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Texas A&M University

Groups and Dynamics Seminar

Organizers: Rostislav Grigorchuk, Volodia Nekrashevych, Zoran Šunić, and Robin Tucker-Drob.

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LocationSpeaker Title click for abstract
iCal 02/06
BLOC 220 Nicolas Matte Bon
ETH Zurich
Orderable groups arising from Cantor dynamical systems
iCal 02/13
BLOC 220 Sarah Witherspoon
Texas A&M
Koszul algebras
iCal 02/27
BLOC 220 Rostislav Grigorchuk
Texas A&M
Spectra of graphs and groups
iCal 03/06
BLOC 628 Brian Simanek
Spectral Theory of Graph Laplacians and Orthogonal Polynomials
iCal 03/08
BLOC 628 Sr. Selim Sukhtaiev
Rice University
Localization for Anderson Models on Metric and Discrete Tree Graphs
iCal 03/13
BLOC 220 Dmytro  Savchuk 
University of South Florida, Tampa
The duality of the affine actions on trees

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GENERAL PROBLEMS Burnside Problem on torsion groups, Milnor Problem on growth, Kaplanski Problems on zero divisors, Kaplanski-Kadison Conjecture on Idempotents, and other famous problems of Algebra, Low-Dimensional Topology, and Analysis, which have algebraic roots.

GROUPS AND GROUP ACTIONS Group actions on trees and other geometric objects, lattices in Lie groups, fundamental groups of manifolds, and groups of automorphisms of various structures. The key is to view everything from different points of view: algebraic, combinatorial, geometric, and probabalistic.

RANDOMNESS Random walks on groups, statistics on groups, and statistical models of physics on groups and graphs (such as the Ising model and Dimer model).

COMBINATORICS Combinatorial properties of finitely-generated groups and the geometry of their Caley graphs and Schreier graphs.

GROUP BOUNDARIES Boundaries of finitely generated groups: Freidental, Poisson, Furstenberg, Gromov, Martin, etc., boundaries.

AUTOMATA Groups, semigroups, and finite (and infinite) automata. This includes the theory of formal languages, groups generated by finite automata, and automatic groups.

DYNAMICS Connections between group theory and dynamical systems (in particular the link between fractal groups and holomorphic dynamics, and between branch groups and substitutional dynamical systems).

FRACTALS Fractal mathematics, related to self-similar groups and branch groups.

COHOMOLOGY Bounded cohomology, L^2 cohomology, and their relation to other subjects, in particular operator algebras.

AMENABILITY Asymptotic properties such as amenability and superamenability, Kazhdan property T, growth, and cogrowth.

ANALYSIS Various topics in Analysis related to groups (in particular spectral theory of discrete Laplace operators on graphs and groups).