Qualifying Exam

10/10/2019 - 12:00pm to 1:00pm
POT 745
Speaker(s) / Presenter(s): 
Andres Vindas Melendez


The Ehrhart polynomial of a lattice polytope $ P$ encodes information about the number of integer lattice points in positive integral dilates of $ P$. The $ h^\ast $-polynomial of $ P$ is the numerator polynomial of the generating function of its Ehrhart polynomial. A zonotope is the Minkowski sum of line segments. In this talk I will present two theorems of Matthias Beck, Katharina Jochemko, and Emily McCullough from their paper, titled, "$ h^\ast$-polynomials of zonotopes". They give a combinatorial description of the $ h^\ast $-polynomial of a lattice zonotope in terms of refined descent statistics of permutations and prove that the $ h^\ast $-polynomial of every lattice zonotope has only real roots. Furthermore, I will outline my current and future research directions and questions. 

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