Past Events

A result of Rademacher is that on the Riemann hypothesis, the positive ordinates of the nontrivial zeros of the Riemann zeta function, that is, the γ with γ>0, are uniformly distributed modulo one. This talk will be on a recent conditional result of...

For every $k\ge 2$ and $\Delta$, we prove that there exists a constant $C_{\Delta,k}$ such that the following holds. For every graph $H$ with $\chi(H)=k$ and every tree with at least $C_{\Delta,k}|H|$ vertices and maximum degree at most $\Delta$, the...

I report recent progress on heat kernel estimates for reflected diffusion on uniform domains where the underlying space admits sub-Gaussian heat kernel bounds. A key novelty of our work is the use of an extension operator that extends functions from...

In this seminar, we have seen that problems in deformation theory are often controlled by differential graded Lie algebras (dgla). For example, in Martin's talk, we saw how the deformations of an associative algebra are controlled by a dgla structure...

Animal tissues exhibit complex spatial architectures that emerge from cell-cell interactions. For instance, transitions between individual cells and multicellular groups occur widely in embryonic development, wound healing, and tumor progression...

Given two isomorphic groups G and H, one may identify representations of H with representations of G along some fixed isomorphism from G to H. However, this process of identifying representations depends crucially on the isomorphism of groups one...

The study of ocean waves, particularly surface waves, is crucial for predicting and preparing for natural disasters such as tsunamis. Although ocean waves naturally occur in three dimensions, there are instances when they can be analyzed within a two...

We introduce a new P basis for the Hopf algebra of quasisymmetric functions that refine the symmetric powersum basis. Its expansion in quasisymmetric monomial functions is given by fillings of matrices. This basis has a shuffle product, a...

Historically, the notion of Pólya fields dates back to some works of George Pólya and Alexander Ostrowski, in 1919, on entire functions with integer values at integers; a number field $K$ with ring of integers $\mathcal{O}_K$ is called a Pólya field...

A central problem in additive combinatorics is to obtain a good lower bound for the size of the product set AB of two subsets A, B of a group G. In this talk, we will be focusing on the setting when G is a locally compact group, where G has a natural...