UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm.

Fall 2020

September 25, 2020, Joseph Landsberg (Texas A&M)

(Hosted by Gurevitch)

From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.

In 1968 Strassen discovered the way we multiply nxn matrices (row/column) is not the most efficient algorithm possible. Subsequent work has led to the astounding conjecture that as the size n of the matrices grows, it becomes almost as easy to multiply matrices as it is to add them. I will give a history of this problem and explain why it is natural to study it using algebraic geometry and representation theory. I will conclude by discussing recent exciting developments that explain the second phrase in the title.