can be deduced in the analytic setting.**Title: On normal forms of vector fields** - Wed. 13 Oct: Speaker:
**Christof Melcher**(Aachen), Room F-123, 16:00-17:00**Title: Landau-Lifshitz-Gilbert dynamics of magnetic vortices** *Wed. 27 Oct: Speaker:***Erik van den Ban**(Utrecht), Room F-123, 16:00-17:00Abstract: The goal of this talk is to give an impression of the theory of Radon transformation on symmetric spaces. We still start with describing the classical Radon transform defined by integration over hyperplanes in Euclidean space. It is natural to view this transform in relation to the group of isometries in Euclidean space. This viewpoint was advocated by S.S.Chern who formulated integral geometry in the context of homogeneous spaces of Lie groups. Later, S. Helgason took up this viewpoint to study several transforms of Radon type in the context of Riemannian symmetric spaces (of which the Poincare disk is the simplest example). For the so-called horospherical transform Helgason established a support theorem, which is closely related to a Paley-Wiener theorem for the Fourier transform for these spaces. Towards the end of the talk I will describe recent work of my PhD student Job Kuit, who obtained an interesting generalization of Helgason's result in the context of pseudo-Riemannian symmetric spaces.**Title: Radon transformation on symmetric spaces**- Wed. 24 Nov: Speaker:
**Stefan Bauer**. Room: M-129, 16:00-17:00*Title: Four Dimensional Manifolds*

Abstract: The world we live in is four dimensional: There are three space dimensions, complemented by time. Manifolds of dimension three and four are mathematical models of our universe,considered either as a space at a fixed time or in its a totality, from beginning to end of time. Of course we don't stand a chance to ever know how our universe looks like as a whole. Nevertheless, we may pose the question, which models there are and how to distinguish them. During the past decades, ideas and methods from topology, geometry and physics revealed phenomena unknown of in other dimensions. Indeed, amongst all dimensions, geometry is most bizarre and least understood in dimension four. The talk aims to elucidate some aspects of the puzzle.

## 2009

- Wed. 16 Dec:
**Frits Beukers**(UU), Room C-648, 16:00-17:00**Title: Monodromy of linear differential equations, the case of Lam\'e's equation**

Abstract: The monodromy group of ordinary linear differential equations in the complex plane is a classical but elusive subject. The case of Fuchsian second order differential equations with three singularities is well-known, they come down to Gauss' hypergeometric functions. However, second order Fuchsian equations with four singular points already present with an almost intractable variety of possibilities. We illustrate this by dealing with a special class of Lam\'e differential equations. - Wed. 2 Dec:
**Ernst Wit**(RUG), Room M-655, 16:00-17:00

L_1 sparse, penalized inference, with applications in genomics

The advent of high-dimensional datasets has presented a challenge to traditional statistical inference. The n>p paradigm turned out to be too restrictive and statisticians seemed to be for a while in high seas. However, they found their (wet) feet again, when they realized the connections between high-dimensional inference on the one hand and model choice and penalized methods on the other. L_1 penalized inference had the additional advantage of also resulting in sparse solutions. We give a background to L_1 penalized inference, consider some extensions to other types of "path estimators" and look at an application of L_1 penalized inference in a genomic network context. - Wed. 18 Nov:
**Jan Sanders**(VU) Room M-655, 16:00-17:00.Abstract: First the concepts of reduction and Automorphic Lia Algebra are introduced. It is then shown that the problem of reduction can be formulated in a uniform way using the classical theory of invariants. It follows that $\mathfrak{sl}_2(\mathbb{C})$ Automorphic Lie Algebras associated to the Platonic groups \(\mathbb{T}, \mathbb{O}, \mathbb{I}\) and $\mathbb{D}_n$ are isomorphic. The proof makes use of Clebsch-Gordan decomposition and transvectants, Molien functions and the trace-form. The result is a crucial step towards the complete classification of $\mathfrak{sl}_2(\mathbb{C})$ Automorphic Lie Algebras associated to finite groups. If time allows, some remarks will be made concerning the McKay correspondence.**Title: Classical Invariant Theory and Automorphic Lie Algebras.** - Wed. 11 Nov:
**Geeke Bruin-Muurling en Irene van Stiphout**, promovendi Eindhoven School of Education (ESoE), Zaal P-663, 16:00-17:00.**Aansluitingsproblematiek in de doorlopende leerlijn rekenen en algebraïsche vaardigheden**

