Type: Seminar

Distribution: World

Expiry: 27 May 2011

CalTitle1: Algebra Seminar: Dani, Williamson

Auth: athomas(.pmstaff;2039.2002)@p615.pc.maths.usyd.edu.au

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.) ----------------------------------------------------------------------------