Events & Seminars

2016 Jun 16

Amitsur Algebra: Gili Golan, "The generation problem in Thompson group F"

12:00pm to 1:15pm

Location: 

Manchester Building (room 209), Jerusalem, Israel
We show that the generation problem in Thompson group F is decidable, i.e., there is an algorithm which decides if a finite set of elements of F generates the whole F. The algorithm makes use of the Stallings 2-core of subgroups of F, which can be defined in an analogue way to the Stallings core of subgroups of a free group. An application of the algorithm shows that F is a cyclic extension of a group K which has a maximal elementary amenable subgroup B. The group B is a copy of a subgroup of F constructed by Brin.
2016 Apr 07

Amitsur Algebra: Ayala Byron (HUJI), "Definable fields in the free group"

12:00pm to 1:15pm

Location: 

Manchester Building (room 209), Jerusalem, Israel
Abstract: In the early 2000s Sela proved that all non-abelian free groups share a common first-order theory. Together with R. Sklinos, we use tools developed in his work to show that no infinite field is definable in this theory. In this talk we will survey the line of proof for a formal solution theorem for a simple sort of definable sets, that have a structure of a hyperbolic tower, and use it to characterize definable sets that do not carry a definable structure of an abelian group.
2017 Apr 27

Group actions: Yair Glasner (BGU) - On Highly transitive permutation representations of groups. 

10:30am to 11:30am

Location: 

Ross 70
Abstract: A permutation representation of a group G is called highly transitive if it is transitive on k-tuples of points for every k. Until just a few years ago groups admitting such permutation representations were thought of as rare. I will focus on three rather recent papers: G-Garion, Hall-Osin, Gelander-G-Meiri (in preparation) showing that such groups are in fact very common.
2017 Nov 02

Group actions: Remi Coulon (Rennes) - Growth gap in hyperbolic groups and amenability

10:30am to 11:30am

Location: 

hyperbolic groups and amenability
(joint work with Françoise Dal'Bo and Andrea Sambusetti) Given a finitely generated group G acting properly on a metric space X, the exponential growth rate of G with respect to X measures "how big" the orbits of G are. If H is a subgroup of G, its exponential growth rate is bounded above by the one of G. In this work we are interested in the following question: what can we say if H and G have the same exponential growth rate? This problem has both a combinatorial and a geometric origin. For the combinatorial part, Grigorchuck and Cohen

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