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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 09/13
BLOC 220 Robin Tucker-Drob
Texas A&M
Invariant means and inner amenable groups
iCal 09/20
BLOC 220 Volodymyr Nekrashevych
Texas A&M
Amenability of iterated monodromy groups for some complex rational functions


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).

Previous Semesters

Spring 200820072006200520042003
Fall 200820072006200520042003