# Groups and Dynamics Seminar

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

Date Time |
Location | Speaker | Title – click for abstract | |
---|---|---|---|---|

01/253:00pm |
BLOC 302 | Nataliya Goncharuk Texas A&M University |
Renormalization operators and Arnold tongues | |

02/013:00pm |
zoom | Volodymyr Nekrashevych Texas A&M University |
Conformal dimension and other numerical invariants of self-similar groups |

## 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).