Past Events

The Hecke orbit conjecture predicts that Hecke symmetries characterize the central foliation on Shimura varieties over an algebraically closed field k of characteristic p. The original conjecture predicts that on the mod p reduction of a Shimura...

The interactions among species in a food web or food chain are inherently complex. Mathematical models provide a framework to closely represent the dynamics observed in ecosystems. However, capturing this complexity within a single mathematical setup...

In recent years, there has been growing promise in coupling machine learning methods with domain-specific physical insights to solve scientific problems based on partial differential equations (PDEs). However, there are two critical bottlenecks that...

Embedding calculus is a powerful tool which is useful in making quantitative and qualitative conclusions about the topology of embedding spaces. In this talk, we will give a geometric description of the fiber of Emb ( M , M ) → T ∞ Emb ( M , M )...

We study the dynamics of a test particle in a system of N randomly distributed stationary spherical obstacles (scatterers) in dimensions d≥2. We assume that the test particle's motion is influenced by two contributing factors. One contribution comes...

Let E be an elliptic curve defined over ℚ. Let p > 3 be a prime such that p - 1 is not divisible by 3, 4, 5, 7, 11. In this article, we classify the groups that can arise as E(ℚ(ζp))tors up to isomorphism. The method illustrates techniques for...

In the first talk of this series, we saw how the first Stiefel-Whitney class is a complete invariant of real line bundles. Building on this, we will now study how to build a complete invariant for complex line bundles: the Chern class. Among other...

An edge mapping of a graph is a function f:E(G) -> E(G) where f(e) \neq e for all e in E(G). A subgraph H of G is called f-free if for every e in E(H) f(e) \notin E(H). A graph G is called unavoidable for a graph H if every edge mapping of G has at...

What happens to Wasserstein gradient flows if one uses entropic optimal transport instead of classical optimal transport? I will explain why it may be relevant to use Sinkhorn divergences, built on entropic optimal transport, as they allow the...

The central question of knot theory is that of distinguishing links up to isotopy. The first polynomial invariant of links devised to help answer this question was the Alexander polynomial (1928). Almost a century after its introduction, it still...