Research interests


My main interest is probability measures on algebraic structures with main attention
on real and p-adic Lie groups, various classes of groups such as Moore, MAP,
groups of polynomial growth, etc., and Gelfand pairs and hypergroups.

I consider the following:
Action of automorphism groups on the space of probability measures on groups which
leads to the study of decomposable measures, stable and semi-stable probability measures, limit theorems;
Questions in dynamical systems related distal, ergodic and proximal, etc., ;
Questions related to convolution powers of probability measures on various algebraic structures;
Arithmetic of probability measures on Gelfand pairs, especially Khinchin theorems;
Existence of recurrent random walks on groups and sufficient conditions for random walks to be recurrent;
The Choquet-Deny theorem, the non-existence of non-constant bounded continuous harmonic functions
on groups and Poisson boundary of probability measures on locally compact groups;
Convergence of averages of unitary representations of various classes of groups and related questions;
Various convergence of averages of finite-dimensional representations;
Ergodic theory on groups and algebraic dynamical systems;
Structure theory of Lie groups and algebraic groups over real and p-adic fields.
I have general interests in abstract harmonic analysis on locally compact groups, especially
unitary representations, abelian groups and Gelfand pairs.