Geometry Seminar

Date: October 12, 2020

Time: 3:00PM - 4:00PM

Location: zoom

Speaker: F. Gesmundo, U. Copenhage

Title: Approaching the boundary of tensor network varieties

Abstract: Tensor network states are particular tensors arising via contractions determined by the combinatorics of a weighted graph and are used as ansatz class for a number of problems in applied mathematics. If the graph contains cycles, the corresponding set of tensor network states is (often) not closed in the Zariski topology; its closure is usually referred to as the tensor network variety. There are several tensors of interest lying on the "boundary", that is the difference between the variety and the set itself. In recent work, we introduced sets of tensors, arising in a natural geometric way, which include tensors at the boundary and offer similar properties as the ansatz class of tensor network states. In this seminar, I will introduce the tensor network variety, will show some properties of the boundary and will illustrate how the new ansatz class comes into play. This is based on joint work with M. Christandl, D. Stilck-Franca and A. Werner.