Announcements
Feb 27, 16:0017:00, Daniel Studenmund (Utah), Abstract commensurators of lattices in Lie groups
Abstract: The abstract commensurator of a group G is the group of all isomorphisms between finite index subgroups of G up to a natural equivalence relation. Commensurators of lattices in semisimple Lie groups are well understood using strong rigidity results of Mostow, Prasad, and Margulis. We will describe commensurators of lattices in solvable groups, where strong rigidity fails. If time permits, we will extend these results to lattices in certain groups that are neither solvable nor semisimple. 
Feb 20, 16:0017:00, Room 5417. Doron Puder (Princeton)
Title: Free Groups and Measure Preservation Abstract: We establish new characterizations of primitive elements and free factors in free groups, which are based on the distributions they induce on finite groups. This new characterization is related to structural phenomena in the set of f.g. subgroups of a given free group. 
Nov 21, Jennifer Taback, Bowdoin College
Quasiisometry classification of the BaumslagGersten groups I will present a quasiisometry classification of the BaumslagGersten groups. Gilbert Baumslag used a group in this family as an example of a noncyclic onerelator group all of whose finite quotients are cyclic. Gersten showed that the Dehn functions of groups in this family are bounded by towers of exponentials, and Platonov proved that each Dehn function is actually equal to a tower of exponentials. I will describe how the geometric models of these groups are constructed from different BaumslagSolitar complexes and how this geometry, combined with earlier rigidity results of Farb and Mosher for the solvable BaumslagSolitar groups BS(1,n), yields a quasiisometry classification for this family of groups which is perhaps more rigid than expected. I'll include a brief overview of quasiisometry classification and rigidity results for other families of groups whose geometric models are constructed from BaumslagSolitar complexes. This is joint work with Tullia Dymarz. 
Nov 14, Yash Lodha, Cornell University, Room 5417
A new solution to the Van NeumannDay Problem for finitely presented groups 
Nov 7. Tim Riley Cornell University, (Room 5417)
Taming the hydra: the word problem and extreme integer compression For a finitely presented group, the Word Problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is the timecomplexity of a direct attack on the Word Problem by applying the defining relations. A "hydra phenomenon" gives rise to novel groups with extremely fast growing (Ackermannian) Dehn functions. I will explain why, nevertheless, there are efficient (polynomial time) solutions to the Word Problems of these groups. The main innovation is a means of computing efficiently with compressed forms of enormous integers. This is joint work with Will Dison and Eduard Einstein. 
NYGT Seminar, Oct 31, Martin Bridson, U. of Oxford
TITLE: Grothendieck pairs and the Infinite Genus Problem Abstract: It has been known since the 1970s that there exist pairs of finitely presented (fp), residually finite (rf) groups H,G that are not isomorphic but have the same finite quotients  i.e. have the same profinite genus. Gilbert Baumslag produced early examples, which were nilpotent. It was also proved at that time that in the nilpotent and related settings, there can be only finitely many fp groups in a given genus. It remained unknown whether, in a more general setting, there might exist genera containing infinitely many nonisomorphic fp, rf groups. In 2004 Fritz Grunewald and I constructed the first Grothedieck pairs, i.e. pairs as above but with H<G such that the inclusion map induces an isomorphism of profinite completions. In this lecture I'll explain how refinements of our construction can be combined with recent advances in the understanding of finiteness properties for fibre products and classical ideas around Nielsen equivalence to construct infinite classes of fp, rf groups that all lie in the same (strong) profinite genus. (the talk will be held at the Science Center) 
NYGT Seminar, Oct 24. Tatiana SmirnovaNagnibeda, University of Geneva
About subgroups in Grigorchuk’s group
Abstract. I’ll survey some old and new results about the subgroup structure of Grigorchuk’s group of intermediate growth. Remark: The talk will be held at the Science Center on the 4th floor at GC
