That Robin Wilson, he doesn't half go on.
To infinity in fact, the topic of Robin's eighteenth and final talk on the equations that made mathematics. With an irritating little paradox to whet your appetite below and the full talk here.
Perhaps you are looking for some summer work. The University of Plymouth is looking for students of home fee status, and in their 2nd or 3rd year of their degree, to undertake funded summer internships on the following projects:Global existence for a cross diffusion system with different mobilities
Abstract
We consider a cross diffusion system of two populations, often called the Busenberg-Travis system. The two species are transported by the same pressure gradient with Darcy’s law, modeling overcrowding effect (populations tend to move away from regions of high pressure). However, their mobility is different: the first species moves with mobility 1, whereas the second moves with mobility \nu. The difficulty to prove existence is to prove strong compactness of each densities, which we achieve with a variant of the div-curl lemma applied to evolution PDEs.
Wasserstein Limits for Empirical Measures of Markov Processes
Abstract
In this talk we summary some recent progress on limit theorems for the Wasserstein distance of empirical measures of Markov processes. For symmetric diffusion processes on Riemannian manifold possibly with reflecting or killing boundary, the sharp convergence rate is derived with renormalization limit formulated by using the spectrum of the generator. Moreover, a general framework is established to estimate the convergence rate in Wasserstein distance of empirical measures for ergodic Markov processes.