Future directions in locally compact groups

TL;DR

This paper summarizes recent progress and highlights open problems in the study of locally compact groups, emphasizing the need for further exploration in this mathematical area.

Contribution

It provides an overview of recent developments in locally compact groups and outlines key open problems for future research.

Findings

Survey of recent progress in locally compact groups

Identification of significant open problems in the field

Emphasis on unexplored research directions

Abstract

This text is the preprint version of the concluding chapter for the book New Directions in Locally Compact Groups published by Cambridge University Press in the series Lecture Notes of the LMS. The recent progress on locally compact groups surveyed in that volume also reveals the considerable extent of the unexplored territories. Therefore, we wish to conclude it by mentioning a few open problems related to the material covered in the book and that we consider important at the time of this writing.