Past Algebra Seminar

6 November 2012
17:00
Peter Symonds
Abstract

We present a new, more conceptual proof of our result that, when a finite group acts on a polynomial ring, the regularity of the ring of invariants is at most zero, and hence one can write down bounds on the degrees of the generators and relations. This new proof considers the action of the group on the Cech complex and looks at when it splits over the group algebra. It also applies to a more general class of rings than just polynomial ones.

• Algebra Seminar
30 October 2012
17:00
Dr Chris Bowman
Abstract

The Kronecker coefficients describe the decomposition of the tensor product of two Specht modules for the symmetric group over the complex numbers. Surprisingly, until now, no closed formula was known to compute these coefficients. In this talk, I will report on joint work with M. De Visscher and R. Orellana where we use the Schur-Weyl duality between the symmetric group and the partition algebra to find such a formula.

• Algebra Seminar
23 October 2012
17:00
Nick Gill
Abstract

I describe recent work with Pyber, Short and Szabo in which we study the width' of a finite simple group. Given a group G and a subset A of G, the width of G with respect to A' - w(G,A) - is the smallest number k such that G can be written as the product of k conjugates of A. If G is finite and simple, and A is a set of size at least 2, then w(G,A) is well-defined; what is more Liebeck, Nikolov and Shalev have conjectured that in this situation there exists an absolute constant c such that w(G,A)\leq c log|G|/log|A|.
I will present a partial proof of this conjecture as well as describing some interesting, and unexpected, connections between this work and classical additive combinatorics. In particular the notion of a normal K-approximate group will be introduced.

• Algebra Seminar
16 October 2012
17:00
Prof Juan Souto
Abstract

There is a well-acknowledged analogy between mapping class
groups and lattices in higher rank groups. I will discuss to which
extent does Margulis's superrigidity hold for mapping class groups:
examples, very partial results and questions.

• Algebra Seminar
9 October 2012
17:00
Nikolay Nikolov
Abstract

We prove that the rank gradient vanishes for mapping class groups, Aut(Fn) for all n, Out(Fn), n > 2 and any Artin group whose underlying graph is connected. We compute the rank gradient and verify that it is equal to the first L2-Betti number for some classes of Coxeter groups.

• Algebra Seminar
12 June 2012
17:00
Professor G. Clif
Abstract
• Algebra Seminar
5 June 2012
17:00
Professor S. Rees
Abstract
I’ll report on my recent work (with co-authors Holt and Ciobanu) on Artin groups of large type, that is groups with presentations of the form G = hx1, . . . , xn | xixjxi · · · = xjxixj · · · , 8i < ji for which both sides of the ‘braid relation’ on xi and xj have length mij 2 N [1 with mij  3. (In fact, our results still hold when some, but not all possible, relations with mij = 2 are allowed.) Recently, Holt and I characterised the geodesic words in these groups, and described an effective method to reduce any word to geodesic form. That proves the groups shortlex automatic and gives an effective (at worst quadratic) solution to the word problem. Using this characterisation of geodesics, Holt, Ciobanu and I can derive the rapid decay property for most large type groups, and hence deduce for most of these that the Baum-Connes conjec- ture holds; this has various consequence, in particular that the Kadison- Kaplansky conjecture holds for these groups, i.e. that the group ring CG contains no non-trivial idempotents. 1
• Algebra Seminar
22 May 2012
17:00
Dr. M. de Visscher
Abstract
• Algebra Seminar
15 May 2012
17:00
Aner Shalev
Abstract
In recent years there has been extensive interest in word maps on groups, and various results were obtained, with emphasis on simple groups. We shall focus on some new results on word maps for more general families of finite and infinite groups.
• Algebra Seminar