Past Events

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...

In this talk I will be speaking about the dimer model sampled on a general Riemann surface. Dimer model on a graph consists of sampling a random perfect matching with the probability proportional to the product of edge weights. In the case when the...

We consider the problem of minimizing the average of a large number of smooth but possibly non-convex functions. For machine learning applications, the loss functions are mostly non-negative and thus can be written as the composition of the square...