TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2022/23)

Leonid Monin (Universität Leipzig)

Abstract: One can associate a commutative, graded algebra which satisfies Poincare duality to a homogeneous polynomial f on a vector space V. One particularly interesting example of this construction is when f is the volume polynomial on a suitable space of (virtual) polytopes. In this case the algebra A_f recovers cohomology rings of toric or flag varieties.

In my talk I will explain these results and present their recent generalizations. In particular, I will explain how to associate an algebra with Gorenstein duality to any function g on a lattice L. In the case when g is the Ehrhart function on a lattice of integer (virtual) polytopes, this construction recovers K-theory of toric and full flag varieties.