# MaPLe

The **Ma**thematical **P**hysics at **Le**eds Seminar Series is aimed at bringing together researchers at any level from across the University of Leeds — from both mathematics and physics departments alike — to give talks on themes in mathematical physics, broadly construed. On occasion, we also host seminars by researchers from outside the University of Leeds. Talks are held every other Tuesday from 10:00 to 11:00 in the MALL on Level 8 in the main building of the School of Mathematics.

The series is being organised by **Linden Disney-Hogg** and **Anup Anand Singh**. Slides/notes from the talks will be made available on the **MaPLe Teams chat**. If you would like to give a seminar or want to be added to the chat and the mailing list, just drop an email to **a.l.disney-hogg[at]leeds.ac.uk** or **mmaasi[at]leeds.ac.uk**.

##### October 22, 2024 | 10:00-11:00

**Anyons**

**Jiannis K. Pachos**

School of Physics and Astronomy

University of Leeds

## Abstract

Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, it is possible to perform quantum simulations with physical systems that reveal central properties of anyons. In this talk I will present encoding and manipulation of anyons with quantum technology platforms that reveal their exotic statistical properties with the goal of eventually employing them for topological quantum computation.##### November 05, 2024 | 10:00-11:00

**How to cheat at billiards: a new open classical and quantum billiard model**

**Katherine Holmes**

Department of Mathematics

Imperial College London

## Abstract

The classical billiard model has been used to study dynamical systems and chaos theory. Its quantum counterpart is the quantum billiard model, a toy model of quantum optical systems in QED cavities and quantum dots. The billiard model in both the classical and quantum regimes has been well-documented in the literature, with a multitude of variations having been constructed. In recent years, we have seen the introduction of leaky billiards, billiards with loss mechanics such as internal holes and permeable boundaries.In this talk, I will introduce the billiard model and debut a new classical leaky billiard model with a permeable internal region. This model allows for the study of intricate structures on the Poincaré-Birkhoff phase space via intensity landscapes. The talk will conclude with a discussion of what may be the quantum and semiclassical counterpart to this classical leaky billiard.

This talk is based on a paper soon to be released on arXiv:

*Intensity landscapes in elliptical and oval billiards with a circular absorbing region*. The final section will implement semiclassical methods inspired by a recent PRL:

*Husimi dynamics generated by non-Hermitian Hamiltonians*, 2023.

##### November 19, 2024 | 10:00-11:00

**The Yang-Baxter equation and quantum group symmetry**

**Benjamin Morris**

School of Mathematics

University of Leeds

## Abstract

We begin with an introduction to the Yang-Baxter equation, as a master equation for integrability in 2D lattice models in statistical mechanics. We will see that through the classification of (classes of) solutions to this equation it is natural to consider solutions related to physical symmetries known as quantum groups. We will then discuss a scheme for obtaining factorised solutions to the Yang-Baxter equation in a class of infinite-dimensional representations of the quantum group*U𝑞sl(n)*.

##### December 03, 2024 | 10:00-11:00

**TBA**

**Peter Gracar**

School of Mathematics

University of Leeds

## Abstract

TBA*A list of all past MaPLe seminars can be found here.*