at the

American Institute of Mathematics, San Jose, California

organized by

Matthias Beck, Benjamin Braun, Katharina Jochemko, and Fu Liu

The main topics for the workshop are:

- Classification problems: What are the possible coefficient vectors of Ehrhart polynomials for lattice polytopes of fixed dimension, especially in dimensions three and four? Is it possible to classify Ehrhart polynomials for sufficiently special families of lattice polytopes, for example, lattice zonotopes?
- Inequalities for polynomial coefficients: What properties of a lattice polytope imply that the Ehrhart polynomial has positive coefficients? For example, do generalized permutahedra have this property? What geometric or arithmetic properties of lattice polytopes imply having a unimodal Ehrhart h*-vector? For example, do lattice polytopes with the integer decomposition property behave in this manner?
- Extremal constructions: How can we demonstrate the existence of (possibly high-dimensional) lattice polytopes with extreme properties for their Ehrhart polynomials? What are efficient strategies for creating examples/counterexamples? What are computationally feasible choices of classes of lattice polytopes to search for examples/counterexamples?

The workshop schedule.

A list of open problems.

Papers arising from the workshop:

Sums of weighted lattice points of polytopes

by Jesús A. De Loera, Laura Escobar, Nathan Kaplan, and Chengyang Wang

Examples and counterexamples in Ehrhart theory

by Luis Ferroni, Akihiro Higashitani

Weighted Ehrhart Theory: Extending Stanley's nonnegativity theorem

by Esme Bajo, Robert Davis, Jesús A. De Loera, Alexey Garber, Sofía Garzón Mora, Katharina Jochemko, Josephine Yu

Local $h^*$-polynomials for one-row Hermite normal form simplices

by Esme Bajo, Benjamin Braun, Giulia Codenotti, Johannes Hofscheier, Andrés R. Vindas-Meléndez

Minimal free resolutions of numerical semigroup algebras via Apéry specialization

by Benjamin Braun, Tara Gomes, Ezra Miller, Christopher O'Neill, Aleksandra Sobieska

Local $h^*$-polynomials for one-row Hermite normal form simplices

by Esme Bajo, Benjamin Braun, Giulia Codenotti, Johannes Hofscheier, Andrés R. Vindas-Meléndez