General Mathematics Colloquium

This colloquium takes place every other Wednesday afternoon, 16:00-17:00. For more information, please contact one of the organizers Joost Hulshof and Dennis Dobler.

A database of earlier years' talks can be found here.

Upcoming talks in 2019:

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.

Previous talks:

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.