Past Events

We consider the restriction to the unit circle of random degree-n polynomials with iid normalized coefficients (Kac polynomials). Recent work of Yakir and Zeitouni shows that for Gaussian coefficients, the minimum modulus (suitably rescaled) follows...

A classical problem in algebraic geometry asks what rational cuspidal curves can be realised in the complex projective plane. In the last few years some substantial advancement regarding this problem have been made, also based on the methods of...

In 1958, Fine and Herstein proved that the an n by n matrix over the finite field F_q has a probability of q^{-n} to be nilpotent. A clever application of this result can lead to the formula \sum_{H: abelian p-group} 1/|Aut(H)| = 1/((1-p^-1)(1-p^-2)...

The purpose of this talk is to explain how to describe the propagation of topological currents along magnetic interfaces (also known as magnetic walls) of a two-dimensional material using K-theory. We initially consider tight-binding magnetic models...

For non-negative integers \(a,b\) and \(n\), let $$ \begin{align*} t(a,b;n)=& \# \left\{ (x_1,\ldots,x_a,y_1,\ldots, y_b) \in \mathbb{Z}^{a+b} ~ \mid ~n= \frac{x_1(x_1-1)}{2} + \cdots + \frac{x_a(x_a-1)}{2} \right. \\ & \left. + 3\frac{y_1(y_1-1)}{2}...

Although the moduli space of genus-zero curves is not a toric variety, it shares an intriguing amount of the combinatorial structure that a toric variety would enjoy. In fact, by adjusting the moduli problem slightly, one finds a moduli space that is...

We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the K\...

In low-dimensional topology we are often interested in determining 3-manifolds that arise as surgery along a knot, and investigating the surfaces they contain. In this talk, we study gluings X of the twisted I-bundle over the Klein bottle to knot...

Zarankiewicz's problem in extremal graph theory asks for the maximum number of edges in a bipartite graph on $n$ vertices which does not contain a copy of $K_{k,k}$, the complete bipartite with $k$ vertices in both classes. We will consider this...

Accessibility is a fundamental tool when working with partially hyperbolic systems. For instance, in the 1970s it was used as a tool to show certain systems were transitive, and in the 1990s it was used to establish stable ergodicity. We will review...