# 2017-2018 Bowen Lectures

**The 2017-2018 Bowen Lectures** were given by Avi Wigderson of the Institute for Advanced Study, on February 7, 8 and 9, 2018. Each lecture begins at 4:10pm and ends at 5:00pm.

Series Title: **Mathematics and Computation (through the lens of one problem and one algorithm)**

Wednesday February 7th

Lecture 1: *The problem, the algorithm and the connections.*

Calvin Laboratory (Simons Institute) Auditorium

Thursday February 8th

Lecture 2: *Proving Algebraic Identities.*

60 Evans Hall

Friday February 9th

Lecture 3: *Proving Analytic Inequalities.*

Calvin Laboratory (Simons Institute) Auditorium

Series Abstract:

Mathematics and computation have gone hand in hand for millennia. Many of the greatest mathematicians we great algorithm designers as well, including Euclid, Newton, Gauss and Hilbert. And since the creation of the theories of computation and then computational complexity, these connections have become far broader, deeper and stronger.

This 3-lecture series will illustrate these connections by focusing on a single computational problem, Singularity of Symbolic Matrices, and a single algorithmic technique for it, Alternate Minimization. As it happens, recent attempts to understand these have uncovered a surprisingly rich web of connections between diverse areas of mathematics and computer science, all of which contributing and benefitting from this interaction. In math these include non-commutative algebra, invariant theory, quantum information theory and analysis. In computer science they include optimization, algebraic complexity and pseudorandomness.

In this first lecture I will give the general set-up, motivating and explaining the problem, algorithm and main results, as well as some of the connections.

In the next two lectures I will survey aspects of two central problems to both math and CS, Proving Algebraic Identities and Proving Analytic Inequalities, motivating and influenced by the research above.

While very related, all three lectures are designed to be independent of each other. They require no special background knowledge.

Lecture notes for much of this material can be found in http://www.math.ias.edu/~avi/PUBLICATIONS/CCC-17-tutorial-lecture-notes.pdf