London PDE Seminar

\( i \partial_t u + \Delta u = 0 \)

The London PDE Seminar is a London-based seminar featuring speakers at the forefront of mathematical research in partial differential equations.


Upcoming Seminars

Date/Time:

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

Location:

Queen Mary University of London

Room MB-503; Mathematics Building

Speaker:

Léo Bigorgne (University of Rennes)

Title:

Decay estimates for massless Vlasov fields on subextremal Kerr spacetimes

Abstract:

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.

Date/Time:

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

Location:

Imperial College London

Room 130; Huxley Building

Speaker:

Josephine Evans (University of Warwick)

Date/Time:

10:00 (London time), Thursday, 14 May 2026

Location:

Queen Mary University of London

Room MB-503; Mathematics Building

Speaker:

Angeliki Menegaki (Imperial College London)

Date/Time:

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

Location:

Queen Mary University of London

Room MB-503; Mathematics Building

Speaker:

Daniel Ginsberg (Brooklyn College)

Date/Time:

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

Location:

Queen Mary University of London

Room MB-503; Mathematics Building

Speaker:

Ludovic Souêtre (Sorbonne University)

Title:

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

Abstract:

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.

Date/Time:

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

Location:

Queen Mary University of London

Room MB-503; Mathematics Building

Speaker:

Nicola De Nitti (Polytechnic University of Bari)

Title:

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

Abstract:

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.

Date/Time:

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

Location:

Queen Mary University of London

Room MB-503; Mathematics Building

Speaker:

Istvan Kadar (ETH)


Organisers


Acknowledgments

The London PDE Seminar is currently partly funded by: