MaPLe

The Mathematical Physics at Leeds 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.


January 28, 2025 | 10:00-11:00

Quantum many-body scars: a new paradigm of order amidst quantum chaos
Zlatko Papic
School of Physics and Astronomy
University of Leeds

Abstract The quest to understand out-of-equilibrium behaviour of complex quantum systems represents one of the frontiers of contemporary quantum science. For a long time, the prevailing belief has been that complex quantum systems, comprising many interacting degrees of freedom, all suffer the same inevitable fate: that of thermalisation, whereby the system relaxes towards a featureless thermal state, completely "forgetting" its initial condition. However, a flurry of recent works has unearthed a new paradigm of behaviour in many well-known physical systems, including Rydberg atoms, lattice gauge theories, and certain kinds of frustrated magnets. Such systems have been understood to possess a subtle breakdown of ergodicity, now commonly known as "quantum many-body scars". Quantum many-body scars exhibit fascinating properties, such as extreme sensitivity to initial conditions: while a system initialised randomly undergoes chaotic dynamics and thermalisation, specific initial conditions can result in persistent dynamical revivals, surpassing native thermalisation timescales. The discovery of quantum many-body scars has not only deepened our understanding of many-body quantum mechanics, but it also has direct practical relevance for improving the control over the delicate physical phenomena underpinning quantum technologies. In this talk, I will present a pedagogical overview of this fascinating new field of physics, highlighting a few of the remaining mysteries for theory and future experiments.

February 11, 2025 | 10:00-11:00

Discrete approximations for the induced connection
Derek Harland
School of Mathematics
University of Leeds

Abstract The induced connection is a natural connection on a subbundle of a vector bundle. In physics, it is known as the Berry connection, and its parallel transport operators give rise to the Berry phase. In this talk I will explain exactly what the Berry/induced connection is and present some work I have done on finding numerical approximations to its parallel transport. This will lead to some interesting(?) questions for the algebraists in the audience!

February 25, 2025 | 10:00-11:00

Integrable vortices in the Abelian Higgs model
Nora Gavrea
School of Mathematics
University of Leeds

Abstract Vortices are 2-dimensional topological solitons defined on a Riemann surface in the context of the Abelian Higgs model. Physically, they model magnetic flux tubes in superconductors. At critical coupling, they satisfy a 1st order system of PDEs called the Bogomolny equations. I will first review the derivation of these equations using a Bogomolny argument, and then derive the Taubes equation. Next, I will introduce a generalised Abelian Higgs energy functional, which gives rise to 5 different vortex equations (this has been carefully investigated by Nicholas Manton). For a constant curvature base surface, these equations turn out to be integrable, reducing to a Liouville equation. One can obtain further integrable vortex equations by choosing suitable conformal factors, and in this case, the Taubes equation becomes the sinh-Gordon or Tzitzeica equation. If we assume radial symmetry, these are equivalent to a Painlevé III ODE. I will discuss the construction of these vortices for the rest of the talk, which is a joint work with Maciej Dunajski.

March 11, 2025 | 10:00-11:00

TBA
Lucas Gosling
School of Mathematics
University of Leeds

Abstract TBA

March 25, 2025 | 10:00-11:00

TBA
Andrés Rodríguez Anadón
Universidade de Santiago de Compostela

Abstract TBA

May 06, 2025 | 10:00-11:00

TBA
Cristian Voinea
School of Physics and Astronomy
University of Leeds

Abstract TBA

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