Back to Algebraic Geometry Seminar: Fall 2015
Algebraic Geometry Seminar
Date: Tuesday, Oct 6, 2015
Time: 3:30PM - 4:30PM
Location: JFB 102
Zach Teitler
Boise State University
Title |
Bounds for Waring rank |
Abstract |
The Waring rank of a complex homogeneous form is the least number of terms in an expression of the form as a sum of powers of linear forms. Waring rank, tensor rank, and various generalized ranks are interesting for a range of applications including secant varieties and geometric complexity theory, but they are difficult to compute. In particular we do not know the maximum Waring rank among forms in a given number of variables and a given degree; it is not even known whether forms of greater than generic rank exist. I will present upper and lower bounds for Waring rank and generalized ranks that narrow the possible ranges of maximum values of generalized ranks (joint work with Grigoriy Blekherman) and in some new cases show the existence of forms of above-generic Waring rank (joint work with Jaros{\l}aw Buczy'nski). |
Algebraic Geometry