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Master's Exam

Date:
-
Location:
318 Patterson Office Tower
Speaker(s) / Presenter(s):
Audrey Lindgren, University of Kentucky

Title:  Zonotopes and Zonal Diagrams

Abstract:  A zonotope is the Minkowski sum of a finite number of closed line segments in some Euclidean space. Peter McMullen's 1971 paper "On Zonotopes" describes the technique of zonal diagrams as a tool for studying combinatorial properties of zonotopes. Zonal diagrams, which are analogous to Gale diagrams for general polytopes and to central diagrams for centrally symmetric polytopes, have proved more effective than these techniques for the particular study of zonotopes.

 

In particular, zonal diagrams yield relationships between zonotopes with n zones of dimensions d and n-d, and lead to the enumeration of all combinatorial types of d-zonotopes with at most d+2 zones. In this master's talk, we will discuss zonotopes and zonal diagrams, describe the combinatorial results mentioned above, and briefly consider the relationship between zonotopes and hyperplane arrangements.

 

 

 

 

December 4, Thursday

Event Series: