Gamma-positivity is an elementary property that polynomials with symmetric coefficients may
have, which directly implies their unimodality. The idea behind it stems from work of Foata …

The enumerative theory of simplicial subdivisions (triangulations) of simplicial complexes
was developed by Stanley in order to understand the effect of such subdivisions on the h …

In algebraic, topological, and geometric combinatorics, inequalities among the coefficients of
combinatorial polynomials are frequently studied. Recently, a notion called the alternatingly …

Ehrhart theory is the study of sequences recording the number of integer points in non-
negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is …

We study the topology of toric maps. We show that if f: X→ Y is a proper toric morphism, with
X simplicial, then the cohomology of every fiber of f is pure and of Hodge–Tate type. When …

We study semigroup algebras arising from lattice polytopes, compute their volume
polynomials (particularizing work of Hochster), and establish strong Lefschetz properties …

The Eulerian polynomials and derangement polynomials are two well-studied generating
functions that frequently arise in combinatorics, algebra, and geometry. When one makes an …

We prove the local motivic monodromy conjecture for singularities that are nondegenerate
with respect to a simplicial Newton polyhedron. It follows that all poles of the local …

We introduce the theory of geometric monodromies in various situations, focusing on its
relations with toric geometry and motivic Milnor fibers, and moreover in the modern …

In this paper, we study the novel notion of thin polytopes: lattice polytopes whose local-
polynomials vanish. The local-polynomial is an important invariant in modern Ehrhart theory …