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

Authors:
Peter Bürgisser;J. M. Landsberg;Laurent Manivel;Jerzy Weyman
Affiliations:
pbuerg@upb.de;jml@math.tamu.edu;Laurent.Manivel@ujf-grenoble.fr;j.weyman@neu.edu
Venue:
SIAM Journal on Computing
Year:
2011

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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.