Groups and Dynamics Seminar
2019 - 2020
RLM 10.176, Friday from 2 to 3 pm
10/11 Rostislav Grigorchuk.
Title: Spectra of graphs and groups.
Abstract: First I will give a short account of what is known about spectrum of discrete Laplace operator on infinite regular graphs and groups.
Then I will discuss the question of Valette and Fujiwara "Can one hear the shape of a group?"
And finally, using the lamplighter group I will explain that the spectrum of the group can have infinitely many gaps.
The relation of the spectral theory of graphs and groups with other topics, in particular with L^2-Betti numbers and random Schrodinger operators, also will be mention if the time permit.
Title: Free harmonic analysis and hyperbolic geometry.
09/13 John Chaika. TBA
Title: A prime system with many and big self-joinings
Abstract: Let (X,mu,T) be a measure preserving system. A factor is a
system (Y,nu,S) so that there exists F with SF=FT and so that F pushes mu
forward to nu. A measurable dynamical system is prime if it has no
non-trivial factors. A classical way to prove a system is prime is to show
it has few self-joinings, that is, few T x T invariant measures that on X
x X that project to mu. We show that there exists a prime transformation
that has many self-joinings which are also large. In particular, its
ergodic self-joinings are dense in its self- joinings and it has a
self-joining that is not a distal extension of itself. As a consequence we
show that being quasi-distal is a meager property in the set of measure
preserving transformations, which answers a question of Danilenko. This is
joint work with Bryna Kra.
09/06 Anthony Quas.
Title: Lyapunov spectral stability and collapse for random composition of Blaschke Products
Abstract: We consider random dynamical systems where at each stage one applies a Blaschke product.
Motivated by questions on mixing of invariant measures on the unit circle, we study the composition
of the associated Perron-Frobenius operators, acting on a Hardy space. We describe the complete
Lyapunov spectrum, and address questions of stability of the spectrum under perturbations to
the operator cocycle.
Room on the 11th floor, Monday 10 am to 2 pm
08/19 Max Chaudkhari.
Title: Superharmonic functions and Northshield's criterion of amenability.
Abstract: We will discuss an extension of Northshield's criterion of amenability to group actions and its applications. In particular, we will describe a new approach to the study of amenability of Thompson's group $F$. The talk is based on a recent preprint by Maksym Chornyi: arxiv