Mon, 02 Nov 2015

16:00 - 17:00
C2

The Arithmetic of K3 Surfaces

Christopher Nicholls
(Oxford)
Abstract

The study of rational points on K3 surfaces has recently seen a lot of activity. We discuss how to compute the Picard rank of a K3 surface over a number field, and the implications for the Brauer-Manin obstruction.

Mon, 26 Oct 2015

16:00 - 17:00
C2

Some ideas on rational/integral points on algebraic curves

Junghwan Lim
(Oxford)
Abstract

I will introduce classical results on finiteness theorem with a way of connecting them to idea of covering spaces. I will talk about the proof of FLT under this connection.

Mon, 19 Oct 2015

16:00 - 17:00
C2

Algebraic Automorphic Forms and the Langlands Program

Benjamin Green
(Oxford)
Abstract

In this talk I will define algebraic automorphic forms, first defined by Gross, which are objects that are conjectured to have Galois representations attached to them. I will explain how this fits into the general picture of the Langlands program and, giving some examples, briefly describe one method of proving certain cases of the conjecture. 

Wed, 04 Nov 2015
16:00
C1

Isometries of CAT(0) Spaces

Giles Gardam
(Oxford)
Abstract

This talk will be an easy introduction to some CAT(0) geometry. Among other things, we'll see why centralizers in groups acting geometrically on CAT(0) spaces split (at least virtually). Time permitting, we'll see why having a geometric action on a CAT(0) space is not a quasi-isometry invariant.

 

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