Seminar on Applied Algebra and Geometry
Tuesday, December 12, 2017 at 5:30pm to 6:30pm
Speaker: Yang Qi, University of Chicago
Title: Geometry of tensor approximations and tensor decompositions
Abstract: Tensors are closely related to secant varieties. It is known the affine cone of the r-th secant variety of the Segre variety is the set of tensors whose border rank is less than or equal to r. Similarly, we have a geometric interpretation of symmetric tensors. By studying the geometry of these secant varieties, we can derive interesting properties of tensors. In this talk, we will show a general complex (symmetric) tensor has a best (symmetric) rank-r approximation, and we will study the relations between the (border) rank and the symmetric (border) rank of a general symmetric tensor. The talk is based on joint works with Lek-Heng and Mateusz Michalek.