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Ehrhart positivity

Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017

September 06, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Fu Liu (University of California, Davis)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • Ehrhart positivity

  • McMullen's formula

  • integral polytope

  • Berline-Vergne valuations

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

8-Liu
Abstract

We say a polytope is Ehrhart positive if its Ehrhart polynomial has positive coefficients. There are different examples of polytopes shown to be Ehrhart positive using different techniques. We will survey some of these results. Through work of Danilov/McMullen, there is an interpretation of Ehrhart coefficients relating to the normalized volumes of faces. We try to make this relation more explicit in the particular case of the regular permutohedron. The goal is to prove Ehrhart positivity for generalized permutohedra. If time permits, I will also discuss some related questions. This is joint work with Federico Castillo.
Supplements
29481?type=thumb Liu Notes 600 KB application/pdf Download
Video/Audio Files

8-Liu

H.264 Video 8-Liu.mp4 120 MB video/mp4 rtsp://videos.msri.org/8-Liu/8-Liu.mp4 Download
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