De onderzoeken van de sprekers richten zich op het zoeken naar diepere oorzaken van de aansluitingsproblemen waar havo/vwo en het hoger onderwijs mee worden geconfronteerd. Tegen deze achtergrond wordt de theoretische basis van het huidige reken- en wiskundeonderwijs besproken. Aan de hand van concrete voorbeelden van lesmateriaal en werk van leerlingen en studenten wordt een gedetailleerd beeld gegeven van waar problemen liggen. - Wed. 4 Nov:
**Leen Stougie**(VU, CWI), Room M-655, 16:00-17:00**Metabolic Pathway Analysis: Polyhedral Cones and Extreme Rays**

Abstract: The mathematical questions in this lecture are raised by the study of metabolic networks in steady state. I will start by sketching this application. The biological problems translate into some problems related to extreme rays of a polyhedral cone {x ∈ R^n | Ax = 0, x ≥ 0}, for some m × n matrix A. These extreme rays correspond one-to-one to the vertices of a bounded poly- hedron (polytope) and as a result the complexity of enumerating the extreme rays of the cone is equivalent to the complexity of enumerating the vertices of a bounded polyhedron, which is a famous and long-standing open question. We will not solve this question but present an intriguing related result: given a coordinate i enumerating all extreme rays r of the cone that have ri > 0 cannot be done with polynomial delay unless P=NP. I will give precise deﬁnitions of enumeration complexity. Our second result, using essentially the same reduction, is: given two coordi- nates i and j does there exist an extreme ray r of the cone that has both ri > 0 and rj > 0 is NP-complete. Both results are based on a reduction to the decision problem on the existence of negative cycles in directed graphs and inspired by the work of Khachyian et al. [Khachyian et al. 2008], who proved that enumerating vertices of any (possibly unbounded) polyhedron cannot be achieved with polynomial delay unless P=NP. - Wed. 21 Oct:
**Theo de Jong**(Univ. Mainz), Room C-648, 16:00-17:00Abstract: There exist several possibilities for introducing the Lebesgue integral of a function f: R^n -> R. The most commonly known uses the notion of step functions. Lebesgue's original definition, however, was very geometric: for f \ge 0 one considers the set O(f) = {(x,y)| 0 \leq y < f(x)} and one defines \int f(x)dx as the Lebesgue measure of O(f). In general one has f = f_+ -f_- with f_+,f_ \ge 0 and one defines \int f(x)dx = \int f_+(x)dx - \int f_-(x)dx. In this talk we discuss this geometric definition and show how the main theorems (Fubini and the Change of Variables Formula), can be proved in an elegant way.**The geometric definition of the Lebesgue integral** - Wed. 7 Oct:
**Mark Peletier**(TUE), Room S-655, 16:00-17:00**Energy-driven pattern formation via competing long- and short-range interactions**

Abstract: I will discuss patterns in block copolymer melts. This is a model system that is mathematically tractable, physically meaningful (and experimentally accessible) and representative for a large class of energy-driven pattern-forming systems. Such systems show a remarkable variety of different patterns, of which only a small fraction is well understood. I will describe a number of mathematical results that provide insight into their behaviour. - Wed. 23 Sept:
**Jeroen Lamb**(Imperial College London), Room S-655, 16:00-17:00**Tilings of Penrose type**

Abstract: The Penrose tiling is a planar tiling with two rhombic tiles, orginally designed by R. Penrose in the early 1970s to illustrate the fact that local properties of tiles (matching rules) can enforce global aperiodicity. Penrose demonstrated this by a renormalization argument that involves a substitution rule. Some ten years later, N. De Bruijn showed that Penrose's tiling can also be viewed as the projection of a slice of a 5-dimensional lattice. In this talk we present a

comprehensive characterisation of all tilings of R^{n}that, like Penrose's original example, can

be constructed by De Bruijn's projection method and admit renormalization by substitution rules.*This is joint work with Edmund Harriss (Leicester).* - Wed. 24 June, 16:00-17:00, Room S-655:
**Marianne Jonker**(VU University)*Statistical Methods for Localizing Disease Genes*

In my talk I will explain two methods for localizing disease genes: case- control association analysis and linkage analysis. In a case-control association study one tries to find genes that cause a disease by comparing the genomes of affected and healthy individuals (cases and controls). In a linkage study family data is considered. Here, the idea is that if a disease runs in a family, a chromosomal region that runs exactly the same way in the family contains the causal gene. Foreknowledge on genetics is not necessary, since I start my talk with a short introduction into genetics. - Wed. 10 June, 16:00-17:00, Room S-655:
**Dave Visser**(VU University)*Homeomorphism groups of Sierpinski carpets and Erdos space*

