C4: Combinatorics of manifolds with symmetries and modularity properties

Bringmann, Sabatini

Abstract: We use the correspondence between integral polytopes and symplectic toric manifolds to study combinatorial and number-theoretic properties of integral polytopes, in particular reflexive polytopes. This connection allows us to use powerful tools coming from equivariant cohomology and K-theory, as well as the rigidity and modularity properties of equivariant genera on toric varieties. We study the Hilbert and Ehrhart polynomials using this new approach, starting with the investigation of questions posed by Rodriguez-Villegas about the position of their roots.