| Date: | September 11, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | Krzysztof Święcicki |
| Title: | A Brief Introduction to 3 Dimensional Manifolds |
| Abstract: | 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. |
|
| Date: | September 18, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | Krzysztof Święcicki |
| Title: | 3-Manifolds |
| Abstract: | 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. |
|
| Date: | October 2, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | James O'Quinn |
| Title: | Topological full groups, amenability, and G-odometers |
| Abstract: | 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 G-odometers, following a paper of Cortez and
Medynets." |
|
| Date: | October 16, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | Amanda Hoisington |
| Title: | Coarse embeddings under group extensions I |
| Abstract: | 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. |
|
| Date: | October 18, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 605AX |
| Speaker: | Josiah Owens |
| Title: | Introduction to Ergodic Ramsey Theory |
|
| Date: | October 23, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | Nóra Gabriella Szőke, Institut Fourier |
| Title: | Extensive Amenability |
| Abstract: | 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. |
|
| Date: | October 25, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 605AX |
| Speaker: | Konrad Wrobel |
| Title: | Furstenberg Correspondence and Szemeredi's Theorem |
| Abstract: | 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. |
|
| Date: | October 30, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | Amanda Hoisington |
| Title: | Coarse embeddings under group extensions II |
| Abstract: | 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. |
|
| Date: | November 1, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 605AX |
| Speaker: | James O'Quinn |
| Title: | An Ergodic approach to Sárközi's theorem |
| Abstract: | 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. |
|
| Date: | November 13, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | Diego Martínez |
| Title: | Quasidiagonality and relations to group theory |
| Abstract: | Given a C*-algebra A we say that it is quasidiagonal if there is a sequence of finite-dimensional 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. |
|
| Date: | November 15, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 605AX |
| Speaker: | Konrad Wrobel |
| Title: | Compact Extensions of Szemeredi Factors |
|
| Date: | November 22, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 605AX |
| Speaker: | Josiah Owens |
| Title: | Weak Mixing Extensions of Szemeredi Factors |
|
| Date: | December 4, 2019 |
| Time: | 1:00pm |
| Location: | BLOC 628 |
| Speaker: | James O'Quinn |
| Title: | The Furstenberg-Zimmer structure theorem and a proof of Szemerédi's theorem |
| Abstract: | The Furstenberg-Zimmer 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 Furstenberg-Zimmer theorem using some measure theoretic techniques, and then show how Szemerédi's theorem follows from this result. |
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