Optimization, Complexity and Math - Can We Prove P!=NP by Gradient Descent?

Explore the intersection of optimization, complexity theory, and mathematics in this 55-minute seminar presented by Avi Wigderson from the Institute for Advanced Study. Delve into the intriguing question of whether gradient descent can prove P≠NP. Begin with an introduction to Perfect Matchings (PMs) and their relationship to symbolic matrices, as explored by Edmonds in 1967. Examine the dual life of symbolic matrices and the concept of matrix scaling. Analyze the algorithm for matrix scaling before transitioning to operator scaling, with a focus on Gurvits' 2004 quantum leap in the field. Investigate the operator scaling algorithm and its applications across six different areas and problems, as discussed in GGOW15-16. Explore connections to invariant theory before concluding with open problems and future directions in this fascinating area of applied geometry and algebra.

Intro
Perfect Matchings (PMs)
PMs & symbolic matrices [Edmonds'67]
Symbolic matrices dual life
Matrix Scaling
Analysis of the algorithm
Operator Scaling Gurvits '04 a quantum leap
Operator scaling algorithm
6 areas, 6 problems GGOW15-16
Invariant theory
Conclusions & Open Problems