QLunch: Apolarity theory, Waring rank and partial derivatives
Speaker: Fulvio Gesmundo from QMATH
Title: Apolarity theory, Waring rank 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 (partiallysymmetric) rank. In this seminar, I will introduce Sylvester's classical apolarity theory, and will show how to employ it to obtain some of the results.