Qualifying Exam

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

Abstract: 

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. 


X
Enter your linkblue username.
Enter your linkblue password.
Secure Login

This login is SSL protected

Loading