Dynamics, difference equations, and the classification of finite simple groups

Given an algebraic dynamical system, can we bound the complexity of the simplest nonobvious invariant subvarieties which appear? Why might we want to do this? In this talk, we'll answer these question while also explaining the connection to difference equations, model theory, and the classification of finite simple groups. 

Math, Quantum & AI: Inspiration from an atypical take on foundations

Could similar structures help complete the mathematics of quantum physics as well as make neural networks more interpretable? In this talk we will learn a little combinatorial game theory and explore these membership-augmented set theoretic foundations in the context of quantum mechanics, topological quantum field theory, and some important symmetries and groups therein. We will hopefully have time to touch on pressing challenges in neural-net-based machine learning, towards improving AI with these very same game structures as well. The hope will be to generate some mathematically-based inspiration and insight on a few cherished concepts, like the complex symmetries of spacetime, while also reflecting on both chance and choice.

Sequential optimality conditions for multi-objective problems and its application to an Augmented Lagrangian method

We will introduce multi-objective problems and its main properties, and then cover some recent work done in the area

 Homogeneous bi-Hamiltonian structures and integrable contact systems

Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator relating both Poisson structures. We show that the recursion operator relating two compatible Jacobi structures cannot produce a maximal set of functions in involution. However, as we illustrate with an example, bi-Hamiltonian structures can still be used to obtain a maximal set of functions in involution on a contact manifold, at the cost of symplectisation.

Communicating math & science to lay audience

Ever tried communicating your research to your mom or your neighbor? Or maybe the passenger sitting next to you on your flight? And when you did, perhaps you found their eyes glazing over as you spoke? If yes, then you are not alone. People may find it hard to relate to science. Particularly math, has a notorious reputation of being esoteric and for many people mathematics is associated with anxiety they experienced in school! Nevertheless, would you like to learn how to communicate math and science stories and make them relatable to a broad audience (and not just your peers)? Could you perhaps introduce a touch of human angle to your science & math stories? In my talk, I will present why science communication is important now, more than ever and present tools to do so effectively. Science communication can not only help you explain your research well to your mom or neighbor but also help cultivate scientific literacy among the general public and disseminate broader societal impact of scientific discoveries that will help build trust in science.

 (Non-AI) PDE-Based Approaches to Image Processing

This talk explores how image processing can be achieved through classical, non-AI methods rooted in partial differential equations (PDEs) and the calculus of variations. From smoothing and denoising to segmentation, we will see how mathematical structure and physical intuition guide the design of algorithms—without learning from data. From there, we will also discover how machine learning enters naturally—not to replace these models, but to enhance them, closing the loop between theory and data.

A Study of the Creation of Safe Zones Using Link Removal in Epidemiology

We will review optimal link-removal strategies to create safe zones in networks, limiting the spread of infections while minimizing disruption. Focusing on one-edge and two-edge-connected graphs, we develop generalizable techniques for disconnecting networks efficiently. We will identify optimal link removal strategies--weak, strong, betweenness centrality (BC), and weighted betweenness centrality (BCw)--each suited to different network structures. 

AI and Its Impact on Mathematics

In this talk, I will give a brief overview of artificial intelligence (AI), of how it works and how it has benefited from employing machine learning. After discussing how mathematicians have used AI methods in the past,  I will then talk about the potential impact of current AI techniques and Large Language Models (LLMs) on the mathematics profession.

 Polya's conjecture for eigenvalues of the Laplacian

Eigenvalues of the Laplacian on domains in Euclidean space appear in a variety of mathematical and physical settings. In 1954, George Polya conjectured a surprising uniform bound for these eigenvalues. Strangely, he proved it several years later... but only for domains which tile Euclidean space without gaps. The general case has remained open and is the subject of intense curiosity in the spectral geometry community. I will discuss the problem, why it is hard, and the modest progress that has recently been made.