#
Monday Lecture and Colloquium

**Monday, January 9, 2017 **

Technische Universität Berlin

Institut für Mathematik

Straße des 17. Juni 136

10623 Berlin

room MA 041

** Lecture - 14:15**

### Raman Sanyal -
Goethe-Universität Frankfurt/M

### On the geometric combinatorics of posets

*Abstract:*

Geometric combinatorics is the art of studying discrete structures
by way of geometry. True gems in this area are Stanley's "two poset
polytopes". The order polytope and the chain polytope reflect much
of the combinatorics of posets in their face structures, their volumes,
and their Ehrhart polynomials. In this talk I will discuss four more such
polytopes associated to partial orders with applications to permutation
statistics, increasing/alternating sequences, and valuations on
distributive lattices. On the geometric side, these polytopes make
interesting connections (and raises plenty of open questions) to
anti-blocking polytopes from combinatorial optimization, compressed
and equidissectable polytopes from discrete geometry, and arrangements
of tropical min- and max-hyperplanes.

**Colloquium - 16:00**

### Karola Mészáros - Cornell University

### Product formulas for volumes of flow polytopes

*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.

Letzte Aktualisierung:
04.01.2017