The asymptotic spectrum of tensors and barriers for fast matrix multiplication
Title: The asymptotic spectrum of tensors and barriers for fast matrix multiplication
What is the optimal algorithm to multiply large matrices? Faster and faster algorithms have been proposed since the sixties, but progress on this problem has slowed down in the last twenty years. I will explain why a very general method, which includes the methods used to obtain the currently best algorithms, cannot give faster matrix multiplication algorithms. These "barriers for fast matrix multiplication" arise from the study of asymptotic properties of tensors.
This talk is based on joint work with Matthias Christandl, Francois Le Gall, Vladimir Lysikov and Peter Vrana.