Category Archives: Abstracts


A theory of Lower Semicontinuity for Integral Functionals with Linear Growth and u-dependence, Giles Shaw (Reading & Cambridge)

Variational problems with linear growth arise naturally in the Calcu- lus of Variations from the study of singular perturbation problems associated to a large number of physical and mathematical applications. These problems must be posed over the class of functions of bounded variation, and their analysis is signifi- cantly more involved than that which is… Read More »

Coherent motion for interacting particles: waves in the Frenkel-Kontorova chain, Johannes Zimmer (Bath)

In 1939, Frenkel and Kontorova proposed a model for the motion of a dislocation (an imperfection in a crystal). The model is simple, a chain of atoms following Newton’s equation of motion. The atoms interact with their nearest neighbours via a harmonic spring and are exposed to a periodic (non-convex) on-site potential. Despite the simplicity, the model has… Read More »

Singular limits of nonlinear elliptic and parabolic systems, Elaine Crooks (Swansea)

Large-interaction limits of certain systems of elliptic and parabolic PDE, such as, for instance, population systems with large competition, both provide a powerful mathematical tool that can be exploited to obtain information about systems that are otherwise difficult to analyse, and correspond to important biological and physical phenomena such as spatial segregation, phase separation, or… Read More »

Homogenisation for mean field games, Nicolas Dirr (Cardiff University)

Mean field games have been introduced by J.-M. Lasry and P.-L. Lions as an effective model for very many competing rational agents. They are a system of Hamilton-Jacobi equations and Kolmogorov-Fokker-Planck equations. One of the challenges is the fact that these two types of equations have different “natural” notions of generalized solutions.  We investigate dynamical mean field… Read More »

Vectorial Calculus of Variations in $L^\infty$ and generalised solutions for fully nonlinear PDE systems, Nikos Katzourakis (Reading)

Calculus of Variations in $L^\infty$ has a long history, the scalar case of which was initiated by G.Aronsson in the 1960s and is under active research ever since. Aronsson’s motivation to study this problem was related to the optimisation of Lipschitz Extensions of functions. Mathematically, minimising the supremum is very challenging because the equations are… Read More »