Computer Science/Discrete Mathematics Seminar I

Algebraic geometry and representation theory have played an important role in obtaining lower bounds in algebraic complexity theory. After giving an overview of the general set-up, I will present very recent results that indicate a possible role for geometry in finding algorithms and proving upper bounds for the matrix multiplication operator. In particular, I will present a purely geometric derivation of Strassen's algorithm to multiply 2x2 matrices using only 7 multiplications instead of the usual 8. This is joint work with L. Chiantini, C. Ikenmeyer, and G. Ottaviani.