Bowen Lectures: Lecture 1: Mathematics and Computation (through the lens of one problem and one algorithm). The problem, the algorithm and the connections.

Lecture | February 7 | 4:10-5 p.m. | Calvin Laboratory (Simons Institute for the Theory of Computing), Auditorium

 Avi Wigderson, Institute for Advanced Study

 Department of Mathematics

In this lecture, we introduce and motivate the main characters in this plot:

- Singularity of symbolic matrices: a basic problem in both computational complexity.

- Alternating Minimization: a basic heuristic in non-convex optimization.

I will explain how variants of this algorithm are applied to variants of this problem, how they are analyzed, and how the analysis gives rise to problems in quantum information theory, non-commutative algebra and invariant theory.