Past Events

This talk focuses on the inverse eigenvalue problem for graphs (IEPG), which seeks to determine the possible spectra of symmetric matrices associated with a given graph G. These matrices have off-diagonal non-zero entries corresponding to the edges...

The question of how species coexist is one of the most fundamental questions in ecology. The standard approach for using models to understand what leads to ecological coexistence can be caricatured as start with a model, specify parameters, and look...

Real-world systems—from academic collaborations and computer networks to biological systems and power grids—are often large, heterogeneous, and highly interconnected. A first step towards understanding these systems is choosing an appropriate...

Given a symmetric matrix with a given sign pattern, what can the sign patterns of its eigenvectors look like? This simple question is closely related to the study of discrete nodal statistics, and draws strong parallels with classical results in...

We will review different notions of anti-concentration, arising from geometry, analysis, and probability. One focus of the talk will be on understanding how these definitions relate to each other, sometimes leading to surprising and nontrivial...

Abstract: Take the unit interval [0,1] and a number, b, between 0 and 1. At each step, split every interval of maximal length into two pieces in proportion b: (1-b). This recursive scheme is known as the Kakutani splitting procedure and in 1976...

In this talk, I will discuss the category of twisted sheaves on a scheme $X$. Let $\mathcal{M}$ be a quasi-coherent sheaf on $X$, and $\alpha$ in $\mathrm{Br}(X)$. We show that the functor $ - \otimes_{\mathcal{O}_X} \mathcal{M} : \operatorname{QCoh}...

Immune cell infiltration in solid tumours was once regarded as clear evidence of the body’s attempt to eradicate a malignant threat. It is, however, now well established that tumours can co-opt immune cells, reprogramming them from tumour-suppressive...

In this talk we will briefly review the modular method, the strategy used by Wiles to prove Fermat’s Last Theorem. We will then explain how hyperelliptic curves have emerged as an important tool in recent years to approach generalized Fermat...

A central tool in additive combinatorics is the polynomial method, a family of powerful techniques for proving results about combinatorial objects by encoding them in algebraic terms. In this talk, we give a brief overview of some iconic modern...