Erdos space is the ‘rational’ Hilbert space, that is, the set of square summable infinite sequences of rational numbers. Erdos showed that this space is one-dimensional and since it is homeomorphic to its own square it is an important example in dimension theory. Let M be either a topological manifold, a Hilbert cube manifold or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group H(M,D) which consists of all homeomorphisms of M that map D onto itself. Dijkstra and van Mill give a complete topological classification of H(M,D) by showing that it is homeomorphic to the countable power of the space of rational numbers, if M is a one-dimensional topological manifold, and that it is homeomorphic to Erdos space in all other cases. The last result is obtained by using their topological characterizations of Erdos space. As a natural continuation of these results we shall consider the homeomorphism group H(S,D) of an n-dimensional Sierpinski carpet S with countable dense subset D. We show that under some appropriate conditions on D we have that H(S,D) is homeomorphic to Erdos space if the dimension of S is not equal to 3. Since the proof of this result is technical and long we restrict ourselves to the main ideas in the proof, including the topological characterization of Erdos space that we use. - Wed. 27 May, 16:00-17:00, Room M-143:
**Marcel de Jeu**(Universiteit Leiden)*Real Paley-Wiener theorems and local spectral radius formulas*

The classical complex Paley-Wiener theorems relate the support of a function on R^n to the growth rate of its Fourier transform on C^n. In the first part of the lecture, we will show how the support can also be related to certain growth rates of the Fourier transform on R^n (as opposed to C^n), and why these so-called real Paley-Wiener theorems are more precise than the complex ones can be. In the second part, we will explain how some of these real Paley-Wiener theorems are manifestations of local spectral radius formulas. This is joint work with Nils Andersen. - Wed. 13 May, 16:00-17:00, Room S-655:
**Erik Koelink**(Radboud Universiteit Nijmegen)*Tridiagonality!*

One usually tries to diagonalise matrices, operators, etc. We will show that tridiagonalisation can also be very useful. The link between tridiagonal operators and orthogonal polynomials is explained. The example of the Schrodinger equation with the Morse potential on the real line is discussed as a basic example for a tridiagonalisation procedure for differential operators. - Wednesday 29 April, 16:00-17:00, Room S-655:
**Erik Winands**(VU UniversityTUE)**Cancelled**. - Wed. 1 April, 16:00-17:00, Room S-655:
**Francesco Calogero**(University of Rome I "La Sapienza")*Isochronous dynamical systems and the arrow of time*

A vector-valued time-dependent function is called isochronous if all its components are periodic in time with the same fixed period T. A dynamical system is called isochronous if its generic solution is isochronous: periodic in all its degrees of freedom with a fixed period T independent of the initial data. It will be shown how essentially any (autonomous) dynamical system can be modified into another (also autonomous) dynamical systems which is isochronous with an (arbitrarily !) assigned period T, and which moreover behaves, over time periods very short with respect to T, essentially as the original (unmodified) system---up to a constant time rescaling. This can also be done for a large class of Hamiltonian systems (both the unmodified and the modified one), including the Hamiltonian describing the most general (classical, nonrelativistic) many-body problem (provided it is, overall, translation-invariant). Some implications of this fact for statistical mechanics and thermodynamics will be mentioned, and for the distinction among integrable and nonintegrable dynamical systems (all isochronous systems are integrable, in fact maximally superintegrable). These findings have all been obtained together with F. Leyvraz: some of them are reported in my monograph entitled Isochronous systems (Oxford University Press, February 2008), others are more recent. - Wed. 18 March, 16:00-17:00, Room S-655:
**Rob van den Berg**(VU University)*Ponds and power laws*

This talk concerns a random spatial growth model with very simple rules but surprisingly rich and complex behaviour. It was introduced around 1980 by reserachers related to the oil (exploitation) industry but soon drew attention from many others, including theoretical physicists and mathematicians. After defining this `invasion percolation' model, I will concentrate on an object called a 'pond', and explain that this object has indeed a natural `hydrologic' interpretation. Although there is no special tuning of a parameter in this model, it turns out that these ponds are, in a sense which will be explained, critical. Such 'self-organized critical behaviour' seems to be quite common in nature, but this is one of the very few 'natural' models where it can be rigorously proved. - Wed. 4 March, 16:00-17:00, Room S-655:
**Olga Holtz**(UC Berkeley/University of Berlin)*Zonotopal Algebra, Analysis and Combinatorics*

