Past Events

Pappas and Rapoport have recently conjectured the existence of canonical integral models for Shimura varieties with parahoric level structure, which are characterized using Scholze's theory of p-adic shtukas. We will illustrate the conjecture using the example of Shimura varieties defined by…

Since the 1980s, the homology cobordism group has been a central object in the development of low-dimensional topology. In this talk, we will discuss its historical roots, present our current knowledge about its algebraic structure, and state open problems about the behaviors…

There are fascinating combinatorial problems arising from that study. One of them is to reduce an important part of the problem to the study of the subset of the symmetric group that leads to complete leftward walks on a monograph. Another is to understand minimal…

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Last week, we saw why the Kakeya conjecture holds in 2 dimensions; this week, I will discuss what is known in the 3-dimensional case. There are a number of additional difficulties, two of the biggest being the presence of two "villainous" near-counterexamples, which are analogous to 5/2-…

Cluster varieties are algebraic varieties obtained by gluing together complex tori using explicit birational transformations. They play an important role in algebra and geometric representation theory, and have the peculiarity to come in pairs (A,X). On the other hand, in…

Let A be drawn uniformly at random from the set of all n x n symmetric matrices with entries in {-1,1}. What is the probability that A is singular? This is a classical problem at the intersection of probability and combinatorics. I will give an…

Spin structures on manifolds, decomposition of the trace

Translators are known as candidates of Type II blow-up  
model for mean curvature flows.  Various examples of mean curvature  
flow translators have been constructed in the convex case and  
semi-graphical case, most of which have either infinite…