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4:00 pm Tuesday, February 2, 2010 Algebraic Geometry Seminar: Ranks of polynomialsby
Zach Teitler (TAMU) in HB 227- The Waring rank of a polynomial of degree d is the least number of terms in an expression for the polynomial as a sum of dth powers. The problem of finding the rank of a given polynomial and studying rank in general has been a central problem of classical algebraic geometry, related to secant varieties; in addition, there are applications to statistics, signal processing, and computational complexity. Other than a well-known lower bound for rank in terms of catalecticant matrices, there has been relatively little progress on the problem of determining or bounding rank for a given polynomial (although related questions have proved very fruitful). I will describe new upper and lower bounds. The improved lower bound is especially interesting, dealing with the geometry of catalecticants. This is joint work with J.M. Landsberg.
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