QLunch: On tensors of minimal border rank

Speaker: Vladimir Lysikov from QMATH

Title: On tensors on minimal border rank

Abstract: Rank of a tensor is a natural measure of its complexity which generalizes usual notion of matrix rank to higher order tensors. Unlike in the matrix case, the set of all tensors of bounded rank is not closed, making it possible for a tensor of high rank to be approximated arbitrarily closely by tensors of lower rank. We explore the connection between these tensor approximations and deformations of commutative algebras. 

This talk is based on a joint work with M. Bläser and a joint work with B. Chokaev under RFBR grant 18-31-00044-mol-a.