16:00
Cotlar identities for groups acting on tree like structures
Abstract
The Hilbert transform H is a basic example of a Fourier multiplier, and Riesz proved that H is a bounded operator on Lp(T) for all p between 1 and infinity. We study Hilbert transform type Fourier multipliers on group algebras and their boundedness on corresponding non-commutative Lp spaces. The pioneering work in this direction is due to Mei and Ricard who proved Lp-boundedness of Hilbert transforms on free group von Neumann algebras using a Cotlar identity. In this talk, we introduce a generalised Cotlar identity and a new geometric form of Hilbert transform for groups acting on tree-like structures. This class of groups includes amalgamated free products, HNN extensions, left orderable groups and many others. This is joint work with Adrián González and Javier Parcet.
16:00
Some algebraic aspects of minimal dynamics on the Cantor set
Abstract
By Jewett-Krieger theorems minimal dynamical systems on the Cantor set are topological analogous of ergodic systems on probability Lebesgue spaces. In this analogy and to study a Cantor minimal system, indicator functions of clopen sets (as continuous integer or real valued functions) are considered while they are mod out by the subgroup of all co-boundary functions. That is how dimension group which is an operator algebraic object appears in dynamical systems. In this talk, I try to explain a bit more about dimension groups from dynamical point of view and how it relates to topological factoring and spectrum of Cantor minimal systems.