# Tomasz Downarowicz (Wroclaw) Multiorder in countable amenable groups; a promising new tool in entropy theory.

Abstract: Let G be a countable group. A mutliorder is a collection of
bijections from G to Z (the integers) on which G acts by a special
"double shift". If G is amenable, we also require some uniform Folner
property of the order intervals. The main thing is that mutiorder exists
on every countable amenable group, which can be proved using tilings.
For now, multiorder provides an alternative formula for entropy of a
process and we are sure in the nearest future it will allow at produce
an effective formula for the Pinsker sigma-algebra. And we hope for
many more applications.

This is work in progress with Piotr Oprocha (Kraków) and Guohua
Zhang (Shanghai).

## Date:

Tue, 21/04/2020 - 14:00 to 15:00

## Location:

E-seminar Zoom meeting ID 914-412-92758