| Date: | February 6, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Nicolas Matte Bon, ETH Zurich |
| Title: | Orderable groups arising from Cantor dynamical systems |
| Abstract: | To every homeomorphism of the Cantor set, we associate a group of
homeomorphisms of the real line. It is defined by an action on the mapping
torus of the dynamical system which preserve each orbit of the suspension
flow. I will explain how this produces a class of finitely generated simple
groups of homeomorphisms of the real line, and investigate further properties
of this construction. |
|
| Date: | February 13, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Sarah Witherspoon, Texas A&M |
| Title: | Koszul algebras |
| Abstract: | We will give several equivalent definitions of Koszul algebras, with examples. |
|
| Date: | February 27, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Rostislav Grigorchuk, Texas A&M |
| Title: | Spectra of graphs and groups |
| Abstract: | After a short introduction in the spectral theory of graphs and groups I will show that the spectrum of a group can have infinitely many gaps. Joint work with Brian Simanek. |
|
| Date: | March 6, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 628 |
| Speaker: | Brian Simanek, Baylor |
| Title: | Spectral Theory of Graph Laplacians and Orthogonal Polynomials |
| Abstract: | Our main object of interest is the spectrum of the discrete Laplacian on the Cayley graph of the Lamplighter Group. We will show how the spectral theory of orthogonal polynomials is relevant to the determination of this spectrum and present some calculations that provide new examples of spectral phenomena. Based on joint work with R. Grigorchuk. |
|
| Date: | March 8, 2019 |
| Time: | 1:50pm |
| Location: | BLOC 628 |
| Speaker: | Sr. Selim Sukhtaiev, Rice University |
| Title: | Localization for Anderson Models on Metric and Discrete Tree Graphs |
| Abstract: | In this talk I will discuss spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies. All results are proved under the minimal hypothesis on the type of disorder: the random variables generating the trees assume at least two distinct values. This level of generality, in particular, allows us to treat radial trees with disordered geometry as well as Schr\"odinger operators with Bernoulli-type singular potentials. This is based on joint work with D. Damanik and J. Fillman. [Note: this is a joint seminar with the Mathematical Physics and Harmonic Analysis Seminar] |
|
| Date: | March 13, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Dmytro Savchuk , University of South Florida, Tampa |
| Title: | The duality of the affine actions on trees |
| Abstract: | Every action on a tree given by a (finite) automaton has an
associated dual action given by the dual automaton. In this talk I will
consider the affine groups of subrings of a global function field,
construct their actions on a regular tree, and describe the dual action.
In particular, this gives a natural family of bireversible automata. The
talk is based on a joint work with Ievgen Bondarenko. |
|
| Date: | April 30, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Mark Shusterman, UW Madison |
| Title: | Balanced presentations for fundamental groups of curves over finite fields |
| Abstract: | We show that the algebraic fundamental group of a smooth projective curve over a finite field admits a finite topological presentation where the number of relations does not exceed the number of generators. |
|
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