Seminar October 6th

We will have a double session this week.


Monday October 6th, 12:30, CRM Small room

Speaker: Sean Cleary, The City College of New York

Title: Rotation distances and generating sets for Thompson's group F

Abstract: Rotation distances measure differences in tree shape between binary trees, by counting a minimum number of rotations needed to transform a first given tree into another. These correspond to word metrics for Thompson's group F with respect to different generating sets, depending upon where rotations are allowed. These connections give useful results in both directions.


Second talk, 13:30

Speaker: Laura Ciobanu, Université de Fribourg

Title: Properties of generic subgroups of free and hyperbolic groups

Abstract: Let F be a finitely generated free group, and K be a finitely generated, infinite index subgroup of F. We show that generically many finitely generated subgroups H have trivial intersection with all conjugates of K, thus proving a stronger, generic form of the Hanna Neumann Conjecture. As an application, we show that the equalizer of two free group homomorphisms is generically trivial, which implies that the Post Correspondence Problem is generically solvable in free groups. Then let G be a word hyperbolic group. We show that generically, finitely generated subgroups of G are free and quasiconvex. This is joint work with Armando Martino and Enric Ventura.

Seminar September 29th

Monday September 29th, 13:00, CRM Small room

Speaker: Francesco Matucci, CRM

Title: Centralizers in R. Thompson's groups

Abstract: R. Thompson's groups F, T and V are countable groups whose elements can be represented as homeomorphisms of a real interval, of the circle, and of the Cantor set, respectively. Elements of the groups can be represented both from a dynamical point of view and from a combinatorial one, using suitable types of diagrams. We give a classification of centralizers of elements in these groups.

We achieve this by using techniques derived from the available solutions of the conjugacy problem. Using the piecewise-linear perspective one can derive centralizers in F by observing the bumps of a map. This description can be "lifted" to centralizers in T, up to finite index. The case of V is treated using the point of view of tree diagrams and choosing a suitable representative that describes the action on the underlying Cantor set by looking at the diagram. We give combinatorial and topological applications of this description.

Seminar September 22nd

The first meeting of the Seminar in the year 2008/09.


Monday September 22nd, 13:00, CRM Small room

Speaker: Jonathan Hillman, University of Sydney

Title: Indecomposable PD3 Complexes

Abstract: $PD$-complexes model the homotopy theory of manifolds. In dimension 3, the unique factorization theorem holds in the sense that a $PD3$-complex is a connected sum if and only if its fundamental group is a free product, and the indecomposables are either aspherical or have virtually free fundamental group [Tura'ev, Crisp]. However in contrast to the 3-manifold case the group of an indecomposable may have infinitely many ends (i.e., not be virtually abelian). We shall sketch the construction of one such example, and outline some recent work using only elementary group theory that imposes strong restrictions on any other such examples.