Speaker: Daniel Woodhouse (North)
Title: Generalizing Leighton's Graph Covering Theorem
Abstract: Before he ran off and became a multimillionaire, exploiting his knowledge of network optimisation, the computer scientist F. Thomas Leighton proved an innocuous looking result about finite graphs. The result states that any pair of finite graphs with isomorphic universal covers have isomorphic finite covers. I will explain what all this means, and why this should be of tremendous interest to group theorists and topologists.
Speaker: Benjamin Fehrman (South)
Title: Large deviations for particle processes and stochastic PDE
Abstract: In this talk, we will introduce the theory of large deviations through a simple example based on flipping a coin. We will then define the zero range particle process, and show that its diffusive scaling limit solves a nonlinear diffusion equation. The large deviations of the particle process about its scaling limit formally coincide with the large deviations of a certain ill-posed, singular stochastic PDE. We will explain in what sense this relationship has been made mathematically precise.