K-Theory and polytopes

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.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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