Description
Speaker: Professor Parthanil Roy
Date: April 20, 2022
Time: 16.00 - 17.00
Venue: Ramanujan Hall at the Department of Mathematics.
Title: Amenable groups, von-Neumann algebras and ergodicity of stable
random fields
Abstract: In this work, it is established that the group measure space
construction corresponding to a minimal representation is an invariant
of a stationary symmetric stable random field indexed by any countable
group G. When G is amenable, we characterize ergodicity of stable fields
in terms of the central decomposition of this crossed product von
Neumann algebra coming from any (not necessarily minimal) Rosinski
representation. This shows that ergodicity is a W^*-rigid property (in a
suitable sense) for this class of fields.
The first part of this talk will focus on the following work of the
speaker: arXiv:2007.14821. The second part will be based on an ongoing
joint work with Mahan Mj (TIFR Mumbai) and Sourav Sarkar (University of
Cambridge).