University of Edinburgh

TBA

TBA

 I will talk about recent progress on (a) a conjecture of Fyodorov and Keating on supercritical asymptotics of moments of moments of characteristic polynomials of the circular beta ensemble and (b) on the correlation functions of the sine beta point process. This is joint work with Joseph Najnudel.

Fracture is usually treated as an outcome to be avoided; here we see it as something we may write into a lattice's microstructure. Maxwell lattices sit at the edge of mechanical stability, where robust topological properties provide a way on how stress localises and delocalises across the structure with directional preference. Building on this, we propose a direct relationship between lattice topology and damage propagation. We identify a set of topology- and geometry-dependent parameters that gives a simple, predictive framework for nonideal Maxwell lattices and their damage processes. We will discuss how topological polarisation and domain walls steer and arrest damage in a repeatable way. Experiments confirm the theoretical predicted localisation and the resulting tuneable progression of damage and show how this control mechanism can be used to enhance dissipation and raise the apparent fracture energy.

Modern deep learning methods provide the state-of-the-art in image reconstruction in most areas of computational imaging. However, such techniques are very data hungry and in a number of key imaging problems access to ground truth data is challenging if not impossible. This has led to the emergence of a range of self-supervised learning algorithms for imaging that attempt to learn to image without ground truth data. 

In this talk I will review some of the existing techniques and look at what is and might be possible in self-supervised imaging.

Dr Anna Lisa Vari will talk about: 'The orbital structure of the Hill's problem'

Hill’s problem is a limiting case of the circular restricted gravitational three-body problem in which the mass ratio between the two massive bodies tends to zero, leaving a small region surrounding the secondary in which it remains gravitationally dominant. Originally formulated in terms of point masses, Hill’s problem may be modified to include a secondary of finite extent, thus providing a more realistic description of the dynamics internal to a stellar cluster orbiting within a host galaxy. By considering stellar energies above the cluster escape energy, we may investigate the dynamics that underpin the process of stellar escape from star clusters -- a topical issue in contemporary astrophysics. Specifically, we construct a self-consistent formulation of Hill’s problem using a tidally perturbed cluster model for the secondary body. The behaviour of energetically unbound stellar orbits within such a self-consistent problem, as characterised using Poincaré surfaces of section, is then numerically explored via a structure-preserving integrator, revealing a previously unknown bifurcation in the orbital structure.

Over the last decade, adversarial attack algorithms have revealed instabilities in artificial intelligence (AI) tools. These algorithms raise issues regarding safety, reliability and interpretability; especially in high risk settings. Mathematics is at the heart of this landscape, with ideas from  numerical analysis, optimization, and high dimensional stochastic analysis playing key roles. From a practical perspective, there has been a war of escalation between those developing attack and defence strategies. At a more theoretical level, researchers have also studied bigger picture questions concerning the existence and computability of successful attacks. I will present examples of attack algorithms for neural networks in image classification, for transformer models in optical character recognition and for large language models. I will also show how recent generative diffusion models can be used adversarially. From a more theoretical perspective, I will outline recent results on the overarching question of whether, under reasonable assumptions, it is inevitable that AI tools will be vulnerable to attack.

This talk will be a case study on the recently discovered boundary Carrollian conformal algebra (BCCA) in theoretical physics. It is an infinite-dimensional subalgebra of an abelian extension of the Witt algebra. A striking feature of this is that it is not integer graded; this already puts us in a rather novel setting, since infinite-dimensional Lie algebras almost exclusively appear with integer grading in physics. But this means that there is new ground to be broken in this direction of research. In this talk, I will present some very early results from our attempt at studying the representations of the BCCA. Any thoughts and comments are very welcome as they could be immensely helpful for us to navigate these unfamiliar waters!