An overview of mathematical issues arising in the Geometric complexity theory approach to VP v.s. VNP

TL;DR

This paper reviews geometric and algebraic methods in Geometric Complexity Theory, focusing on orbit closures and Kronecker coefficients, to address fundamental questions in algebraic complexity class separations.

Contribution

It provides an overview of the mathematical issues in GCT related to VP versus VNP, emphasizing orbit closure geometry and asymptotic Kronecker coefficient behavior.

Findings

Analysis of orbit closure geometry in GCT

Insights into asymptotic Kronecker coefficients

Proposed complexity class separation framework

Abstract

We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker coefficients in the context of the Geometric Complexity Theory program to prove a variant of Valiant's algebraic analog of the P not equal to NP conjecture. We also describe the precise separation of complexity classes that their program proposes to demonstrate.