Geometry Seminar

Date: December 13, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Tim Seynnaeve, MPI Leipzig

Title: Uniform Matrix Product States from an Algebraic Geometer’s point of view

Abstract: Uniform matrix product states are certain tensors that describe physically meaningful states in quantum information theory. We apply methods from algebraic geometry to study the set of uniform matrix product states. In particular, we provide many instances in which the set of uniform matrix product states is not closed, answering a question posed by Hackbusch. We also confirm a conjecture of Critch and Morton asserting that, under some assumptions, matrix product states are ``identifiable''. Roughly speaking, this means that the parametrizing map is as injective as it could possibly be. Finally, we managed to compute defining equations for the variety of uniform matrix product states for small parameter values. This talk is based on joint work with Adam Czaplinski and Mateusz Michalek.