Several astounding conjectures on the asymptotic geometry of tensors

Thursday, October 25, 2018 - 1:00pm
110 Math Science Building
Joseph Landsburg
(Texas A&M)

Abstract: Many computer scientists believe the astounding conjecture that asymptotically (as n goes to infinity), it becomes almost as easy to multiply nxn matrices as to add them. Since progress on this conjecture stalled around 1989, Strassen made an even more astounding conjecture that would imply the matrix multiplication conjecture. Later Burgisser-Clausen-Shokrollahi made a further generalization to the effect that all tensors "asymptotically look the same" in a way I'll explain precisely. In this talk (joint work with A. Conner, F. Gesmundo, Y. Wang and E. Ventura), I will discuss these conjectures from the perspective of  representation theory and algebraic geometry (moment polytopes, secant varieties).