Department of Mathematics Calendar
Yang Qi, University of Chicago, On approximations and decompositions of a general tensor
- This event has passed.
Tensors are closely related to secant varieties. In fact, 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 rank and the symmetric rank of a symmetric tensor. The talk is based on joint works with Lek-Heng Lim and Mateusz Michalek.