Sieve in discrete groups, especially sparse

TL;DR

This paper surveys recent advances in sieve methods applied to discrete groups, focusing on their use with infinite index subgroups of arithmetic groups, highlighting new developments and applications.

Contribution

It provides a comprehensive overview of recent applications and developments of sieve techniques in the context of discrete groups, especially for infinite index subgroups.

Findings

Sieve methods have been successfully applied to infinite index subgroups of arithmetic groups.

Recent developments have expanded the scope of sieve applications in discrete group theory.

The survey highlights key applications and open problems in the field.

Abstract

We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.