# Mathematics Colloquia and Seminars

### Triangulations of root polytopes and subdivision algebras

Algebra & Discrete Mathematics

 Speaker: Karola Meszaros, MIT Location: 2112 MSB Start time: Fri, Apr 24 2009, 1:10PM

A type A_{n-1} root polytope is the convex hull in R^n of the origin and a subset of the points e_i-e_j, 1\leq i< j \leq n. A collection of triangulations of these polytopes can be described by reduced forms of monomials in the subdivision algebra, which is a commutative algebra generated by n^2 variables x_{ij}, for 1\leq i< j \leq n. In a closely related noncommutative algebra, the reduced forms of monomials are unique, and correspond to shellable triangulations whose simplices are indexed by noncrossing alternating trees. Using these triangulations Ehrhart polynomials are computed. The results are extended to a more general family of polytopes.