Abstracts
for the Seminar

Spring 2017

**Speaker: ** Karola Mészáros, Cornell University

**Title: **Product formulas for volumes of flow polytopes

**Time:** 2:30 PM, Monday, Feb 6, 2017

**Place:** Malott 206

**Abstract:** 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 examine flow polytopes arising from permutation matrices, alternating sign matrices and Tesler matrices. Our inspiration is the Chan-Robins-Yuen polytope (a face of the polytope of doubly-stochastic matrices), whose volume is equal to the product of the first n Catalan numbers (although there is no known combinatorial proof of this fact!). The volumes of the polytopes we study all have nice product formulas.

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