Algorithms for Matrix Multiplication via the Representation Theory of Finite Groups and Coherent Configurations

Abstract.  Better understanding the computational complexity of matrix multiplication could shed light on computational complexity – and thereby complexity science – in general. We aim to find better algorithms to multiply matrices and to solve linear systems of equations. Specifically, we plan to pursue the recent ideas of Cohn, Umans, et al. on how to apply symmetry (group theory) and highly symmetric combinatorial structures (coherent configurations) to the discovery of such algorithms.