11:00 (London time), Thursday, 29 January 2026

Imperial College London

Room 411; Huxley Building

Hanne Van Den Bosch (University of Chile)

Keller-Lieb-Thirring estimates for Dirac operators

The classical Keller-Lieb-Thirring inequality bounds the ground state energy of a Schrödinger operator by a Lebesgue norm of the potential. This problem can be rewritten as a minimization problem for the Rayleigh quotient over both the eigenfunction and the potential. It is then straightforward to see that the best potential is a power of the eigenfunction, and the optimal eigenfunction satisfies a nonlinear Schrodinger equation. This talk concerns the analogous question for the smallest eigenvalue in the gap of a massive Dirac operator. This eigenvalue is not characterized by a minimization problem. By using a suitable Birman-Schwinger operator, we show that for sufficiently small potentials in Lebesgue spaces, an optimal potential and eigenfunction exists. Moreover, the corresponding eigenfunction solves a nonlinear Dirac equation.

This is joint work with Jean Dolbeault, David Gontier and Fabio Pizzichillo.

11:00 (London time), Thursday, 05 February 2026

Imperial College London

Room 411; Huxley Building

Massimo Sorella (Imperial College London)

Alpha unstable flows and the fast dynamo problem

The fast dynamo problem is a fundamental question in MHD concerning the ability of a flow to maintain magnetic fields without their growth being slowed down by resistive effects. In the passive vector equation, a simplified model, this can be formulated as the exponential growth in time of the \( L^2 \) norm of the solution under a Lipschitz flow, at a rate independent of resistivity. In this talk, I will present recent results showing subsequent growth for the linear passive vector equation, driven by the so called alpha effect.

11:00 (London time), Wednesday, 18 February 2026

Imperial College London

Room 411; Huxley Building

Elliot Marshall (University of Crete)

Singularities, Fluids, and the BKL Conjecture

The Penrose-Hawking singularity theorems guarantee that a wide class of cosmological models are past geodesically incomplete, indicating that these spacetimes contain ‘big bang’ singularities. However, these theorems do not provide any information about the nature of the singularity. A longstanding problem in mathematical cosmology, therefore, has been to understand the dynamical behaviour of solutions to the Einstein equations near the big bang. In the seminal work of Belinski, Khalatnikov, and Lifschitz (BKL), it was conjectured that the initial singularity is generically spacelike, local, and oscillatory. Roughly speaking, this means that solutions to the Einstein equations are well-approximated by a chaotic system of ODEs near the big bang. Rigorous results in this setting have thus far been limited to spatially homogeneous spacetimes, although there is an extensive body of numerical work for vacuum spacetimes which supports the BKL picture. Roughly speaking, this means that solutions to the Einstein equations are well-approximated by a chaotic system of ODEs near the big bang. Rigorous results in this setting have thus far been limited to spatially homogeneous spacetimes, although there is an extensive body of numerical work for vacuum spacetimes which supports the BKL picture. However, there has been comparatively little research (numerical or otherwise) into the dynamics of inhomogeneous cosmologies containing non-stiff matter near the big bang. In this talk, I will give an overview of the BKL conjecture and discuss recent numerical work for inhomogeneous cosmologies containing a non-stiff perfect fluid. In particular, I will show that the fluid velocity in these models develops chaotic oscillatory behaviour, known as tilt transitions.