Oxford

Recent developments in 3-dimensional topological quantum field theory allow us to understand the vector spaces assigned to surfaces as spaces of string diagrams. In the Reshetikhin-Turaev model, these string diagrams live inside a handlebody bounding the surface, while in the Turaev-Viro model, they live on the surface itself. There is a "lifting map" from the former to the latter, which sheds new light on a number of constructions. Joint with Gerrit Goosen.

Oxford Mathematics Public Lectures

MC Escher - Artist, Mathematician, Man 

Roger Penrose and Jon Chapman

This lecture has now sold out

The symbiosis between mathematics and art is personified by the relationship between Roger Penrose and the great Dutch graphic artist MC Escher. In this lecture Roger will give a personal perspective on Escher's work and his own relationship with the artist while Jon Chapman will demonstrate the mathematical imagination inherent in the work. 

The lecture will be preceded by a showing of the BBC 4 documentary on Escher presented by Sir Roger Penrose. Private Escher prints and artefacts will be on display outside the lecture theatre.

5pm

Lecture Theatre 1

Mathematical Institute

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

OX2 6GG

Roger Penrose is Emeritus Rouse Ball Professor at the Mathematical Institute in Oxford

Jon Chapman is Statutory Professor of Mathematics and Its Applications at the Mathematical Institute in Oxford

We give a classification of open Klein topological conformal field theories in terms of Calabi-Yau $A_\infty$-categories endowed with an involution. Given an open Klein topological conformal field theory, there is a universal open-closed extension whose closed part is the involutive version of the Hochschild chains associated to the open part.

This'll be a nice and slow paced introduction to topological quantum field theory in general, and 1-2-3 dimensional theories in particular. If time permits I will explain the spin version of these and their connection to physics. There will be lots of pictures. 

I will report on recent progress towards understanding the growth of the torsion of the homology of subgroups of finite index in a given residually finite group G.

The cases I will consider are when G is amenable (joint work with P, Kropholler and A. Kar) and when G is right angled (joint work with M. Abert and T. Gelander).

In the classification of surfaces, K3 surfaces hold a place not dissimilar to that of elliptic curves within the classification of curves by genus. In recent years there has been a lot of activity on the problem of rational points on K3 surfaces. I will discuss the problem of finding the Picard group of a K3 surface, and how this relates to finding counterexamples to the Hasse principle on K3 surfaces.