Geometry Seminar

Date: February 24, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: JM Landsberg, TAMU

Title: Symmetry v. Optimality

Abstract: The talk will be a colloquium style talk - all are welcome. I will discuss uses of algebraic geometry and representation theory in complexity theory. I will explain how these geometric methods have been successful in proving lower complexity bounds: unblocking the problem of lower bounds for the complexity of matrix multiplication, which had been stalled for over thirty years, and providing the first exponential separation of the permanent from the determinant in any restricted model. (The permanent v. determinant problem is an algebraic cousin of the P v. NP problem.) I will also discuss exciting new work that indicates that these methods can also be used to provide complexity upper bounds, in fact construct explicit algorithms. This is joint work with numerous co-authors including G. Ballard, A. Conner, C. Ikenmeyer, M. Michalek, G. Ottaviani, and N. Ryder.