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Volumes and Lattice Points of Flow Polytopes of Graphs

12 Feb
Wednesday, 02/12/2020 12:15pm to 1:15pm
Computer Science Building Room 140
Theory Seminar

A flow polytope of a directed acyclic graph is the set of flows on the edges of the graph with prescribed netflows on vertices. This is a rich family of polytopes that includes polytopes of interest in probability, optimization, and representation theory. These polytopes are related to partially ordered sets when the graphs are planar and special cases have remarkable formulas for their volumes and lattice points due to Baldoni-Vergne and Postnikov-Stanley. I will talk about the theory of these polytopes, their triangulations/subdivisions and a combinatorial model for their volumes.

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