Vrana Péter: The asymptotic restriction problem and the asymptotic spectrum of tensors

The aim of this talk is to give an overview of the asymptotic restriction problem for tensors. In this problem, one considers tensors of some given order and asks if there exist restriction maps between their Kronecker tensor powers, generalizing the notion of (asymptotic) tensor rank. The main motivation comes from complexity theory, due to the fact that the asymptotic arithmetic complexity of matrix multiplication is characterized by the asymptotic rank of a particular tensor of order 3. While studying this problem, Strassen introduced the asymptotic spectrum of tensors and more generally, developed the theory of asymptotic spectra of preordered semirings, the main result of which is a powerful duality theorem connecting the asymptotic preorder to a space of functions on the semiring, called the asymptotic spectrum. In the case of tensors, he introduced the support functionals, an infinite family of elements of the asymptotic spectrum of a certain subsemiring of tensors. I will explain a recent result from our joint work with Christandl and Zuiddam, in which we construct for the first time an infinite family of elements of the asymptotic spectrum of all tensors over the complex field, extending the support functionals. Az előadást Zoom-on is közvetítjük: https://us06web.zoom.us/j/82770480461?pwd=mZJtNTVURjgwIDX7oEaoasG5LK5FOD.1 Meeting ID: 827 7048 0461 Passcode: 601951