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Texas A&M University

Events for 02/05/2019 from all calendars

Student/Postdoc Working Geometry Seminar

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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.