Alejandro Morales (University of Massachussetts Amherst)
A flow polytope of a directed acyclic graph is the set of flows on the edges of the graph with prescribed netflows on vertices. The conservation of flow is analogous to conservation of momentum in physics. Flow polytopes of graphs are a rich family of polytopes that includes polytopes of interest in probability, optimization, physics, representation theory, and algebraic combinatorics. 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 recent results on these polytopes including a relation between seemingly different triangulations by Postnkov-Stanley and Danilov-Karzanov-Koshevoy. This talk is based on joint work with Mészáros and Striker.
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