Lancaster

This talk reports on two projects. The first work (in progress), joint  with Amanda Hirschi, constructs (genus 0) open Gromov-Witten invariants for any Lagrangian submanifold using a global Kuranishi chart construction. As an application we show open Gromov-Witten invariants are invariant under Lagrangian cobordisms. I will then describe how open Gromov-Witten invariants fit into mirror symmetry, which brings me to the second project: obtaining open Gromov-Witten invariants from the Fukaya category.

It has long been expected, and is now proved in many important cases, 
that quantum algebras are more rigid than their classical limits. That is, they 
have much smaller automorphism groups. This begs the question of whether this 
broken symmetry can be recovered.

I will outline an approach to this question using the ideas of noncommutative 
projective geometry, from which we see that the correct object to study is a 
groupoid, rather than a group, and maps in this groupoid are the replacement 
for automorphisms. I will illustrate this with the example of quantum 
projective space.

This is joint work with Nicholas Cooney (Clermont-Ferrand).

This is joint work with Diaz, Glesser and Park.

In Proc. Instructional Conf, Oxford 1969, G. Glauberman shows that

several global properties of a finite group are determined by the properties

of its p-local subgroups for some prime p. With Diaz, Glesser and Park, we

reviewed these results by replacing the group by a saturated fusion system

and proved that the ad hoc statements hold. In this talk, we will present

the adapted versions of some of Glauberman and Thompson theorems.