Non-abelian fundamental groups in arithmetic geometry

TL;DR

This paper introduces the role of non-abelian fundamental groups in arithmetic geometry, highlighting their significance in modern mathematical research and motivation for ongoing studies.

Contribution

It provides an accessible overview of non-abelian fundamental groups and their importance in arithmetic geometry for a broad mathematical audience.

Findings

Highlights the connection between non-abelian fundamental groups and arithmetic geometry

Motivates further research in the area

Serves as an accessible introduction for non-specialists

Abstract

This is a brief exposition of the mathematical themes that motivate the special programme at the Newton Institute in 2009. It is mostly intended for the general public having mathematical training up to the level of secondary school.