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Hyperdeterminants and Triangulations of the 4-cube

Algebra & Discrete Mathematics

Speaker: Peter Huggins, UC Berkeley
Location: 1147 MSB
Start time: Thu, May 25 2006, 12:10PM

Hyperdeterminants, in the sense of Gelfand, Kapranov and Zelevinsky, are generalizations of determinants to higher tensors, and are intimately related to triangulations of products of simplices. Applications of hyperdeterminants abound, from quantum information theory to computational biology. Yet despite their potential uses, hyperdeterminants of modest format still present major computational challenges. After touring the relevant background, we report on recent computational advances regarding the 2x2x2x2-hyperdeterminant, its Newton polytope, and the secondary polytope of the 4-cube. (Joint work with Debbie Grier, Bernd Sturmfels, and Josephine Yu)