Combinatorial Algebraic Geometry

Date: March 22, 2019

Time: 11:00AM - 11:50AM

Location: Bloc 605AX

Speaker: Emanuele Ventura, Texas A&M University

Title: On the monic rank

Abstract: We introduce the monic rank of a vector relative to an affine-hyperplane section of an irreducible Zariski-closed affine cone X. This notion is well-defined and greater than or equal to the usual X-rank. We describe an algorithmic technique based on classical invariant theory to determine, in concrete situations, the maximal monic rank. Using this technique, we establish three new instances of a conjecture due to Shapiro which states that a binary form of degree d\times e is a sum of d many d-th powers of forms of degree e. This is joint work with A. Bik, J. Draisma, and A. Oneto.