Geometric Complexity Theory: an introduction for geometers

TL;DR

This paper introduces Geometric Complexity Theory (GCT), a geometric approach to tackling fundamental computational complexity questions like P vs. NP, providing an accessible survey for graduate students and highlighting open problems in algebraic geometry and representation theory.

Contribution

It offers an accessible tutorial and survey of GCT, connecting algebraic geometry and representation theory to complexity theory, and presents open questions in the field.

Findings

Survey of recent GCT developments

Identification of open problems in algebraic geometry

Tutorial aimed at graduate students

Abstract

This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). It is written to be accessible to graduate students. Numerous open questions in algebraic geometry and representation theory relevant for GCT are presented.