A wealth of geometric and combinatorial properties of a given linear endomorphism X of RN is captured in the study of its associated zonotope Z(X), and, by duality, its associated hyperplane arrangement H(X). This well-known line of study is particularly interesting in case n := rank X << N. We enhance this study to an algebraic level, and associate X with three algebraic structures, referred herein as external, central, and internal. Each algebraic structure is given in terms of a pair of homogeneous polynomial ideals in n variables that are dual to each other: one encodes properties of the arrangement H(X), while the other encodes by duality properties of the zonotope Z(X). The algebraic structures are defined purely in terms of the combinatorial structure of X, but are subsequently proved to be equally obtainable by applying suitable algebro-analytic operations to either of Z(X) or H(X). The theory is universal in the sense that it requires no assumptions on the map X (th e only exception being that the algebro-analytic operations on Z(X) yield sought-for results only in case X is unimodular), and provides new tools that can be used in enumerative combinatorics, graph theory, representation theory, polytope geometry, and approximation theory. Special attention in this talk will be paid to the case when X is the incidence matrix of a graph (and therefore unimodular), when the general theory provides interesting combinatorial information about the graph, refining the statistics recorded by its Tutte polynomial and related generating functions. - Wed. 18 February, 16:00-17:00, Room S-655:
**Ronald Meester**(VU University)*The evidential value in the DNA database search controversy and the two-stain problem*

Does the evidential strength of a DNA match depend on whether the suspect was identified through database search or through other evidence? In Balding and Donnelly (1995) and elsewhere, it has been argued that the evidential strength is slightly larger in a database search case than in a probable cause case, while Stockmarr (1999) reached the opposite conclusion. Both these approaches use likelihood ratios. By making an excursion to a similar problem, the two-stain problem, we argue in this paper that there are certain fundamental difficulties with the use of a likelihood ratio, which can be avoided by concentrating on the posterior odds. This approach helps resolving the above-mentioned conflict. - Wed. 4 February, 16:00-17:00, Room S-655:
**Miroslav Kramar**(VU University)*Conley index theory for braids and forcing in fourth order conservative systems*

We study dynamical systems coming from fourth order conservative equations. We combine variational and topological methods to find periodic solutions of the equations. The dynamics of these systems is restricted to energy manifolds which foliate the phase space. Since the solutions lie on three dimensional energy surfaces the orbits can be regarded as braids in the energy surface. The space of braids decomposes into braid classes. We define topological invariants for braids that allow us to prove forcing results for periodic solutions. In order to avoid analytical difficulties of infinite dimensional spaces we use the concept of discretized braid diagrams. To pass from infinite dimensional space to a finite dimensional one, variational techniques are employed.

## 2008

- Wednesday 10 December, 16:00-17:00, room S2.05:
**Marco Bijvank**(VU)*Periodic Review Inventory Models with Lost Sales*

The majority of the models available in the literature assume backlogging when customer demand can not be fulfilled immediately with inventory on hand. The main reason for this development is because there is a simple replenishment policy that is proven to be optimal for periodic review inventory models with a fixed lead time and backorders. However, the retail market has become very competitive and customers are not as loyal anymore to a specific brand or store as they used to be. Therefore, it is not reasonable to assume that customers are willing to wait for the next order delivery when a product is out of stock. When there is a positive lead time and excess demand is lost rather than backordered, the optimal policy is extremely complex. During this presentation I consider the performance of several replenishment policies for inventory systems with periodic reviews and lost sales. A heuristic procedure is used to determine near-optimal values for the order moment and order size. - Wednesday 26 November, 16:00-17:00, room S2.05:
**Wouter Kager**(VU)*Reflected random walks in wedges*

I will review some remarkably elegant properties of reflected random walks in wedges and their scaling limit, reflected Brownian motion. I will focus on properties that can be proved by simple yet beautiful arguments. Finally, I will sketch one direction of ongoing work. - Wednesday 12 November, 16:00-17:00, room C6.48:
**Arjen Doelman**(CWI)*The Dynamics of Reaction-Diffusion Patterns*

This talk is intended as an overview of the field of pattern formation in reaction-diffusion equations. Since this is a huge subject that includes many phenomena and a multitude of mathematical approaches, a personalized selection will be presented. - Wednesday 29 October, 16:00-17:00, room C6.38:
**Cor Kraaikamp**(TU Delft)*Arithmetic and metric properties of continued fractions*

