11:00 (London time), Thursday, 04 June 2026

Queen Mary University of London

Istvan Kadar (ETH)

Smooth singularity formation for the energy critical wave equation without quantization

The energy-critical nonlinear wave equation (NW) in three dimensions admits a stationary solution. In their foundational work, Krieger-Schlag-Tataru constructed (non-smooth) solutions to (NW) that develop singularities with arbitrarily polynomial blow-up rates exceeding the self-similar rate by adiabatically shrinking to a single soliton in spherical symmetry. For comparison, their analogous results for the wave map equation stand in sharp contrast to the quantized blow-up rates for smooth solutions obtained by Raphaël-Rodnianski. In this talk, I discuss a new result establishing the existence of a family of smooth solutions to (NW) that develop singularities at a continuum of polynomial rates, achieved through the collapse of multiple solitons.

10:00 (London time), Thursday, 04 June 2026

Queen Mary University of London

Nicola De Nitti (Polytechnic University of Bari)

Singular limit for a class of nonlocal conservation laws via compensated compactness

We study a class of nonlocal conservation laws arising in traffic flow, where the flux depends on a spatial convolution with a rescaled kernel. As the kernel concentrates to a Dirac mass, we prove strong \( \mathrm{L}^1_{\mathrm{loc}} \) convergence of the averaged densities to the entropy solution of the corresponding local conservation law. In contrast to previous approaches, we obtain compactness of the averaged family without total variation bounds or Oleĭnik-type estimates. Instead, we derive \( \mathrm{L}^2 \)-type bounds on the entropy production and rely on compensated compactness techniques. We assume only \( \mathrm{L}^1 \cap \mathrm{L}^\infty \) initial data and treat either strictly monotone kernels or a piecewise constant kernel combined with the affine velocity from Greenshields' traffic model. These results address the open problem of nonlocal-to-local convergence in the presence of non-convex kernels. The talk is based on joint work with G. M. Coclite and K. Huang.

11:00 (London time), Thursday, 28 May 2026

Queen Mary University of London

Ludovic Souêtre (Sorbonne University)

The homogeneous Robin boundary conditions for asymptotically Anti-de Sitter spaces

Modelled on Anti-de Sitter, asymptotically Anti-de Sitter spaces can be defined as Lorentzian manifolds that possess a timelike conformal boundary. Due to their lack of global hyperbolicity, finding asymptotically Anti-de Sitter solutions to the Einstein equations (necessarily with a negative cosmological constant) through the Cauchy problem requires tackling the latter as an initial boundary value problem. In this talk, I will present the two known types of geometric boundary conditions leading to the local existence and uniqueness of solutions in dimension \(4\): the Dirichlet boundary conditions, which were introduced by Friedrich in 1995, and the homogeneous Robin boundary conditions, which I introduced in a recent work.

11:00 (London time), Thursday, 14 May 2026

Queen Mary University of London

Angeliki Menegaki (Imperial College London)

Phonon Boltzmann Equation: Entropy maximisers and their stability

In this talk we consider the four-waves spatially homogeneous kinetic equation arising in weak wave turbulence theory from one-dimensional microscopic oscillator chains. This is the Phonon Boltzmann Equation. I will discuss the entropy maximisation problem, the collisional invariants, and properties of solutions of the kinetic equation near the Rayleigh-Jeans (RJ) thermodynamic equilibria. This is based on joint works with Pierre Germain (Imperial College London), Joonhyun La (KIAS) and with Miguel Escobedo (Bilbao).

11:00 (London time), Thursday, 07 May 2026

Imperial College London

Josephine Evans (University of Warwick)

Nonlinear kinetic equations converging to the fast diffusion/porous medium equation

We are interested in the derivation of nonlinear diffusions of the form \( \mathrm{d}_t \rho = \Delta_x( \rho^a) \) from kinetic equations. Formally we can see that these can be derived from a scale of nonlinear kinetic equations. I will discuss our results when the \( x \) variable is placed on the torus and the challenges we see in extending them to the whole space.

11:00 (London time), Friday, 01 May 2026

Queen Mary University of London

Léo Bigorgne (University of Rennes)

Decay estimates for massless Vlasov fields on subextremal Kerr spacetimes

We will present a commutation vector field approach for the solutions to the massless Vlasov equation on the exterior of a Schwarzschild spacetime, together with extensions to subextremal Kerr black holes. The approach satisfies two properties. First, it provides decay estimates for the energy flux induced by the energy-momentum tensor of Vlasov fields and its derivatives. Secondly, it is compatible with the methods used to study wave equations on black hole spacetimes. For this, we make use of a weight function that captures the concentration properties of the geodesic flow. By using a well-chosen modification of its symplectic gradient, we construct a norm for which any smooth solution to the massless Vlasov equation satisfies an integrated energy decay estimate without relative degeneration. This is joint work with Renato Velozo.

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

Imperial College London

Allen Fang (University of Münster)

On the uniqueness of Kerr-de Sitter

The uniqueness of the Kerr-de Sitter family of black hole spacetimes as stationary solutions to the Einstein vacuum equations is a crucial ingredient to understanding the final states of positive cosmological constant universes, such as our physical universe. In the asymptotically flat case, Kerr was shown to be the unique analytic stationary solution to the Einstein vacuum equations via a combination of results by Hawking, Carter, and Robinson. Outside of analyticity, Alexakis, Ionescu, and Klainerman showed several conditional \( C^\infty \) rigidity results for Kerr. In this talk, I will discuss some recent work in the spirit of Alexakis, Ionescu, and Klainerman showing the uniqueness of the stationary region of Kerr-de Sitter within the smooth class of stationary solutions to the Einstein vacuum equations with a positive cosmological constant.

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

Imperial College London

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.

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

Imperial College London

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), Thursday, 29 January 2026

Imperial College London

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.