Seminar Calendar
for Group Theory Seminar events the year of Wednesday, November 4, 2009.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
     October 2009          November 2009          December 2009    
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Thursday, January 22, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, January 22, 2009
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Submitted by kapovitc.
Organizational meeting

Thursday, February 5, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 5, 2009
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Submitted by kapovitc.
Patrick Reynolds (Department of Mathematics, University of Illinois)
Train Tracks for Irreducible Injective Endomorphisms of the Free Group
Abstract: In their highly influential paper, Bestvina and Handel introduced train track maps for automorphisms of the free group and used these to solve the Scott Conjecture. A train track map for an (outer) automorphism \alpha \in Out(F_n) is a very nice homotopy equivalence of a finite graph G, where rank(G) = rank(F_n)=n, that induces \alpha. The train track map allows for very precise control over the cancellation that can occur in \alpha(u)*\alpha(v), where u*v is freely reduced. Since their introduction, train track maps have proven to be extremely useful in the study of individual (outer) automorphisms as well as in the study of Out(F_n) and were used essentially in the work of Bestvina-Feighn- Handel establishing the Tits Alternative for Out(F_n). We show that any expansive irreducible injective (outer) endomorphism of the free group has a train track representative with no illegal turns, giving very precise and uniform control of the growth of elements of F with respect to the endomorphism.

Thursday, February 12, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 12, 2009
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Submitted by kapovitc.
Patrick Reynolds (Department of Mathematics, University of Illinois)
Train Tracks for Irreducible Injective Endomorphisms of the Free Group, Part II
Abstract: We finish the proof that every expansive irreducible injective endomorphism of F_n has a train track representative with no illegal turns. Levitt and Lustig have introduced, for any very small tree $T$ with dense orbits, a continuous, surjective, $F_n$-equivariant map $Q: \partial F_n \rightarrow \hat&ob;T&cb;$, where $\hat&ob;T&cb; = \bar&ob;T&cb; \cup \partial T$, and $\bar&ob;T&cb;$ is the metric completion of $T$. We introduce this map, along with some basic facts about very small trees with dense orbits, and use these tools to rule out the case that a stable tree of an endomorphism is free with dense orbits.

Thursday, February 26, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 26, 2009
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Submitted by kapovitc.
Ilya Kapovich (UIUC Math)
Stabilizers in Out(F_N)
Abstract: We prove that if T is an R-tree with a minimal free isometric action of F_N the the Out(F_N)-stabilizer Stab([T]) of the projective class of [T] is virtually cyclic. This generalizes a result of Bestvina, Feighn and Handel who established this statement for the case where T=T(\phi) is an attracting stable eigentree of an iwip outer automorphism \phi\in Out(F_N). This is joint work with Martin Lustig.

Thursday, March 5, 2009

Group Theory Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, March 5, 2009
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Submitted by dsrobins.
Derek Robinson (UIUC Math)
Quotients of Generalized Baumslag-Solitar Groups
Abstract: A generalized Baumslag-Solitar group is the fundamental group of a graph of groups with infinite cyclic vertex and edge groups. After a review of known properties of GBS-groups, I will present some new results on their quotients. In particular a classification will be given of GBS-groups with few GBS-groups as quotients.

Thursday, March 12, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, March 12, 2009
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Submitted by kapovitc.
Greg Kelsey (UIUC Math)
Combinatorics of Polynomial Iterations
Abstract: We will present some recent findings of Nekrashevych regarding iterated monodromy groups of postcritically finite backward polynomial iterations. This class of groups has proven to be a rich source of examples of interesting properties relating to growth and amenability, and we provide a nice description of their actions on rooted trees and also their generating automata.

Thursday, March 19, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, March 19, 2009
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Submitted by kapovitc.
Slawomir Solecki (UIUC Math)
Ramsey theorems, concentration of measure, geometric tomography, and dynamics of Polish groups
Abstract: A topological group is called extremely amenable if all its continuous actions on compact spaces have fixed points. Many well-studied non-locally compact Polish groups are extremely amenable, for example, the unitary group of the infinite dimensional separable Hilbert space (Gromov-Milman) or the group of order preserving permutations of the rationals (Pestov). The groups of interests in this talk are of the form $L_0(\phi, H)$, where $\phi$ is a submeasure and $H$ is a locally compact, second countable group. Deciding whether $L_0(\phi, H)$ is extremely amenable depending on $\phi$ and $H$ involves the mathematical phenomena mentioned in the title. In the talk, partly based on a joint work with Ilijas Farah and partly on my own, I will explain why this is so.

Thursday, April 2, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 2, 2009
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Submitted by kapovitc.
Florin Boca (UIUC Math)
Continued fractions, the Stern-Brocot sequence, and operator algebras

Thursday, April 9, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 9, 2009
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Submitted by kapovitc.
Jerome Los (Marseille)
Bowen-Series like maps for surface groups
Abstract: In this talk the goal is to give a new construction of a Markov map on the circle whose dynamical properties reflect the action of a surface group on it's boundary, namely the group and the map are orbit equivalent. This map is well defined for every geometric presentation of the group and enable to compare the topological entropy of the map with the volume entropy of the presentation.