What continued fractions are, why one could/should be interested in them, and what the relation is to other parts of mathematics (in particular Diophantine approximation and ergodic theory) will be outlined in this talk. Motivated by this, we will also briefly look at other number theoretic expansions, in particular expansions to non-integer bases &beta >1. - Wednesday 15 October, 16:00-17:00, room S2.01:
**Tilman Bauer**(VU)*Modular forms in stable homotopy theory*

Homotopy theorists study spaces by means of homology theories. These are algebraic invariants (abelian groups, rings) which, chosen carefully, strike a good balance between being computable on the one side and carrying a lot of information about the original space on the other side. A good test of the expressiveness of a homology theory is which maps from spheres to spheres it can detect. Ordinary singular homology, while very easy to compute, is exceptionally bad at this: it can only detect maps between spheres of the same dimension. On the other hand, stably homotopy is a homology theory that, by definition, detects all the maps between spheres, but it is notoriously hard to compute. Starting with ground-breaking work of Quillen, it has turned out there is a strong connection between a certain class of homology theories ("complex oriented") and one-dimensional formal group schemes. This surprising link to algebraic geometry begs the question whether classical group constructions in algebraic geometry, for example elliptic curves, have a counterpart on the homotopy side. Work of Hopkins, Miller, Mahowald et al., starting in the late 90s, has given an intriguing and beautiful answer to this: not only can a single elliptic curve be realized by a homology theory, but also the whole moduli space of elliptic curves. This leads to an interesting connection between the stable homotopy groups of spheres and the ring of modular forms. I will discuss this construction, show some explicit computations, and briefly touch on applications. - Wednesday 1 October, 16:00-17:00, room C6.38:
**Jan Bouwe van den Berg**(VU)*Braids in dynamical systems*

Pieces of string or curves in three dimensional space may be knotted or braided. This topological tool can be used to study certain types of dynamical systems. In particular, such an approach leads to forcing theorems in the spirit of the famous "period three implies chaos" for interval maps. Applications to ordinary and partial differential equations will be discussed. - Wednesday 17 September, 16:00-17:00, room S2.01:
**Richard Gill**(University of Leiden)*Careless statistics costs lives*

The PROPATRIA randomized clinical trial of probiotics treatment in acute pancreatitis ended in drama, recriminations, and intense media interest, when it turned out that there had been many more deaths in the treatment group than in the control group. Yet the trial had been apparently carefully designed using state-of-the-art statistical methodology, including interim analysis and early-stopping rules. How could the researchers not have noticed that things were going wrong? I will explain the beautiful mathematics behind the Snapinn early-stopping protocol used by the researchers, and explain how a basic design error in the statistical package SPSS, well-known (to professionals) for years but still uncorrected, contributed to the occurrence of maybe 5 unnecessary deaths in this most carefully planned and executed clinical trial. In brief technical terms: you cannot compute a one-sided p-value without specifying the direction of the alternative. SPSS looks at the data and then chooses the direction which gives the most exciting result. My findings lead to several recommendations for the future conduct of randomized clinical trials; the most important being that the monitoring and safety committee should always be advised by a professional statistician who is not blinded to the identity of the treatment and the control groups. - Wednesday 25 June, 16:00-17:00, room S2.01:
**Fetsje Bijma**(VU University Amsterdam)*Mathematical models for magnetoencephalographic brain signals*

Magnetoencephalographic signals are measurements of the magnetic field generated by neural activity in the (human) brain. In this talk I will discuss some mathematical topics that occur during the analysis of these data: the so-called forward model, regarding the calculation of the predicted measurements based on known activity in the brain, and different models for the covariance of the background/error signal. Furthermore the question of how to compare the different covariance models in an adequate way is addressed. - Wednesday 11 June, 16:00-17:00, room S2.01:
**Frank den Hollander**(Leiden University en Eurandom)*Metastability under stochastic dynamics*

A physical, chemical or biological system driven by a noisy microscopic dynamics may explore different regions of its state space on different time scales, i.e., for certain values of the interaction parameters the dynamics may move fast within regions but slow between regions. The macroscopic phenomenon associated with this separation is called metastability.

In this talk we consider one such system, namely, particles hopping on a lattice subject to on-site repulsion and off-site attraction. This system serves as a model for condensation of a supersaturated gas. We explain what has been achieved in past years and what are the key challenges for the future. - Wednesday 14 May, 16:00-17:00, room S2.01:
**Marcel Oliver**(Jacobs University, Bremen) - Wednesday 23 April, 16:00-17:00, room N3.43:
**Chris Rogers**(University of Cambridge)*Contracting for optimal investment with risk control*

The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem.

