Algebra Seminars: Dani, Williamson

On Friday 27 May there will be two Algebra Seminars, the first by Pallavi Dani at the
usual time 12 noon, and the second by Geordie Williamson at 2.30pm.  We will take the
speakers for lunch between the talks.  

--------------------------------------------------------------------------- 

Speaker: Pallavi Dani (Louisiana State University) 

Date: Friday 27 May 

Time: 12.05-12.55pm 

Venue: Carslaw 175 

Title: 

Filling invariants for groups 

Abstract: 

Every finitely generated group can be endowed with the word metric.  Gromov initiated a
program of classifying such groups up to quasi-isometry, a coarse equivalence on metric
spaces, leading to an interest in quasi-isometry invariants.  I will talk about a class
of invariants that arise from considering "fillings" of spheres by balls in a suitable
model space for the group.  I will then discuss joint work with Abrams, Brady, Duchin
and Young investigating certain filling invariants in the class of right-angled Artin
groups.  

---------------------------------------------------------------------------- 

Speaker: Geordie Williamson (University of Oxford) 

Date: Friday 27 May 

Time: 2:35-3:25pm 

Venue: Carslaw 175 

Title: 

Coxeter groups, Soergel bimodules and higher representation theory 

Abstract: 

Many important representation theoretic objects (for example Hecke algebras and
enveloping algebras) can be categorified.  Over the last decade important new results in
representation theory have been obtained by studying actions of these
categorifications.  

In my talk I will try to explain this in a simple example: that of actions of Coxeter
groups on categories.  Even this naive example is somewhat subtle, and one is led
naturally to certain generalisations of the Zamolodchikov equations arising from the
Platonic solids.  I will explain how this leads to a generators and relations
description of the monoidal category of Soergel bimodules.  This answers a question of
Rouquier and formed the starting point of this work.  (Joint work with Ben Elias.)  

----------------------------------------------------------------------------