I will talk in down to earth terms about several main features of this theory.
We describe how p-adic height pairings allow us to find integral points on hyperelliptic curves, in the spirit of Kim's nonabelian Chabauty program. In particular, we discuss how to carry out this ``quadratic Chabauty'' method over quadratic number fields (joint work with Amnon Besser and Steffen Mueller) and present related ideas to find rational points on bielliptic genus 2 curves (joint work with Netan Dogra).
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.
Congratulations to Dr Catherine Wilkins from Oxford Mathematics who has won a MPLS (Mathematical Physical and Life Sciences Division) award for teaching excellence. Oxford Teaching Awards are given either to individuals or to teams as a public acknowledgement of excellence in teaching and learning.
Patrick Farrell, Early Career Research Fellow in Applied Mathematics in Oxford, together with colleagues from the Simula Research Laboratory and Imperial College London, has won this year's 2015 Wilkinson Prize.
