Mathematics Colloquium 2025-26 Abstracts
Term 1
- 10 October 2025: Laura Monk (University of Bristol): Typical hyperbolic surfaces have an optimal spectral gap
The first non-zero Laplace eigenvalue of a hyperbolic surface, or its spectral gap, measures how well-connected the surface is: surfaces with a large spectral gap are hard to cut in pieces, have a small diameter and fast mixing times. For large hyperbolic surfaces (of large area or large genus g, equivalently), we know that the spectral gap is asymptotically bounded above by 1/4. The aim of this talk is to present joint work with Nalini Anantharaman, where we prove that most hyperbolic surfaces have a near-optimal spectral gap. That is to say, we prove that, for any ε>0, the Weil-Petersson probability for a hyperbolic surface of genus g to have a spectral gap greater than 1/4-ε goes to one as g goes to infinity. This statement is analogous to Alon’s 1986 conjecture for regular graphs, proven by Friedman in 2003. I will present our approach, which shares many similarities with Friedman’s work, and introduce new tools and ideas that we have developed in order to tackle this problem.
- 17 October 2025: Beatrice Pelloni (Heriot-Watt University): Optimal transport methods in geophysical fluid dynamics
I will discuss the use of semi-discrete optimal transport to give new proofs of existence and regularity of weak solutions to a system of equations, both incompressible and compressible, modelling large-scale atmospheric flows. This method also yields the first fully 3D numerical simulations, and several new theoretical side results. More generally, I will outline the formulation of a variety of geophysical fluid problems using optimal transport, yielding naturally the proof of physically conjectured properties.
This is work in collaboration with David Bourne and two former PhD students, Charles Egan and Théo Lavier.
Given an algebraic curve C over the rationals, a natural question is to ask what we can say about the rational points on C. In arithmetic statistics, we instead ask, for example, what we can say about rational points on average as C varies over some family of curves. In this talk, we'll see that graded Lie algebras give a uniform approach to many questions of this kind. Time permitting, I'll mention joint work with Jack Thorne and with Jef Laga in this area. I won't assume familiarity with arithmetic statistics or graded Lie algebras; instead I'll give an introduction to these ideas via examples.
- 31 October 2025: Yuji Nakatsukasa (University of Oxford): Randomisation and model order reduction for linear algebra problems
Numerical Linear Algebra (NLA) is a field that develops algorithms for solving large-scale problems involving matrices, such as linear systems, eigenvalue problems, and the SVD. Randomisation is among the most exciting developments in NLA, and has led to algorithms that are fast, scalable, robust, and reliable. In this talk I will first introduce the key ideas in randomised NLA and highligh some of its major success stories. I will then present recent work at the intersection of randomised NLA and model order reduction, for the efficient solution of many linear systems depending on a parameter p, that is, A(p)x(p) = b(p). We introduce an algorithm called SubApSnap (for Subsampled A(p) times Snapshot), which constructs a snapshot matrix and solving the resulting tall-skinny least-squares problems using a subsampling-based dimension-reduction approach. We show that SubApSnap is a strict generalisation of the popular DEIM algorithm in nonlinear model order reduction. SubApSnap is a sublinear-time algorithm, and once the snapshot and subsampling are determined, it solves A(p∗)x(p∗) = b(p∗) for a new value of p∗ at a dramatically improved speed: it does not even need to read the whole matrix A(p∗) to solve the linear system for a new value of p∗. In model problems arising in model reduction and kernel ridge regression, SubApSnap achieves speedups of many orders of magnitude compared with standard solvers by factors as large as 20,000.
- 07 November 2025: David Stainforth (London School of Economics): Predicting Our Climate Future: How would you spend $15B?
The existence and the scale of the threat from human-induced climate change has robust foundations in classical physics, but today’s research has moved well beyond generic statements of concern. The focus now is on ever increasing levels of detail. Scientists, policy makers and society at large want to know the consequences of climate change for specific parts of the climate system. These range from the Atlantic Meridional Overturning Circulation (AMOC) and the chances of it “shutting down”, to changes in flood risks in specific towns for use in guiding local development plans and investments, to assessments of the national economic impacts of different global approaches to energy policy.
To what extent are such “predictions” possible?
To get a handle on this question, in this colloquium I will discuss the foundational characteristics that frame the study of human-induced climate change, and the key challenges that researchers across multiple disciplines need to address. My talk will touch on what it means to make climate predictions within a low-order dynamical system, and what we can learn from such systems for how we should use high-dimensional, multi-component Earth System Models. I will go on to discuss the relationship between climate models and reality, and how the characteristics of “model error” impact the target for future research initiatives. There have been calls to spend billions of dollars on high resolution, increasingly complex models but can this ever be worth the investment? Finally, I will reflect on the use of the natural sciences in the economics and policy of climate change.
- 14 November 2025: Keith Ball (University of Warwick): Surface areas of polyhedra
Isoperimetric inequalities play crucial roles in many areas of analysis, probability and combinatorics. The classical one in Euclidean space states that the largest volume that can be enclosed with a given surface area is an Euclidean ball. In this talk I will explain how to find the (essentially) optimal improvement in this inequality for a polyhedron with $m$ faces in $d$ dimensions (for all $m$ and $d$). I will also explain a light-hearted application to the construction of a convex polyhedron with the same volume as an Euclidean ball but much larger shadows in all directions. In the process I will describe a number of beautiful classical principles from high-dimensional geometry. The talk will be intelligible to undergraduates. - 21 November 2025: Nira Chamberlain (AtkinsRéalis): A mathematician's journey for social justice
Bringing the social issue of EDI into a scientific realm, Nira will also discuss the mathematician’s journey for social justice to answer the question: can we scientifically measure the effectiveness of an EDI strategy?
- 28 November 2025: Martin Bridson (University of Oxford):
- 05 December 2025: Edriss Titi (University of Cambridge):
- 12 December 2025: Sebastian Herr (University of Bielefeld):
Term 2
- 16 January 2026:
- 23 January 2026:
- 30 January 2026:
- 06 February 2026:
- 13 February 2026:
- 20 February 2026:
- 27 February 2026: (B3.02)
- 06 March 2026:
- 13 March 2026:
- 20 March 2026:
Term 3
- 01 May 2026:
- 08 May 2026:
- 15 May 2026:
- 22 May 2026:
- 29 May 2026:
- 05 June 2026:
- 12 June 2026:
- 19 June 2026:
- 26 June 2026:
- 03 July 2026: Speaking with Style