Postgraduate Seminars Spring 2026
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.
22 January 2026 - 2pm in Maths Room 416
Speaker: Sara Drummond-Curtis
Title: Far-field models for multi-timescale microswimmers near a boundary
Abstract:
Although the presence of boundaries can significantly affect microswimmer trajectories, simple swimmer models typically assume the swimmer is in the far field and neglect near-field effects for convenience. In this talk, we’ll introduce a minimal swimmer model and account for the effect of the rapid deformation of the swimmers by exploiting the separated timescales with multiscale analysis. We will then explore the qualitatively different behaviour that emerge as a result of our analysis compared to the dynamics predicted by the simple swimmer models.
29 January 2026 - 2pm in Maths Room 416
NO SEMINAR
5 February 2026 - 2pm in Maths Room 416
SEMINAR CANCELLED
12 February 2026 - 2pm in Maths Room 416
Speaker: Nikhita Vas
Title: Black Holes in a Swirling Universe
Abstract:
We will look at the properties of Kerr black holes immersed in a swirling spacetime (KBHSU). We will first review the derivation of the metric using the Ernst formalism and will then look at how the spin-spin interaction between the angular momentum of the black hole and the swirling of the background leads to interesting effects of the ergoregions, photon rings and shadows. We find that there are three disconnected patches of ergoregions and a pair of light rings. However, as the value of the swirling parameter is increased, the patches of the ergoregions eventually merge. The light ring at this merger possesses no angular velocity (as measured by an asymptotic observer) and is called a light point. Finally, we present the shadows of KBHSU for various parameter values and observe that, due to the presence of the swirling background, the shadows are twisted.
19 February 2026
NO SEMINAR - READING WEEK
26 February 2026 - 2pm in Maths Room 416
Speaker: Michail Manthios
Title: Naked Singularities in General Relativity
Abstract: In this talk, I will discuss the formation of singularities for the Einstein Equations, with a particular emphasis on naked singularities. I will briefly recall the Cauchy problem in General Relativity and the connection between geodesic incompleteness and singularity formation. I will introduce self-similarity and explain its role in reducing the field equations to tractable dynamical systems that can reveal singular behaviour. I will review some rigorous constructions of naked singularities in several different matter models and outline ongoing work on the Einstein–Vlasov system aimed at constructing self-similar profiles which may yield dynamically forming naked singularities.
5 March 2026 - 2pm in Maths Room 416
Speaker: Thomas Caussade
Title: On numerical steepest descent methods for oscillatory integrals.
Abstract: The evaluation of highly oscillatory integrals is an important topic in many areas of computational wave propagation. The Numerical Steepest Descent (NSD) method is a powerful approach to computing such integrals, which combines complex contour deformation with quadrature rules. Remarkably, these techniques produce numerical schemes where accuracy improves as frequency increases, unlike conventional approaches that become prohibitively expensive at high frequencies. In this talk, I will describe a novel framework to rigorously analyse this class of methods and present a simple “black-box” interface that automates the application of the NSD method.
12 March 2026 - 2pm in Maths Room 416
Speaker: Catinca Mudjei
Title: Statistics of families of L-functions
Abstract: The Riemann zeta function serves as the fundamental prototype for a vast class of Dirichlet series known as L-functions, which encode deep arithmetic and geometric information. It turns out to be very difficult to study properties of one L-function at a time. Experience shows that, to understand an individual L-function, it can be convenient to embed it within a suitable family and study the family’s statistics. In this talk, I will present a few instances of such statistics, which remarkably suggest a link between L-functions and random matrix theory.
19 March 2026 - 2pm in Maths Room 416
Speaker: Nirmal Krishnan
Title: Derandomization of nodal sets of Laplacian eigenfunctions
Abstract: The zero sets of Laplacian eigenfunctions were first studied by Hooke and later Chladni, who found that placing sand on vibrating plates would lead them to fall into regular patterns. A celebrated result of Courant establishes an upper bound for the number of nodal domains, but this bound is rarely sharp and exceptional eigenfunctions with few nodal domains exist. Recently, ensembles of random eigenfunctions have been considered, with significant results being obtained in this case. Bourgain established a procedure of de-randomization on the torus, where one could transfer these results for random eigenfunctions to specific, deterministic eigenfunctions.