Upcoming talks in 2018:
Wed 16 Mei: 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 30 Mei: TBA, Room WN-M143, 16:00-17:00
Wed 13 Juni: TBA, Room WN-M143, 16:00-17:00
Previous talks in 2018:
Wed 02 Mei: Joris Mooij (UvA), Room WN-M143, 16:00-17:00
Title: Joint Causal Inference from Observational and Experimental Data
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
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.