# Events for 02/05/2019 from all calendars

## Student/Postdoc Working Geometry Seminar

**Time:** 1:00PM - 2:00PM

**Location:** BLOC 628

**Speaker:** E. Ventura, TAMU

**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.