The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal then proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal's optimal choice. - Wednesday 16 April, 16:00-17:00, room S2.01:
**Udayan Darji**(University of Louisville)*Two notions of small sets and their applications*

In this talk we discuss two notions of small sets, one topological and one analytic. We discuss how these basic notions of smallness can be exploited in various areas of mathematics by giving some applications in infinite group theory and topological dynamics. In particular, we discuss applications to the highly transitive subgroups of the permutation group on the integers and the persistence of adding machines in a generic topological dynamical system on a manifold. - Wednesday 2 April, 16:00-17:00, room S2.01:
**Hansjörg Geiges**(University of Cologne)*A contact geometric proof of the Whitney-Graustein theorem*

I shall give a very gentle introduction to some basic concepts of contact geometry, notably concerning knots in contact 3-manifolds. This will be used to give a contact geometric proof of the Whitney-Graustein theorem in planar geometry: immersions of the circle in the 2-plane are classified, up to regular homotopy, by their rotation number. - Wednesday 19 March, 16:00-17:00, room S2.05:
**Marek Fila**(Comenius University, Bratislava)*Reaction versus diffusion: blow-up induced and inhibited by diffusivity*

We review results on the relation of the dynamics of a system of ordinary differential equations to the dynamics of the corresponding reaction-diffusion system when diffusion is added. We are mainly interested in the influence of diffusion on the global existence of solutions. We present examples of systems where diffusion induces or inhibits blow-up. - Wednesday 27 February, 16:00-17:00, room S2.05:
**Don Zagier**(Bonn)*Mock theta functions and their applications*

In 1920 Ramanujan introduced a class of functions that he called "mock theta functions". They had properties similar to those of classical modular forms but did not belong to any known class. The mystery was finally solved in 2002 in the thesis of Sander Zwegers. We will discuss his theory and its generalizations and applications. - Wednesday 20 February, 16:00-17:00, room S2.03:
**Dietrich Notbohm**(VU University Amsterdam)*Lie group theory from the homotopy point of view*

Compact Lie groups have a very rich structure. They can be considered as analytic objects (Lie 's original point of view), as objects of Differential Geometry (homogeneous spaces), Differential Topology (manifolds), Combinatorics (root systems), Algebra (group structure, Lie algebra, representations of Weyl groups) and of Homotopy Theory (topological spaces, H-spaces). We will look at them from the homotopy theoretic point of view and show how all the information about a compact Lie group can be encoded in purely homotopy theoretic terms. This development culminated in the notion of p-compact groups, developed by Dwyer and Wilkerson. p-compact groups provide a class of very interesting topological spaces, which "behave" completely like compact Lie groups. - Wednesday 6 February, 16:00-17:00, room S2.03:
**Juan Luis Vázquez**(Universidad Autónoma de Madrid)*Asymptotics of diffusion equations via entropies and functional inequalities*

The large time behaviour of diffusion processes is a main topic in partial differential equations and probability. We consider classes of nonlinear diffusion equations and prove nonlinear central limit theorems using either scaling groups or entropies. The latter go back to L. Boltzmann. In the more specific technical setting, we show how the entropy/ entropy-entropy dissipation method alows to obtain the fine detail of the large time behaviour of renormalized fast diffusion flows. Rates of convergence are obtained through spectral gap estimates of associated linearization which take the form of Hardy Poincare functional inequalities. The method has potential application in many different equations and problems.

## 2007

- Wednesday 28 November, 16:00-17:00, room S2.03:
**Harry van Zanten**(VU University Amsterdam)*Representations of fractional Brownian motion and related processes*

Fractional Brownian motion (fBm) is the simplest stochastic process exhibiting self-similarity and long-range dependence properties. It arises in scaling limits of models having these propererties (for instance in telecommunication) and is also frequently considered directly as a building block for models in e.g. queuing theory or finance. A less attractive feature of the fBm is that it does not belong to one of the particularly "nice" classes of processes: it is not a Markov process and it is not a semimartingale. It is therefore desirable to have representation results expressing the fBm somehow in terms of better understood objects. After introducing some basic notions from stochastic process theory we will focus in this talk on series representations for the fBm. We will discuss how these can be found using some classical Sturm-Liouville-type theory. It will turn out that this approach is in fact applicable to the whole class of Gaussian processes with stationary increments. - Wednesday 14 November, 16:00-17:00, room S2.03:
**Jaap van der Vegt**(Twente University)*A posteriori error analysis for the Maxwell equations*

