Geometry Seminar

Date: April 20, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: F. Gesmundo, U. Cophenhagen

Title: Cactus rank and multihomogeneous polynomials

Abstract: The standard notion of matrix rank has several generalizations in algebraic geometry. Classical examples are Waring rank for homogeneous polynomials, tensor rank and in general X-rank with respect to an algebraic variety X. One additional generalization, of a more algebraic nature, is cactus rank, defined for every (smooth) algebraic variety and studied in the recent years in the settings of homogeneous polynomials and tensors. In this seminar, I will introduce cactus rank and present some of its features. In particular, we will see that whereas cactus rank presents a strong barrier in the study of other notions of rank, some of its characteristics are of great help in determining Waring rank and more generally partially symmetric rank in the tensor setting.