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Texas A&M University
Mathematics

Groups and Dynamics Seminar

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

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  Date
  Time
LocationSpeaker Title click for abstract
iCal 06/03
  Noon
940 9667 3668 Andrew Marks
UCLA
Measurable realizations of abstract systems of congruence
iCal 06/10
  Noon
940 9667 3668 Mark Sapir
Vanderbilt U.
Groups with quadratic Dehn function and undecidable conjugacy problem
iCal 06/17
  Noon
940 9667 3668 Bogdan Stankov
ENS, Paris
Non-triviality of the Poisson boundary of certain random walks with finite first moment
iCal 06/24
  Noon
940 9667 3668 Nicolás Matte Bon
ETH Zürich
A commutator lemma for confined subgroups and URS's and application to groups acting on rooted trees.

group picture

Topics

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).

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