AMS Special Session on
Tensor decompositions and secant varieties

January 6, 2016
Seattle WA

This session will showcase recent tremendous activity in this area, which brings together classical algebraic geometry, computational and experimental methods, representation theory, and a wide range of applications throughout statistics, the sciences, and engineering. The basic question motivating this area is, given a tensor, what is the least number of terms in a decomposition into simple tensors? Especially important are certain particular tensors such as the matrix multiplication tensor, whose rank is somewhere between quadratic and cubic in the size of the matrix. This leads to a vast array of related questions: under what conditions is the decomposition into simple tensors essentially unique; what are the dimension and other geometric properties of the locus of tensors of a given rank; what are the generic and maximum ranks of tensors; is the rank of a sum of tensors in separate variables equal to the sum of their ranks? The same questions arise for related notions of rank, such as Waring rank, where in the last 5 years there has been a renewal of interest and some real progress: new lower and upper bounds on Waring rank, determination of Waring rank of monomials, proof that in at least some cases the rank of an ``independent'' sum is the sum of the ranks, proof of unique decomposition in many cases.

This session is an activity of the AGATES group.

AMS web page for meeting


* contact organizer

Schedule of talks:

Day Time Speaker Title (click for abstract) Slides
Wednesday 8:00 am Hirotachi Abo Most secant varieties of tangential varieties to Veronese varieties are nondefective
Wednesday 8:30 am Brooke Ullery Normality of Secant Varieties slides
Wednesday 9:00 am Cameron Farnsworth Secants of the Veronese and the Determinant slides
Wednesday 9:30 am Ke Ye Structural tensors of bilinear maps
Wednesday 10:00 am Elina Robeva Orthogonal Tensor Decomposition
Wednesday 10:30 am Kristian Ranestad Tensor decompositions and cubic sections of rational surface scrolls slides