TALK: JM Landsberg: Geometry and the Complexity of Matrix Multiplication

Wednesday, April 29, 2015 - 4:00pm to 5:00pm
JM Landsberg
Texas A&M

Ever since Strassen showed that nxn matrices can be multiplied using O(n^2.81) arithmetic operations as opposed to the usual
O(n^3), there has been substantial research to determine just how efficiently matrices can be multiplied. This has led to the astounding conjecture that asymptotically, it is nearly as easy to multiply matrices as it is to add them, more precisely,  that matrices can be multiplied using O(n^{2+s}) arithmetic operations for any s>0.

I will explain how geometry has been useful in proving lower complexity bounds, and describe very recent work that indicates
how geometry may also be used to prove upper bounds.

This is joint work with L. Chiantini, C. Ikenmeyer, G. Ottaviani and M. Michalek.