The efficient numerical solution of the Maxwell equations, which describe the behavior electromagnetic waves, is complicated due to the limited regularity of the solution, such as near sharp and non-convex corners and at material interfaces. Resolving these local structures requires solution adaptive finite element techniques, which either locally refine the computational mesh or adjust the polynomial order. For the control of the adaptation process detailed knowledge about the error distribution is necessary which can be provided by a posteriori error analysis. Compared to elliptic partial differential equations, the a posteriori error analysis of the Maxwell equations is considerably more complicated due to lack of regularity and the fact that the bilinear form is in general not coercive. After a brief introduction to finite element methods for the Maxwell equations several techniques for a posteriori error estimation will be discussed in this presentation. Special attention will be given to the efficiency and reliability of the error estimates and their relation to the true error. In particular, implicit a posteriori error estimates are quite accurate and results for several test problems, including the application of a posteriori error estimates in an adaptive algorithm, will be discussed. - Wednesday 31 October, 16:00-17:00, room S2.03:
**Peter Lancaster**(University of Calgary)*Matrices, Polynomials, and Conditioning*

I will introduce problems known as "conditioning" in the context of numerical linear algebra. This is closely connected with the coincidence or near-coincidence of eigenvalues or polynomial zeros. Conditioning will then be considered in the unifying context of matrix polynomials, and recent results on their pseudospectra. In particular, the role played by the new notion of "fault-lines" for pseudospectra will be discussed. - Wednesday 17 October, 16:00-17:00, room S2.03:
**Hans Duistermaat**(Utrecht University)*QRT and elliptic surfaces* - Wednesday 3 October, 16:00-17:00, room S2.03:
**Rob de Jeu**(VU University Amsterdam)*K-groups and zeta-functions*

K-groups are groups with a somewhat complicated definition, but they are related to explicit arithmetic in many ways. For example, the structure of K_2 of the rationals is strongly related to quadratic reciprocity. In a different direction, the values of the Riemann zeta function at 2,4,6,... can be expressed in terms of Bernoulli numbers and factors pi, whereas those at 3,5,7,... apparently cannot; this difference can be explained by a relation between the K-groups of Q and the values of the Riemann zeta function. We discuss this, and a seemingly ad hoc generalization for every prime number, illustrating everything with examples. - Wednesday 19 September, 16:00-17:00: TALK CANCELLED
**Hansjörg Geiges**(University of Cologne)*A contact geometric proof of the Whitney-Graustein theorem* - Wednesday 20 June, 16:00-17:00, room S2.01:
**Mathisca de Gunst**(VU Amsterdam)*Statistics for neuronal networks* - Wednesday 6 June, 16:00-17:00, room S2.01:
**Frits Beukers**(Utrecht University)*Algebraic hypergeometric functions*

In the first half of the lecture we give a few elementary examples of hypergeometric functions which are at the same time algebraic function of their argument(s). Then we introduce a general class of several variable hypergeometric functions, the so-called GKZ-functions, and describe a combinatorial criterion for their algebraicity. - Wednesday 23 May, 16:00-17:00, room S2.03:
**Ronald Meester**(VU Amsterdam)*1/2=p*_{c} - Wednesday 9 May, 16:00-17:00, room S2.01:
**Bill Kalies**(Florida Atlantic University)*Building a Database for Global Dynamics of Multi-parameter Systems*

Nonlinear dynamical systems can exhibit complicated behavior occurring on a variety of spatial scales and changing subtly with respect to system parameters. In many applications there are models for dynamics but specific parameters are unknown or not directly measurable. This suggests the need to be able to search through parameter space for specific types of dynamical behavior. Ideally, this would be done computationally in some automated manner, and then later the researcher would be able to query the results. In this talk, we discuss computational topological methods which can extract coarse, but rigorous, global descriptions of dynamics and changes with respect to parameters. Moreover, we discuss ongoing efforts to develop a method for building databases that contain useful, rapidly identifiable information about the types of dynamics computed. We will emphasize the essential information that such a database must contain and the open problems that must be resolved before such a database can be efficiently constructed and queried. - Wednesday 25 April, 16:00-17:00, room S2.01:
**Joost Hulshof**(VU Amsterdam)*Why are the Navier-Stokes equations difficult?*

The Navier-Stokes equations describe the flow of an incompressible fluid in a container which is completely filled. Assuming the fluid velocity at the boundary to be zero (no-slip), it would seem obvious that the initial velocity field uniquely determines the velocity field for all future times. I will explain why this problem is so hard that the Clay institute decided to put a price on it.

