Postgraduate Seminars Autumn 2025
These seminars (unless otherwise stated) will take place on Thursdays at 2pm-3pm on an almost weekly basis.
Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students.
09 October 2025 - 2pm in Maths Room 416
Speaker: Yuze Jiang
Title: The Berstein problem, Junctions, and Smoothness of Soap Films
Abstract:
An introduction to modelling soap films as minimal surfaces—from the smooth PDE to weak models that allow junctions. We’ll ask how smooth they can be: Bernstein-type theorems and their limits, Plateau-type junction laws, and when and why area-minimizing hypersurfaces are smooth or the opposite.
16 October 2025
NO SEMINAR
23 October 2025 - 2pm in Maths Room 416
Speaker: Eissa Alnasrallah
Title: Non-minimal matter-curvature couplings in modified gravity
Abstract:
General relativity has been a successful theory of gravity with strong evidences and predictions confirmed, most recently the detection of gravitational waves. Yet, more than 95% of the universe remains “dark” and unexplained by current theories, motivating the development of alternative theories of gravity. In this talk, I will begin by presenting a brief introduction to general relativity and the motivation to modify gravity. I will then focus on a specific class of those theories, namely, non-minimal curvature-matter couplings and their application to perfect fluids.
30 October 2025 - 2pm in Maths Room 416
Speaker: Edwina Aylward
Title: Points on Elliptic Curves and Where to Find Them
Abstract:
This talk will give a gentle introduction to elliptic curves, explaining what they are and why they continue to fascinate number theorists today. I’ll then explore how we try to understand their rank—a measure of how many rational points they have—using ideas that often depend on deep conjectures. Finally, I’ll describe a recent approach I explored for predicting when the rank is positive, and compare it with the more familiar parity-based methods.
06 November 2025
NO SEMINAR - READING WEEK
13 November 2025 - 2pm in Maths Room 416
Speaker: Alberto Acosta Reche
Title: Counting problems and analytic properties of Dirichlet series
Abstract:
A typical problem in analytic number theory is finding the asymptotic behaviour of the partial sums of a sequence of arithmetic significance. In this talk, I will explain how such a problem is related to studying the analytic properties of certain Dirichlet series, and I will introduce some of the standard tools that are useful to solve it. The prototypical example of this situation is the relation between the prime number theorem and the Riemann hypothesis, but I will give plenty of other examples. In particular, the relation between closed geodesics on a hyperbolic surface and Selberg zeta functions is of great importance for my research.
20 November 2025 - 2pm in Maths Room 416
Speaker: Jinhui Gong
Title: The rotating stratified flow
Abstract:
Stratified oceans support propagating internal waves of many tens of metres of amplitude. These waves can disrupt offshore moorings, drilling and cabling. The linear, small amplitude, dynamics of these waves is well understood, and much progress has also been made with weakly nonlinear theories. However, the fully nonlinear, arbitrary amplitude, dynamics of these waves are less well studied. In particular when the waves are sufficiently long, and propagate over sufficiently large distances, the background rotation of the Earth introduces vorticity with a large vertical component that renders invalid all classical methods based on introducing a velocity potential for nonlinear non-rotating waves. This project proposes computing arbitrary amplitude rotating stratified waves, using methods that do not require the existence of a velocity potential, and examining their behaviour in various asymptotic limits.
In the nonlinear problem, the primary objects of study are two-dimensional waves of the external modes. Prior to this, the linear solutions are obtained analytically using a first-order asymptotic method, and the linear analysis also includes the corresponding internal-mode solutions. Three types of stratification are considered—no stratification, constant stratification, and a two-layer constant-density structure—and for each case both the linear and nonlinear solutions are summarised.
27 November 2025
NO SEMINAR
04 December 2025
NO SEMINAR
11 December 2025
NO SEMINAR