Unlikely intersections in Shimura varieties and beyond: a survey

TL;DR

This survey introduces the problems of unlikely intersections in Shimura varieties, reviews recent advances, and discusses broader contexts and related results in the field.

Contribution

It provides a concise overview of unlikely intersection problems in Shimura varieties and summarizes current research developments.

Findings

Summarizes key results in unlikely intersections for Shimura varieties

Discusses extensions to more general settings

Highlights open problems and future directions

Abstract

The aim of this note is to provide a concise introduction to so-called problems of unlikely intersections for (pure) Shimura varieties and to review the current state-of-the-art. In the process, we will touch upon more general settings and some of the results in those contexts.