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Topic: Courant Geometry Seminar
Replies: 8   Last Post: Jan 25, 2005 9:53 PM

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Ricky Pollack

Posts: 18
Registered: 12/3/04
Sturmfels lecture at Courant
Posted: Jan 25, 2005 9:53 PM
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\newcommand{\R}{{\bf R}}
\title{Geometry Seminar\\
Tuesday March 8 in room 613 WWH at 6:00 P.M\\
Groebner Bases and Triangulations of the Second Hypersimplex

Bernd Sturmfels\\Cornell University
The second hypersimplex $\Delta(2,n)$ is the convex hull of the columns
of the vertex-edge incidence matrix of the complete graph $K_n$.
In this talk we employ the algebraic technique of Groebner bases
to study triangulations of this polytope. We compare the secondary
polytope of $\Delta(2,n)$ with the state polytope of the associated
toric ideal, and we present an explicit non-regular triangulation
for $n \geq 9$. Relations to combinatorial optimization and random graphs
will be indicated. This is joint work with Jesus DeLoera and Rekha


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