The theory of asymptotic spectra describes asymptotic behavior of basic objects in mathematics like graphs and tensors. Example applications are the matrix multiplication problem, the cap set problem, the sunflower problem, the quantum entanglement problem, and the problem of efficient communication over a noisy channel.

In this talk we will focus on one application: the matrix multiplication problem. We will use the asymptotic spectrum of tensors to prove that a very general method, which includes the methods used to obtain the currently best algorithms, cannot give much faster matrix multiplication algorithms.