Bernd Sturmfels : How to subdivide the 4-cube

Posted by , part of the Departmental Colloquium.

At

April 7, 2006, 2 p.m.

In

SEO 636

Abstract

The hyperdeterminant of format 2 x 2 x 2 x 2 is a polynomial of degree 24 in 16 unknowns which has 2894276 terms. We compute the Newton polytope of this polynomial and the secondary polytope of the 4-cube. The 87959448 regular triangulations of the 4-cube are classified into 25448 D-equivalence classes, one for each vertex of the Newton polytope. The 4-cube has 80876 coarsest regular subdivisions, one for each facet of the secondary polytope, but only 268 of them come from the hyperdeterminant. Joint work with Debbie Grier, Peter Huggins and Josephine Yu (math.CO/0602149)