Thursday, April 23, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 23, 2009
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Submitted by kapovitc.
Desmond Cummings (UIUC Math)
S-Machines
Abstract: The question of whether or not a Turing machine M in a configuration c may execute a given command depends on both the state of the machine and the symbols that are close to the heads of M -- informally, the heads of the machine can "see" nearby symbols. The fact that the machine depends on its "sight" becomes an inconvenience when we try to represent Turing computation group theoretically. Sapir was able to overcome this difficulty by defining S machines and showing that they are equivalent to Turing machines in computational power and speed. We will define S-machines, give some examples, and if time permits state some very nice group theory theorems that are proven using S machines.

Thursday, April 30, 2009

Group Theory Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, April 30, 2009
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Submitted by clein.
Khalid Bou-Rabee (U. Chicago Math)
Reconstructing a Group from its Finite-Nilpotent Quotients
Abstract: Let G be a finitely generated group. My talk will focus on the following two questions: How well do finite nilpotent quotients approximate G? And when can we reconstruct G from its finite-nilpotent quotients?

Thursday, August 27, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, August 27, 2009
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Submitted by kapovitc.
Organizational meeting

Thursday, September 10, 2009

Group Theory Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, September 10, 2009
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Submitted by ivanov.
Sergei Ivanov (UIUC Math)
A property of groups and the Kurosh rank of the intersection of subgroups in free products of groups
Abstract: We will discuss the Kurosh rank of the intersection of subgroups in free products of groups and a property of groups which turns out to be useful in getting upper bounds for the Kurosh rank and which traces back to Cauchy who proved in 1813 what is now called the Cauchy-Davenport theorem.

Thursday, September 17, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, September 17, 2009
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Submitted by kapovitc.
Brent Solie (UIUC Math)
Algorithmic and Genericity Properties of Filling Elements
Abstract: Let F be a free group of finite rank. An element w in F is said to be filling if it has positive translation distance on every very small R-tree on which F acts by isometries. I will present an algorithm that identifies the filling elements in a free group of rank 2 and an algorithm that identifies a certain type of non-filling element in higher rank. I will also give a proof that almost every element of a free group is filling, based directly on the work of Kapovich, Schupp, and Shpilrain.

Thursday, October 1, 2009

Group theory seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, October 1, 2009
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Submitted by dsrobins.
Derek Robinson (Department of Mathematics, University of Illinois)
The Schur multiplier of a generalized Baumslag-Solitar group
Abstract: A generalized Baumslag-Solitar group (or GBS-group) is the fundamental group of a finite connected graph of groups whose vertex groups are infinite cyclic. It is known that the homology and cohomology of a GBS-group vanish in dimensions 3 and higher. This leaves open the question of dimensions 1 and 2, and in particular the structure of the Schur multiplier of a GBS-group. We will describe a method for computing the multiplier of an arbitrary GBS-group and then give some applications to central extensions by GBS-groups.

Thursday, October 8, 2009

Group Theory Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, October 8, 2009
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Submitted by clein.
Chris Leininger (UIUC Math)
Commensurators of of non-free Kleinian groups
Abstract: Work of Margulis shows that a lattice in PSL(2,C) is arithmetic if and only if its commensurators is indiscrete. I'll discuss joint work with Long and Reid in which we consider commensurators of finitely generated Kleinian groups which are NOT lattices.

Thursday, October 15, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, October 15, 2009
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Submitted by kapovitc.
Johanna Mangahas (University of Michigan)
"Short-word" pseudo-Anosovs
Abstract: The problem of finding "short-word" pseudo-Anosovs relates to proving effective versions of the Tits alternative for the mapping class group. I'll describe both problems, their relation, and their solutions.

Thursday, October 29, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, October 29, 2009
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Submitted by kapovitc.
Nathan Dunfield (UIUC Math)
To Be Announced
Abstract: The talk is cancelled due to the speaker's illness

Thursday, November 5, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, November 5, 2009
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Submitted by kapovitc.
Lewis Bowen (Texas A&M)
Free subgroups of lattices
Abstract: Let G be any locally compact, unimodular, metrizable group. The main result of the talk, roughly stated, is that if $F < G$ is any finitely generated free group and $\Gamma < G$ any lattice, then up to a small perturbation and passing to a finite index subgroup, F is a subgroup of $\Gamma$. This result has recently been used by Lackenby, Long and Reid to show that, for cocompact Kleinian groups, LERF implies the Lubotzky-Sarnak conjecture. Another application, due to Lackenby, is that every Kleinian group that contains a finite noncyclic subgroup is either finite, virtually free, or contains a surface subgroup.

Thursday, November 19, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, November 19, 2009
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Submitted by kapovitc.
Martin Evans (University of Alabama)
Relation Modules of Infinite Groups.
Abstract: Let A and B be relation modules of a d-generator group G, associated with presentations on $m\geq d$ generators, and let R denote the integral group ring of G. In general A and B are not isomorphic as R-modules although they are STABLY isomorphic. We discuss the minimal rank k such that the direct sum of A and the free R-module of rank k is isomorphic to the direct sum of B and the free R-module of rank k.

Thursday, December 3, 2009

Group Theory Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, December 3, 2009
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Submitted by nmd.
David Fisher (Indiana University)
To Be Announced