Mathematics Colloquia and Seminars

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Given a finite, loopless graph, its flow polytope consists of assignments of weights to the edges satisfying certain conservation constraints. Given a finite poset, we obtain the order polytope as assignments of weights on the vertices which respect the partial order. Given a finite set of matrices, we can define a polytope as their convex hull. We find a surprising correspondence between all three perspectives on a face of the alternating sign matrix polytope and discuss the implications of this correspondence to mysterious volume questions on related polytopes. This is work in progress with Karola Meszaros and Alejandro Morales.