Forthcoming events in this series

Tue, 05 Jun 2007

The beginning of the Atlas of self-similar groups

Prof. R. Grigorchuk
(Texas A&M)

We will speak about the problem of classification of self-similar groups. The

main focus will be on groups generated by three-state  automata over an

alphabet on two letters. Numerous examples will be presented, as well as some

results concerning this class of groups.


Tue, 29 May 2007

Anosov diiffeomorphisms and strongly hyperbolic elements in arithmetic subgroups of SL_n(R)

Dr. Ben Klposch
(Royal Holloway)

I will talk about some ongoing work, motivated by a long standing problem in

the theory of dynamical systems. In particular, I will explain how p-adic

methods lead to the construction of elements in SL_n(Z) whose eigenvalues e_1,

., e_n generate a free abelian subgroup of rank n-1 in the multiplicative group

of positive real numbers. This is a special instance of a more general theorem,

asserting the existence of strongly hyperbolic elements in arithmetic subgroups

of SL_n(R).


Tue, 15 May 2007


Tue, 08 May 2007

Cluster algebra structures on co-ordinate ring of flag varieties

Prof. Bernard Leclerc
  Let G be a complex semisimple algebraic group of type A,D,E. Fomin and Zelevinsky conjecture that the coordinate rings of many interesting varieties attached to G have a natural cluster algebra structure. In a joint work with C. Geiss and J. Schroer we realize part of this program by introducing a cluster structure on the multi-homogeneous coordinate ring of G/P for any parabolic subgroup P of G. This was previously known only for P = B a Borel (Berenstein-Fomin-Zelevinsky) and when G/P is a grassmannian Gr(k,n) (J. Scott). We give a classification of all pairs (G,P) for which this cluster algebra has finite type. Our construction relies on a finite-dimensional algebra attached to G, the preprojective algebra introduced in 1979 by Gelfand and Ponomarev. We use the fact that the coordinate ring of the unipotent radical of P is "categorified" in a natural way by a certain subcategory of the module category of the preprojective algebra.  
Tue, 27 Feb 2007

Spectra of Groups

Professor Andrzej Zuk
(Paris & Newton Inst.)
Tue, 31 Oct 2006

Phan theory

Prof. S. Shpectorov
(University of Birmingham)