Wed, 23 Oct 2013
11:30
Queen's College

Group word problems related to the context-free languages

Tara Brough
(St Andrews)
Abstract
The word problem of a group $G$ with respect to a generating set $X$ is the set of all words in elements of $X$ and their inverses which represent the identity in $G$.  A formal language is a set of words over a finite alphabet, and so word problems of groups can be viewed as formal languages.
In this talk I will give an introduction to formal languages, concentrating on context-free languages and several related classes.  I will define these languages by means of automata.  I will then give a survey of research on groups whose word problem belongs to the language classes I have introduced, beginning with the classification of groups with context-free word problem (Muller and Schupp, 1983).  I will also discuss some of the open problems in this area.
Thu, 06 Nov 2008

14:30 - 15:30
L3

q-Schur algebras, Wedderburn decomposition and James' conjecture

Max Neunhoeffer
(St Andrews)
Abstract

In this talk we present a new construction of a Wedderburn basis for

the generic q-Schur algebra using the Du-Kazhdan-Lusztig basis. We show

that this gives rise to a new view on the Du-Lusztig homomorphism to the

asymptotic algebra. At the end we explain a potential plan for an attack

on James' conjecture using a reformulation by Meinolf Geck.

The talk starts with a gentle recollection of facts about

Iwahori-Hecke-Algebras of type A and q-Schur algebras and aims to be

accessible to people who are not (yet) experts in the representation

theory of q-Schur algebras.

All this is joint work with Olivier Brunat (Bochum).

Tue, 11 Nov 2008

17:00 - 18:00
L3

What does a generic measure looks like?

Lars Olsen
(St Andrews)
Abstract

The talk will give two entirely different answers to the question asked in the title of the talk. A topological answer will be based on the classical notion of Baire category. A measure theoretical answer will be based on the much newer notion of prevalence/shyness.

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