Student Working Seminar in Groups and Dynamics
Organizers:
David Carroll (carroll math.tamu.edu)
Krzysztof Swiecicki (ksas math.tamu.edu)
The Student Working Seminar in Groups and Dynamics is an informal, studentrun seminar that meets approximately
once a week to discuss topics related to group theory and dynamical systems. Talks are at the graduate/postdoctoral
level and can be presentations of original results, exposition of the literature, or simply openended
conversations. If you would like to give a talk or be added to the mailing list, please email one of the organizers.
This semester (Fall 2015), the seminar will meet weekly on Mondays from 34 PM in Blocker 624.

Date Time 
Location  Speaker 
Title – click for abstract 

09/11 1:00pm 
BLOC 628 
Krzysztof Święcicki 
A Brief Introduction to 3 Dimensional Manifolds
In his celebrated work from 2003, Perelman finished the proof
of Poincare conjecture in dimension 3. His result is in fact far
stronger and implies Thurston's geometrization conjecture, which
classifies possible geometric structures on 3 manifolds. I'll give an
overview of the result and introduce all eight basic geometries and
their connection to group theory. I won't assume any knowledge outside
of basic topology, so any newcomers are welcome. 

09/18 1:00pm 
BLOC 628 
Krzysztof Święcicki 
3Manifolds
In his celebrated work from 2003, Perelman finished the proof of Poincare conjecture in dimension 3. His result is in fact far stronger and implies Thurston's geometrization conjecture, which classifies possible geometric structures on 3 manifolds. I'll give an overview of the result and introduce all eight basic geometries and their connection to group theory. I won't assume any knowledge outside of basic topology, so any newcomers are welcome. 

10/02 1:00pm 
BLOC 628 
James O'Quinn 
Topological full groups, amenability, and Godometers
Topological full groups were first introduced by
Giordano,Putnam, and Skau as an invariant related to orbit equivalence
for minimal cantor systems. However, more recent interest has been given
to these groups because they provide examples of groups with interesting
properties related to amenability. In this talk, I will give an overview
of some of the basic concepts of topological dynamics, as well as
introduce topological full group and the concept of amenability. The
goal is to explicitly describe the structure of the topological full
groups coming from Godometers, following a paper of Cortez and
Medynets." 

10/16 1:00pm 
BLOC 628 
Amanda Hoisington 
Coarse embeddings under group extensions I
I will be going over a paper by Arzhantseva and Tessera (2017)
which proves, by construction, that admitting a coarse embedding into
Hilbert space is not preserved under group extension. 

10/18 3:00pm 
BLOC 605AX 
Josiah Owens 
Introduction to Ergodic Ramsey Theory 

10/23 1:00pm 
BLOC 628 
Nóra Gabriella Szőke Institut Fourier 
Extensive Amenability
A group action is called amenable if there exists an invariant mean on the space. In this talk I will present a stronger property, namely the extensive amenability of group actions. This property was introduced by Juschenko and Monod, they used it to construct the first examples of finitely generated infinite amenable simple groups. We will discuss some properties of extensive amenability and see an application for topological full groups. 

10/25 3:00pm 
BLOC 605AX 
Konrad Wrobel 
Furstenberg Correspondence and Szemeredi's Theorem
I will present a very rough outline of Furstenberg's proof of Szemeredi's theorem. In doing so, I plan to translate the problem into a problem in ergodic theory and outline the classification of measure preserving systems due to Furstenberg and Zimmer. 

10/30 1:00pm 
BLOC 628 
Amanda Hoisington 
Coarse embeddings under group extensions II
I will be going over a paper by Arzhantseva and Tessera (2017) which proves, by construction, that admitting a coarse embedding into Hilbert space is not preserved under group extension. 

11/01 3:00pm 
BLOC 605AX 
James O'Quinn 
An Ergodic approach to Sárközi's theorem
In order to demonstrate the usefulness of ergodic theory techniques to
solve problems in number theory, I will present a proof for a general
version of Sárközi's theorem using basic techniques in ergodic theory.
This also gives an example of Furstenberg's Correspondence principle
discussed in the previous talk. 

11/13 1:00pm 
BLOC 628 
Diego Martínez 
Quasidiagonality and relations to group theory
Given a C*algebra A we say that it is quasidiagonal if there is a sequence of finitedimensional almost representations that are almost isometric. Even though this seems to be a very C*algebraic definition, it has proven useful in many other areas, such as geometric group thery, index theory and numerical analysis. In this introductory talk we'll discuss how quasidiagonality is related to those contexts, and the role quasidiagonality has had in the theory of operator algebras. 

11/15 3:00pm 
BLOC 605AX 
Konrad Wrobel 
Compact Extensions of Szemeredi Factors 

11/22 3:00pm 
BLOC 605AX 
Josiah Owens 
Weak Mixing Extensions of Szemeredi Factors 

12/04 1:00pm 
BLOC 628 
James O'Quinn 
The FurstenbergZimmer structure theorem and a proof of Szemerédi's theorem
The FurstenbergZimmer structure theorem is a way to partially recover the dichotomy between weak mixing and compact vectors inherent in the study of unitary representations of groups into the p.m.p. action setting. During this talk, I will prove one version of the FurstenbergZimmer theorem using some measure theoretic techniques, and then show how Szemerédi's theorem follows from this result. 