Geometry Seminar

Date: November 26, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: F. Gesmundo, U. Copenhagen

Title: Rank of forms and partial derivatives

Abstract: The polynomial Waring problem consists in determining a decomposition of a (homogeneous) polynomial as sum of powers of linear forms; the length of a minimal decomposition of this type is called Waring rank. A classical generalization considers a number of homogeneous polynomial and attempts to determine a simultaneous decomposition of all of them. In recent work with A. Oneto and E. Ventura, we established connections between the simultaneous Waring rank of the partial derivatives of a polynomial and its (partially symmetric) tensor rank. In this seminar, I will introduce Sylvester's classical apolarity theory, which is the most used tool in this study, and I present some of the results.