Pointwise ergodic theorems for actions of groups

TL;DR

This survey reviews recent progress in pointwise ergodic theorems for measure-preserving group actions, highlighting solutions to longstanding open problems and recent advances in ergodic theory.

Contribution

It compiles and explains the latest developments and solutions to open problems in pointwise ergodic theorems for locally compact group actions.

Findings

Resolution of several longstanding open problems

Introduction of new techniques in ergodic theory

Recent solutions not previously published

Abstract

The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long standing open problems in ergodic theory, some of which are very recent and have not yet appeared elsewhere.