An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to $\mathbf{VP}\neq\mathbf{VNP}$

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 analogue of the $\mathbf{P}\neq\mathbf{NP}$ conjecture. We also describe the precise separation of complexity classes that their program proposes to demonstrate.