Max Koelbl

Symmetric edge polytopes and Ehrhart polynomial roots

The study of roots of Ehrhart polynomials goes back to a paper by Bump, Choi, Kurlbeck, and Vaaler (2000) in the context of number theory. They noticed that cross-polytopes have their Ehrhart polynomial roots on the canonical line (CL), i.e. the line in ℂ with real part -1/2. I will introduce the class of symmetric edge polytopes -- a generalisation of cross-polytopes --and a conjecture pertaining to the CL-ness of a subclass of them. Then I will show methods and results that have sprung from investigating this still wide open conjecture.