Postgraduate Seminar
Welcome to the Postgraduate Seminar! This is a weekly seminar for PhD students to give talks, whether on the topics that our PhDs are focused on or just on something mathematical we find interesting. As well as helping students to gain experience giving talks, these seminars are designed to build a sense of community amongst the PhD students, and so we favour talks that are not too specialised and those which are pitched at a broad mathematical audience.
Time: Wednesdays in term time, 12pm-1pm
Location: B3.02, Zeeman Building
The organisers for the postgraduate seminar in 2025-26 are Michael Cavaliere and Dan Roebuck. Please get in touch with us if you are interested in giving a talk!
Term 1
Week 1 (8th October)
Laura Bradby - The maximum principle (my favourite theorem)
The maximum principle is my favourite theorem, because for something so intuitively obvious, it turns out to be surprisingly useful! In this talk, we’ll take a look at the maximum principle in its simplest formulation, and showcase both its obviousness and its utility. Then we’ll discuss why the maximum principle is relevant to current research, and see one of its applications to the study of Ricci flow.
Week 2 (15th October)
Isaac Weaver - From approximate subgroups to approximate lattices
In recent years the idea of an approximate group has been formalised by, among others, Tao. In particular there has been a concrete categorisation of approximate subgroups in finite (local) groups. In this talk, however, I will discuss how we can apply these ideas to infinite Locally Compact Second countable groups, specifically ways in which approximate subgroups can approximate lattices in these groups either through dynamical definitions or simpler group theoretic definitions. I aim to discuss the relationships between such definitions and explore how these objects exist at the intersection of several areas of mathematics.
Week 3 (22nd October)
Chunkai Xu - Counting Lines in Space: From School Geometry to Schubert Calculus
How many lines in space meet four given lines in general position?
Questions like this lie at the heart of enumerative geometry — the art of “counting” geometric figures satisfying geometric conditions. In this talk, we’ll start from familiar high-school geometry problems (“how many lines pass through two points?”) and see how these ideas naturally lead to projective geometry and intersection theory. We’ll meet the Grassmannian — the space of all lines in projective 3-space — and see how its geometry encodes the answers to such counting problems through the elegant language of Schubert calculus.
Week 4 (29th October)
Alex Pilakoutas - Harris' ergodic theorem on Markov chains and applications to linear kinetic equations
Harris’ theorem is a powerful tool for showing that Markov chains settle down to equilibrium at an exponential rate. Recently, Martin Hairer discovered a simple and elegant proof that makes this important result much easier to understand and use. In this talk, I’ll explain Hairer’s proof and show how the theorem can be applied to a basic example of a linear kinetic equation.Week 5 (5th November)
Yunus Cobanoglu - Implicit Bias: How Gradient Dynamics Choose Solutions
Training overparameterized machine learning models with gradient descent often yields many parameter settings that fit the data exactly. Yet optimization reliably converges to a particular one. This talk introduces implicit bias—the effective regularization induced by the parameterization—and explains how gradient-flow dynamics select among perfect-fit solutions, with implications for generalization and algorithm design. This fairly recent theory was developed to clarify why simplified deep-learning models work in practice.
Week 6 (12th November)
Shing Tak Lam - Symmetries and Dynamics - an introduction to symplectic geometry
When introduced to groups, we are told that they correspond to symmetries. In classical dynamics, Noether's theorem says (roughly) that when a group acts on a physical system, these symmetries give us conserved quantities, or momentum. In this talk, I'll introduce symplectic geometry, which is the mathematical language of classical dynamics, and how we can view Noether's theorem in this context. To conclude, I'll discuss how this relates to many different areas of mathematics, from dynamics, geometric analysis and mathematical physics, to representation theory and algebraic geometry. No knowledge of any of the above is necessary, I'll try to keep the prerequisites to a minimum.
Week 7 (19th November)
Sasha Glendinning - Kinetic models of opinion formation and applications to consensus control
The Boltzmann equation is a classical tool for modelling the collisions between active gas particles. In this talk, we will liken the collisions between gases to random interactions between members of a population. We begin from a Hegselmann-Krause, individual based model for opinion formation and develop a Boltzmann-like kinetic description that maintains key properties of the microscopic system. Following the derivation of Toscani (2008), we can then show that under a quasi-invariant limit, the system simplifies to a Fokker-Planck equation. Finally, we will discuss the uses of this model in the context of consensus control.