| Date: | January 29, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Tianyi Zheng, UCSD |
| Title: | Properties and construction of FC-central extensions |
| Abstract: | We discuss a few properties of groups that are preserved under FC-central extensions. Various examples of FC-central extensions of groups constructed via taking diagonal products of marked groups will be explained.
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| Date: | February 5, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Arman Darbinyan, TAMU |
| Title: | Subgroups of left-orderable simple groups |
| Abstract: | Answering an old question of Rhemtulla, Hyde and Lodha (and later, Matte Bon and Triestino) showed the existence of finitely generated left-orderable simple groups. I will discuss how to extend the result of Hyde and Lodha to show that any countable left-orderable group is a subgroups of a finitely generated left-orderable simple group. Certain computability aspects will also be discussed. Based on a joint work with M.Steenbock.
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| Date: | February 12, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Florent Baudier, Texas A&M |
| Title: | On the metric geometry of the planar lamplighter group |
| Abstract: | In 2011, Naor and Peres showed that the L1-compression of the lamplighter group over a group of polynomial growth is 1. In particular, Naor-Peres embedding resul applies to the planar lamplighter group, and they raised the question whether the planar lamplighter group admits a bi-Lipschitz embedding into L1. I will briefly discuss the connection of the embedding problem with Jones' traveling salesman theorem and present some recent progress obtained in collaboration with P. Motakis (UIUC), Th. Schlumprecht (Texas A&M), and A. Zsàk (Peterhouse,
Cambridge). |
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| Date: | February 19, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Jintao Deng, Texas A&M |
| Title: | The Novikov conjecture and group extensions |
| Abstract: | The Novikov conjecture is an important problem in higher dimensional topology. It claims that the higher signatures of a compact smooth manifold are invariant under orientation preserving homotopy equivalences. The Novikov conjecture is a consequence of the strong Novikov conjecture in the computation of the K-theory of group C^*-algebras. In this talk, I will talk about the Novikov conjecture for groups which are extensions of coarsely embeddable groups. |
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| Date: | February 26, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Yuri Bakhturin, Memorial University of Newfoundland |
| Title: | Actions of maximal growth |
| Abstract: | We study acts and modules of maximal growth over finitely generated free monoids and free associative algebras as well as free groups and free group algebras. The maximality of the growth implies some other specific properties of these acts and modules that makes them close to the free ones; at the same time, we show that being a strong "infiniteness" condition, the maximality of the growth can still be combined with various finiteness conditions, which would normally make finitely generated acts finite and finitely generated modules finite-dimensional. (Joint work with Alexander Olshanskii) |
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| Date: | March 18, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | David Kerr, Texas A&M |
| Title: | (Talk is cancelled due to epidemics) |
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| Date: | March 25, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Bin Sun, UC Riverside |
| Title: | (Talk is cancelled due to epidemics) |
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| Date: | April 29, 2020 |
| Time: | Noon |
| Location: | https://tamu.zoo |
| Speaker: | Volodymyr Nekrashevych, Texas A&M |
| Title: | Conformal dimension and iterated monodromy groups |
| Abstract: | ZOOM Meeting ID: 940 9667 3668
We will discuss a connection between Ahlfors-regular conformal
dimension of Julia sets and algebraic properties of the corresponding
iterated monodromy groups. We will associate a number called "critical
exponent" of a self-similar contracting group and prove that the
conformal dimension is an upper bound on the critical exponent.
Relation between critical exponent and such group properties as
growth, word problem, and amenability will be discussed. For example,
one can prove that the word problem of the iterated monodromy group of
a complex rational function is polynomial of degree bounded from above
by the Hausdorff dimension of the Julia set.
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| Date: | May 6, 2020 |
| Time: | Noon |
| Location: | ZOOM ID: ID: 940 |
| Speaker: | Bin Sun, UC Riverside |
| Title: | Acylindrical hyperbolicity of non-elementary convergence groups |
| Abstract: | The notion of a convergence group was introduced by Gering and Martin in order to study Kleinian groups through the dynamical properties of their actions on the ideal sphere of H^3. The works of Bowditch, Freden, Tukia, and Yaman reveal the close relationship between convergence groups and hyperbolic and relatively hyperbolic groups. Along this line of ideas, we show that non- elementary discrete convergence groups are acylindrically hyperbolic. Our result implies that various techniques in the theory of acylindrically hyperbolic groups, such as the Monod-Shalom rigidity theory, group theoretic Dehn filling, and small cancellation theory, can be applied to the study of non-elementary discrete convergence groups.
ZOOM ID: ID: 940 9667 3668 |
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| Date: | May 13, 2020 |
| Time: | Noon |
| Location: | 940 9667 3668 |
| Speaker: | Joshua Frisch, Caltech |
| Title: | The Poisson Boundary and the ICC property |
| Abstract: | The Poisson Boundary of a random walk on a group is a space which describes the set of possible tail behaviors of the random walk. It has long been known that abelian and nilpotent groups always have trivial Poisson Boundary (groups with this property are called Choquet Deny) and that non-amenable groups never have trivial Poisson Boundary. In this talk I will define the Poisson Boundary, discuss some of these results and prove a new one, classifying exactly which groups are Choquet Deny. This is joint work with Yair Hartman, Omer Tamuz, and Pooya Vahidi Ferdowsi.
ZOOM ID: 940 9667 3668 |
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