Mixing, wine, and serendipity

TL;DR

This paper discusses the concept of mixing in ergodic theory, highlighting a significant result that 2-mixing implies mixing of all orders for certain group actions, and shares a personal narrative about the author's interest in the topic.

Contribution

It explains the historical development of mixing properties in ergodic theory and the influence of chance encounters on mathematical research.

Findings

2-mixing implies mixing of all orders for commuting automorphisms of connected groups

Historical insight into ergodic theory development

Personal account of research inspiration

Abstract

Mixing for measure-preserving group actions is a fundamental notion in ergodic theory, with different phenomena arising for different acting groups. In 1993, Klaus Schmidt and Tom Ward proved that 2-mixing implies mixing of all orders for actions by commuting automorphisms of connected groups. Tom Ward explains how he became interested in this problem, and describes how a chance encounter with a paper on a seemingly unrelated problem in number theory played a key role.