New York Group Theory Seminar

• gilbert.baumslag@gmail.com
• Sean Cleary
• Vladimir Shpilrain

The Group Theory Seminar is organized by the New York Group Theory Cooperative.

All talks

• Friday, November 20, 2009, 04:15PM, CUNY Graduate Center: 365 Fifth Avenue at 34th Street, 5th Floor, Room 5417

  Tatiana Smirnova-Nagnibeda (Université de Genève), Schreier graphs of self-similar groups

  Given an action of a group $G$ on a set $X$, and a generating set $S $ of $G$, one can define the Schreier graph $\Gamma(G,S,X)$ with the vertex set $X$ and the edge set consisting of pairs of vertices $(x,y)$ such that there exists $s\in S\cup S^{-1}$ with $s\cdot x=y$. We shall be interested in self-similar groups, defined by their actions by automorphisms on a regular rooted tree. Such an action preserves the levels of the tree and induces also an action of $G$ on the boundary of the tree. First examples of corresponding families of finite and infinite Schreier graphs were considered by R.Grigorchuk et al as a source of interesting new examples of spectral computations. I shall report on recent progress in our understanding of this class of graphs, with both new examples and general results.

  Tea will be served at 3:30 in the Mathematics Lounge

• Friday, November 13, 2009, 04:15PM, CUNY Graduate Center: 365 Fifth Avenue at 34th Street, 5th Floor, Room 5417

  Dmytro Savchuk (Binghamton University), Automata generating free products of groups of order 2

  We construct a family of automata with n states, n>3, acting on a rooted binary tree that generate the free products of cyclic groups of order 2. This family generalizes the so-called Bellaterra automaton, which is a 3-state automaton generating the free product of 3 groups of order 2. I will give short exposition of the history of this question, explain the construction and main ideas behind the proof. This is a joint result with Yaroslav Vorobets of Texas A&M University.

• Friday, November 06, 2009, 04:15PM, CUNY Graduate Center: 365 Fifth Avenue at 34th Street, 5th Floor, Room 5417

  Lucas Sabalka (Binghamton University), Braid Groups on Graphs

  One class of groups of great importance is Artin's classical and much studied braid groups. These groups may be defined topologically, in terms of configurations of points on a disk. A natural generalization of classical braid groups is to replace the disk with other spaces. This leads us to consider braid groups on graphs. In this talk, we will discuss the definition of graph braid groups and give a survey of some known results. In particular, we will discuss the relationship between graph braid groups and right- angled Artin groups, and possibly the isomorphism problem for certain tree braid groups.

• Friday, October 30, 2009, 04:15PM, CUNY Graduate Center: 365 Fifth Avenue at 34th Street, 5th Floor, Room 5417

  Tullia Dymarz (Yale University), Bilipschitz equivalence is not equivalent to quasi-isometric equivalence for finitely generated groups

  We show that certain lamplighter groups that are quasi-isometric (even commensurable) are nevertheless not bilipschitz equivalent. The proof involves structure of quasi-isometries from rigidity theorems, analysis of bilipschitz maps of the n-adics and uniformly finite homology.

• Friday, October 23, 2009, 04:15PM, CUNY Graduate Center: 365 Fifth Avenue at 34th Street, 5th Floor, Room 5417

  Alexei Miasnikov (McGill University), Limits of groups, Cantor-Bendixon rank, and Krull dimension

  The Gromov-Hausdorff-Grigorchuk topology provide a very efficient way to measure similarity of finitely generated groups. Thus limits of free groups are obviously “free-like” groups, while limits of finite groups are “approximately finite” groups, etc. It turns out that this geometric similarity (on the level of the Cayley graphs) can be expressed also in model-theoretic terms (in the language of universal sentences), as well as in the language of algebraic –geometry (via the coordinate groups of irreducible varieties). In this talk I would like to go a bit further and discuss relations between some logic al, topological and algebraic invariants of a given group that naturally occur in this framework.