Mon, 11 Jul 2016

14:45 - 15:45
L3

(COW SEMINAR) Higgs bundles and determinant divisors

Nigel Hitchin
(Oxford)
Abstract

Following an idea of Gaiotto, a symplectic representation of a complex Lie group G defines a complex Lagrangian subvariety inside the moduli space of G-Higgs bundles. The talk will discuss the case of G=SL(2) and its link with determinant  divisors, or equivalently Brill-Noether loci, in the moduli space of semistable SL(2)-bundles. 

Mon, 11 Jul 2016

13:30 - 14:30
L3

(COW SEMINAR) Categorification of shifted symplectic geometry using perverse sheaves

Dominic Joyce
(Oxford)
Abstract

Given a (-1)-shifted symplectic derived scheme or stack (X,w) over C equipped with an orientation, we explain how to construct a perverse sheaf P on the classical truncation of X so that its hypercohomology H*(P) can be regarded as a categorification of (or linearisation of) X. Given also a Lagrangian morphism L -> X equipped with a relative orientation, we outline a programme in progress to construct a natural morphism of constructible complexes on the truncation of L from the (shifted) constant complex on L to a suitable pullback of P to L. The morphisms and resulting hypercohomology classes are expected to satisfy various identities under products, composition of Lagrangian correspondences, etc. This programme will have interesting applications, such as proving associativity of a Kontsevich-Soibelman type COHA multiplication on H*(P) when X is the derived moduli stack of coherent sheaves on a Calabi-Yau 3-fold Y, and defining Lagrangian Floer cohomology and the Fukaya cat!
 egory of an algebraic or complex symplectic manifold S.

The mathematics of poaching and gamekeeping

How do we stop poaching? You may think the answer lies in finding a way of giving gamekeepers an advantage over poachers. Oxford Mathematician Tamsin Lee and David Roberts from the University of Kent decided to look at the interaction between rhino poachers and a gamekeeper to predict the outcome of the battle. Their conclusions suggest alternative ways of tackling the problem.

Heather Harrington to give LMS Popular Lectures

Oxford Mathematician Heather Harrington will be giving the London Mathematical Society (LMS) Popular Lectures this summer in London on 29 June and in September in Birmingham. The Lectures present exciting topics in mathematics and its applications to a wide audience and feature two lecturers who have been chosen for their mathematical distinction and communication skills.  

G is for Growth Tensor - the latest in our Oxford Mathematics Alphabet

A tree branch, a ram's horn, your hand - how have these distinct and consistent shapes come about? The growth and form of a biological entity is a complex matter that involves integrated activities across a number of length scales. Viewed at the scale of tissues, or large clusters of cells, understanding growth and form is a problem well suited for continuum mechanics and mathematical modelling.

First combined search for neutrino point-sources in the Southern Hemisphere with the ANTARES and IceCube neutrino telescopes
 Adrián-Martínez, S Albert, A André, M Sarkar, S Astrophysical Journal volume 823 issue 1 (23 May 2016)
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