Chris Umans, Caltech 

Title: Matrix multiplication via group theory

Abstract: A famous and consequential open problem in computer science is to design algorithms that multiply n x n matrices in (nearly) n^2 operations. For more than 50 years, the quest for such an "exponent 2" algorithm for matrix multiplication has captured the imagination of computer scientists and mathematicians alike, and it continues to do so today.

In this talk I will describe how this algorithmic problem is cast as a mathematically appealing question about tensor rank, and describe a novel approach that imports the problem into the domain of group theory and representation theory. I'll discuss generalizations to algebraic objects beyond groups, connections to problems in combinatorics and other areas of math, and give a sense of the current state-of-the-art in this program aimed at finding an exponent 2 algorithm for matrix multiplication.