Linear Spaces of Matrices - Avi Wigderson

Explore the fascinating world of linear spaces of matrices in this comprehensive 2-hour 13-minute seminar by Avi Wigderson, Herbert H. Maass Professor at the School of Mathematics, Institute for Advanced Study. Delve into the natural emergence of this topic across various mathematical and computer science disciplines. Examine structural and algorithmic results, both classic and contemporary, while uncovering numerous open problems in the field. Learn about alternative determinants, field polynomials, polynomial-time deterministic algorithms, singular spaces, circuits, randomization, complexity, and symbolic determinants. Gain insights into the connections between linear spaces of matrices and diverse areas such as GCT (Geometric Complexity Theory) and the permanent function. This in-depth exploration offers a valuable survey of the subject, suitable for researchers and advanced students in computer science and discrete mathematics.

Introduction
Alternative
Determinants
Field
polynomial time deterministic algorithm
singular spaces
polynomials
Circuits
Polynomial
PID
Randomization
Complexity Circuit
Reduction
Proof
Addition
Return
Permanent
The trivial robot
GCT
Symbolic determinant
Low values