The physically less relevant 2-dimensional version of this problem does come with the expected answer. This can be seen from integral estimates (such as the Sobolev estimates) which are dimension dependent. Scaling arguments lie at the heart of this dependence. As it turns out dimension 2 is critical. A version of Navier-Stokes with the dimension N as a parameter would be hard for*N>2*.

Joint work by (not with) Leray et al. - Wednesday 11 April, 16:00-17:00, room S2.01:
**Erik Broman**(VU Amsterdam)*Percolation in general and continuity of percolation functions in particular*

I intend to introduce a basic model in statistical mechanics called percolation, which is a parametrized model. I will motivate the usefulleness of the model and discuss some basic properties of it. I will introduce the so called percolation function which describes a very central macroscopic behaviour and talk about some of its properties. Some of the results presented dates back to the 50's while other results will be presented here for the first time. - Farewell party Geurt Jongbloed

Wednesday 4 April,**15:00-16:00**, room S2.09:**Piet Groeneboom**(TU Delft and VU Amsterdam)*Isotonic considerations*

When I started thinking about a topic for my dissertation (at a time when Ph. D. students were often still deciding on these matters themselves), I first thought of the area of isotonic regression. But then one of the Dutch professors of Statistics assured me that "the topic was dead". So, for this reason (and possibly other reasons as well), my dissertation was on probabilities of large deviations and not on isotonic regression, although I presently think that isotonic regression is a much more interesting topic. What makes isotonic regression problems so fascinating is that they arise quite naturally in lots of contexts and that, at the same time, there is usually no standard machinery available to tackle them. So, when I got my chance with my own Ph. D. students, such as Geurt Jongbloed, I encouraged them to work on topics related to isotonic regression. In my lecture I will try to explain what isotonic regression is all about and will also discuss some recent work in the area.

The drinks following the colloquium will be in G0.76 - Wednesday 28 March, 16:00-17:00, room S2.03:
**Gunther Cornelissen**(Utrecht University)*Graphs: their zeta functions and their operator algebras*

On the space integer linear combinations of oriented edges of a finite graph, consider the linear operator*T*that assigns to an edge the sum of its outgoing edges. The operator was constructed by Bass and Hashimoto in connection with the zeta function of the graph. I will show an elementary way to calculate the kernel and cokernel of*1-T*on these integral spaces, and then apply this to a classification problem in the theory of*C**-algebras. Joint work with Oliver Lorscheid (Utrecht) and Matilde Marcolli (MPIM Bonn). - Wednesday 14 March, 16:00-17:00, room S2.03:
**Guit-Jan Ridderbos**(VU Amsterdam)*Power homogeneity in Topology*

A topological space is called homogeneous if all of its points are topologically equivalent. An example of such a space is the real line. The unit interval is not homogeneous, but an infinite power of it is. Spaces with this property are called power homogeneous. In this talk we investigate the topological behaviour of power homogeneous spaces. It turns out that some of the homogeneity in a power space reflects down to the space itself. These observations can be used for showing that certain spaces are not power homogeneous. - Wednesday 28 February, 16:00-17:00, room F2.53:
**Jussi Behrndt**(TU Berlin)*Sturm-Liouville operators with indefinite weights*

In this talk we first review the classical spectral theory of Sturm-Liouville differential operators of the form

*|r|*[^{-1}*-d/dx (p d/dx) + q*]

and then we drop the assumption on the definiteness of the weight function, i.e., we replace*|r|*by*r*. We will discuss some of the spectral properties of such indefinite Sturm-Liouville operators, and it will turn out that they differ essentially from the spectral properties of usual definite Sturm-Liouville operators. - Wednesday 14 February, 16:00-17:00, room S2.05:
**André Ran**(VU Amsterdam)*Stability of invariant subspaces of matrices*

In several instances problems that appear in applications of mathematics in science and engineering can be solved if one can find an invariant subspace (with certain properties) of a given matrix. From point of view of computation it is then interesting to study the behaviour of the invariant subspace under small perturbations of the given matrix. This will be discussed in the talk. - No colloquium on Wednesday 31 January.
- Wednesday 17 January, 16:00-17:00, room S2.03:
**Aad van der Vaart**(VU Amsterdam)*Bayesian estimation with Gaussian process priors*

A Bayesian method to estimate a function (log probability density, regression function, logit classifier, etc.) is to model the function a-priori as the sample path of a Gaussian process, to assume that the data is generated according to the distribution specified by this sample path, and next to derive the distribution of the function given the data using Bayes' rule. We explain this principle on an example (perhaps Brownian motion in log density estimation), and present some results on the accuracy of the method in terms of properties of the Gaussian process.