Past 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
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.
1 May 2012
17:00
Professor R. Marsh
Abstract

 Finite reflection groups are often presented as Coxeter groups. We give a
presentation of finite crystallographic reflection group in terms of an
arbitrary seed in the corresponding cluster algebra of finite type for which
the Coxeter presentation is a special case. We interpret the presentation in
terms of companion bases in the associated root system. This is joint work with 
Michael Barot (UNAM, Mexico)

6 March 2012
17:00
Dr Kobi Kremnitzer
Abstract
By recent work of Voevodsky and others, type theories are now considered as a candidate for a homotopical foundations of mathematics. I will explain what are type theories using the language of (essentially) algebraic theories. This shows that type theories are in the same "family" of algebraic concepts such as groups and categories. I will also explain what is homotopic in (intensional) type theories.
28 February 2012
17:00
Ashot Minasyan
Abstract

 Graph products of groups naturally generalize direct and free products and have a rich subgroup structure. Basic examples of graph products are right angled Coxeter and Artin groups. I will discuss various forms of Tits Alternative for subgroups and
their stability under graph products. The talk will be based on a joint work with Yago Antolin Pichel.

Pages