Alcoved polytopes

Thomas Lam


December 12,
2:15pm (Note new time!)
refreshments at 3:15pm (Holiday Social)


I will talk about convex polytopes which are unions of alcoves of an affine Coxeter arrangement. The motivating examples are two triangulations of the hypersimplex given by Stanley and Sturmfels respectively. The volume of the hypersimplex is an Eulerian number and this allows us to define generalised `descents' and Eulerian numbers for all Weyl groups. Other aspects of these polytopes I will talk about are formulae for their volumes, Groebner bases which lead to these triangulations, and connections with matroids and with geometry.

This is joint work with Alex Postnikov.

Speaker's Contact Info: tfylam(at-sign)

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

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