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Secondary Polytopes and the Chamber Complex
Student-Run Discrete Mathematics| Speaker: | Eddie Kim, UC Davis |
| Location: | 1147 MSB |
| Start time: | Thu, Feb 15 2007, 11:02AM |
Description
Many infinite families of polytopes are described by the direction of their
facet normals. This is the data that becomes encoded in the "left hand
side" constraint matrix $A$ of the family.
It is interesting, from an experimental point of view, to consider all
polytopes with a fixed constraint matrix $A$. In this talk, we will
consider the theoretical framework for generating a representative
collection of polytopes (one per combinatorial type) by studying a bijection
first given by L. J. Billera, I.M. Gelf'and, and B. Sturmfels: There is a
correspondence between the chambers of $cone(A)$ and the regular
triangulations of the Gale transform of $A$.