 Location
 MSRI: Simons Auditorium
 Video

 Abstract
In the field of Ehrhart theory, identification of lattice polytopes with unimodal Ehrhart h*polynomials is a cornerstone investigation. The study of h*unimodality is home to numerous longstanding conjectures within the field, and proofs thereof often reveal interesting algebra and combinatorics intrinsic to the associated lattice polytopes. Proof techniques for h*unimodality are plentiful, and some are apparently more dependent on the lattice geometry of the polytope than others. In recent years, proving a polynomial has only realroots has gained traction as a technique for verifying unimodality of hpolynomials in general. However, the geometric underpinnings of the realrooted phenomena for h*unimodality are not wellunderstood. As such, more examples of this property are always noteworthy. In this talk, we will discuss a family of lattice nsimplices that associate via their normalized volumes to the n^thplace values of positional numeral systems. The h*polynomials for simplices associated to special systems such as the factoradics and the binary numerals recover ubiquitous hpolynomials, namely the Eulerian polynomials and binomial coefficients, respectively. Simplices associated to any baser numeral system are also provably realrooted. We will put the h*realrootedness of the simplices for numeral systems in context with that of their cousins, the slecture hall simplices, and discuss their admittance of this phenomena as it relates to other, more intrinsically geometric, reasons for h*unimodality.
 Supplements

