Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with even first Betti number. However, not all solutions of the Einstein-Maxwell equations on such manifolds arise in this way. In this lecture, I will describe a construction of new compact examples that are Hermitian, but not Kaehler.
 

I will talk about the fluid equations used to model pedestrian motion and traffic. I will present the compressible-incompressible Navier-Stokes two phase system describing the flow in the free and in the congested regimes, respectively. I will also show how to approximate such system by the compressible Navier-Stokes equations with singular pressure for the fixed barrier densities and also some recent developments for the barrier densities varying in the space and time.
This is a talk based on several papers in collaboration with: D. Bresch, C. Perrin, P. Degond, P. Minakowski, and L. Navoret.
 

The National Physical Laboratory is the national measurement institute. Researchers in the Data Science Division analyse various types of data using mathematical, statistical and machine learning based methods. The goal of the workshop is to describe a set of exciting mathematical problems that are of interest to NPL and more generally to the Data Science community. In particular, I will describe the problem of clustering using minimum spanning trees (MST-Clustering), Non-Negative Matrix Factorisation (NMF), adaptive Compressed Sensing (CS) for tomography, and sparse polynomial chaos expansion (PCE) for parametrised PDE’s.