Proving Algebraic Identities

Explore the intricacies of proving algebraic identities in this 54-minute lecture delivered by Avi Wigderson at the 2018 AMS Colloquium Lectures during the Joint Mathematics Meetings. Delve into topics such as algebraic complexity in representing polynomials and rational functions, the complexity of determinants, and methods for solving the Polynomial Identity Testing (PIT) problem. Examine symbolic matrices singularity in the context of PIT and investigate non-commutative identities and algebra. Gain insights into invariant theory, including linear actions and left-right actions. This comprehensive presentation offers a deep dive into advanced mathematical concepts, providing a valuable resource for mathematicians and students interested in algebraic theory and its applications.

Intro
Plan
Algebraic identities
Algebraic complexity representing polynomials (& rational functions)
Complexity of Det
How to solve PIT?
PIT: symbolic matrices singularity
Non-commutative identities
Non-commutative algebra
Invariant theory Linear actions
Invariant theory Left-Right action
Summary