Karim Adiprasito, Ehrhart theory revisited: Algebraic aspects, unimodality and more

Ehrhart theory is the study of lattice polytopes, specifically aimed at understanding how many lattice points are inside dilates of a given lattice polytope, and the study has a wide range of connections ranging from coloring graphs to mirror symmetry and representation theory. Recently, we introduced new algebraic tools to understand this theory, and resolve some classical conjectures. I will explain the combinatorial underpinnings behind two of the key techniques: Parseval identities for semigroup algebras, and the character algebra of a semigroup.