MATHEMATICS COLLOQUIUM - Lutz Hille (U Muenster)

Speaker: 
Lutz Hille (U of Muenster)
Topic: 
Catalan numbers, Polytopes and the Number of Tilting Modules

Abstract: There is an extensive study of Catalan numbers in combinatorics. Some of this is closely connected to the number of tilting modules for quivers of type A. Since the number of tilting modules is independent of the orientation for any Dynkin quiver, the number of tilting modules should be defined already in terms of the root system. It turns out, that there is a polytop, the so-called root polytop, and its volume is closely related to the number of tilting modules.
In the talk we review some of the Catalan combinatorics, introduce the root polytopes and relate them to the counting problem. It turns out, that we can also count the number of strongly exceptional sequences with this method. At the end we give a short view to the corresponding problem for tame and wild quivers.

 

 

 

 

 

 

Event Date: 
September 17, 2015 - 3:30pm to 4:30pm
Location: 
213 MLH
Host: 
Ryan Kinser
Calendar Category: 
Colloquium