Karola Meszaros

Cornell University; von Neumann Fellow, School of Mathematics

December 10, 2018

The flow polytope associated to an acyclic graph is the set of all nonnegative flows on the edges of the graph with a fixed netflow at each vertex. We will discuss a family of subdivisions of flow polytopes and

explain how they give rise to a family of Schubert polynomials, which generalize the well known basis of the ring of symmetric functions, Schur polynomials. We will also show that the Newton polytopes of Schubert polynomials are generalized permutahedra; the latter were (re)introduced by Postnikov in 2005. We explain the connections between generalized

permutahedra and flow polytopes, thereby tying all our main players together..

Based on joint work with Laura Escobar, Alex Fink and Avery St. Dizier.