Seminarios de teoría de grupos

El próximo lunes 27 por la tarde habrá dos seminarios de teoría de grupos, en el ICMAT a las 15 y a las 16:30.


Titulo:  A Gentle Introduction to Sofic Entropy

Speaker: Ben Hayes (Vanderbilt University)

Lugar: ICMAT, Aula gris 1.

Dia y Hora: Lunes, 27 de junio de 2016, a las 15:00.

Abstract:

Sofic entropy is a version of dynamical entropy for actions of sofic groups developed stunning and landmark of Bowen, under the mild assumption of existence of a finite generating partition. Kerr-Li later removed this assumption and defined topological entropy. Sofic entropy extends the usual dynamical entropy for amenable groups developedby Kolmogorov-Sinai and Kieffer. The class of sofic groups is vastly larger than the class of amenable groups, including all amenable groups, residually finite groups and being closed under free products with amalgamation over amenable subgroups. I wil give a basic introduction to the subject. I will also discuss my role in the subject exploring how functional analytic  techniques can play an important role in the study of entropy. Prior knowledge of sofic groups and the probabilistic notion of entropy will not be assumed.

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Titulo:  When the outer automorphism groups of RAAGs are vast.

Speaker: Andrew Sale  (Vanderbilt University)

Lugar: ICMAT, Aula gris 1.

Dia y Hora: Lunes, 27 de junio de 2016, a las 16:30.

Abstract:

Right-angled Artin groups (RAAGs) are a class of groups that bridge the gap between free groups and free abelian groups. Thus, their outer automorphism groups give a way to build a bridge between GL(n,Z) and Out(F_n). We will investigate certain properties of these groups which could be described as a "vastness" property, and ask if it possible to build a boundary between those which are "vast" and those which are not.

One such property is as follows: given a group G, we say G has all finite groups involved if for each finite group H there is a finite index subgroup of G which admits a surjection onto H. From the subgroup congruence property, it is known that the groups GL(n,Z) do not have every finite group involved for n>2. Meanwhile, the representations of Out(F_n) given by Grunewald and Lubotzky imply that these groups do have all finite groups involved. We will describe conditions on the defining graph of a RAAG that are necessary and sufficient to determine when it's outer automorphism group has this property.
This is joint work with V. Guirardel.