Week 24.10.2022 – 30.10.2022

We will describe the duality between two integrable systems: the 2D Sine-Gordon model and the 2D Thirring model. We will spend some time describing the classical and quantum Sine-Gordon model, in particular its spectrum, S-matrices and underlying quantum-group symmetry. We will then present the duality with the Thirring model as originally stated by Coleman and refined in subsequent literature. All the basic elements will be provided without relying on too many pre-requisites beyond standard graduate-level quantum field theory. The notes comprise a series of exercises.

We study the problem of detecting and locating change points in high-dimensional models with low rank structure. We develop a simple two step algorithm for the problem at hand and establish performance guarantees in the form of finite sample bounds for the accuracy of the estimated locations of the change points and the underlying model parameters. We illustrate the detection strategy on data from three different domains that employ different statistical models: macroeconomics, neuroimaging and political science.

TBA

Speaker: Rob Rockwood (14:00)

Title: Arithmetic applications of spherical varieties

Abstract: We discuss how the theory of spherical varieties can be applied to study p-adic variation of cohomology classes and how these can be applied to prove new cases of the Birch—Swinnerton-Dyer conjecture for abelian surfaces.

Speaker: Oliver McGrath (14:30)

Title: Applications of sieves

Abstract: We look at some applications of sieve methods in analytic number theory. In particular, we will look at how sieves can be used to detect patterns in prime numbers and, if there is time, how sieves can be used to count solutions to Diophantine equations.