This colloquium takes place every other Wednesday afternoon, 16:00-17:00, in room WN-M143 . 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 2018:

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

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

Wed 16 Mei: **Viresh Patel** (UvA), Room WN-M143, 16:00-17:00
*Title:* TBA*Abstract:* TBA

Wed 30 Mei: **TBA**, Room WN-M143, 16:00-17:00
*Title:* TBA*Abstract:* TBA

Wed 13 Juni: **TBA**, Room WN-M143, 16:00-17:00
*Title:* TBA*Abstract:* TBA

## Previous talks in 2018:

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.