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 typically held from 10:00 to 11:00 every other Tuesday during term time 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
Magnetic buoyancy in the solar tachocline
Lucas Gosling
School of Mathematics
University of Leeds
Abstract
Magnetic buoyancy is the phenomenon for strong magnetic fields to reduce the pressure of electrically-conducting plasma, which can lead to gravitational instabilities. Starting from a toy model primarily of academic concern, magnetic buoyancy was seen as an interesting phenomenon with no known applications. Just one year after its conception, Eugene N. Parker hypothesised that magnetic buoyancy could be a component of the solar dynamo, explaining how the Sun uses this mechanism to redistribute its magnetic field generated deep beneath its surface. The first part of this talk will be a brief literature review summarising how our knowledge of magnetic buoyancy evolved over time, and how its applications were discovered.The second part of the talk will focus on overstability, i.e., states which exhibit oscillations which grow in time. There are two well-known physical mechanisms within the magnetic buoyancy instability (MBI) which drive overstable modes. I will describe these physical mechanisms and present the findings of my second paper, including the discovery of a third mechanism for overstability. Furthermore, generalising MBI to include variable diffusion restricts overstability, and our newly discovered mechanism is the only one possible in solar interiors. However, our fluid model does not provide sufficient physical insight to describe it, and we instead create a secondary flux tube model to capture the physics of the problem.
March 18, 2025 | 10:00-11:00
From the quantum sine-Gordon model to number theory via partitions
Clare Dunning
School of Engineering, Mathematics and Physics
University of Kent
Abstract
Partitions of integers play a role in a variety of fields including number theory, representation theory and random matrix theory as well as being of independent interest in enumerative combinatorics. I will present several key concepts and discuss various places where partitions have arisen in my research.May 06, 2025 | 10:00-11:00
Regularizing 3D conformal field theories via the fuzzy sphere
Cristian Voinea
School of Physics and Astronomy
University of Leeds
Abstract
Understanding the universal properties of continuous phase transitions has been a long-standing area of focus. A powerful tool in this endeavor have been conformal field theories (CFTs) — a class of interacting field theories with a rich symmetry structure that can emerge in statistical mechanics models tuned to a critical point. The recently introduced “fuzzy sphere” method has enabled accurate numerical regularizations of certain three-dimensional (3D) CFTs. The regularization is provided by the non-commutative geometry of the lowest Landau level filled by electrons, such that the charge sector is trivially gapped due to the Pauli exclusion principle at filling factor ν = 1, while the electron spins encode the desired CFT. In this talk, along with key concepts for CFT in 3D, I will provide an overview of the fuzzy sphere method and its application to the paradigmatic 3D Ising CFT. I will also present recent results for encoding the same CFT using strongly correlated fractional quantum Hall states, setting the stage for the fuzzy-sphere exploration of conformal critical points between topologically ordered states.A list of all past MaPLe seminars can be found here.