School of Mathematics

Persistence modules and their associated barcodes were intensively studied since the early 2000s with a view towards applied mathematics. Recently they have also found numerous applications in pure mathematics. We will discuss a few examples from...

Deep generative models offer powerful tools for solving astrophysical inference problems by enabling flexible representations of prior knowledge and likelihood functions.

In the first part of the talk, I will discuss how generative models can be...

Given a triple (X,π,s) consisting of a homogeneous space X=G/P, a dominant weight π giving a projective embedding of X, and a reduced expression s for the minimal coset representative of w_0 in the parabolic quotient W/W_P, we construct a polytope...

It is a classical fact that countable groups of homeomorphisms of the interval and the circle are characterized by purely algebraic properties, namely linear and circular orderability. It remains a difficult and deep problem to understand countable...

I will present recent work with Hairer, Rosati and Yi establishing quantitative lower bounds for the top Lyapunov exponent of linear PDEs driven by two-dimensional stochastic Navier-Stokes equations on the torus. For both the advection-diffusion...

In this talk, we will present a proof of contact big fiber theorem, based on invariants read off from contact Hamiltonian Floer homology. The theorem concludes that any contact involutive map on a Liouville fillable contact manifold admits at least...

A locally testable code (LTC) is an error-correcting code equipped with a tester T that, given an input string x, queries only a small number of positions and rejects x with probability proportional to its distance from the code. Classic examples of...

Selmer groups are a cohomological tool used to reduce the task of finding solutions of certain diophantine equations to easier field and modular arithmetic. I'll explain how this works in down to earth terms and give some concrete applications...

Private Information Retrieval (PIR) is a method for a user to interact with t non-colluding servers and read some entry of a database of size n without revealing to the servers anything about which entry of the database was read. After a long line...

The double bubble plumbing, first studied by Smith and Wemyss, is a Stein neighborhood of two Lagrangian 3-spheres intersecting cleanly along an unknotted circle in some 6-dimensional symplectic manifold. Depending on the identification of the...