Non-commutative Geometry Indomitable

TL;DR

This paper provides a gentle introduction to non-commutative geometry, highlighting its historical background, motivation from local symmetries, and recent developments in applications like physics and number theory.

Contribution

It offers an accessible overview of non-commutative geometry, connecting historical context, groupoid symmetries, and recent advances for physicists and geometers.

Findings

Overview of non-commutative toric geometry

Applications to the standard model in particle physics

Connections to the Riemann Hypothesis

Abstract

This paper is a very brief and gentle introduction to non-commutative geometry geared primarily towards physicists and geometers. It starts with a brief historical description of the motivation for non-commutative geometry and then goes on to motivate the subject from the point of view of the the understanding of local symmetries affordee by the theory of groupoids. The paper ends with a very rapid survey of recent developments and applications such as non-commutative toric geometry, the standard model for particle physics and the study of the Riemann Hypothesis.