# Seminar at SMU Delhi

June 28, 2011 (Tuesday) , 3:30 PM at Webinar
Speaker: Apoorva Khare, Stanford University, USA
Title: Generalizing the notion of convexity: weak faces of weight polytopes
Abstract of Talk
The notion of convexity and faces of polytopes is well known: a subset is a face if it maximizes a linear functional, and also if and only if it satisfies a condition involving convex linear combinations. In joint work with Chari and Ridenour, we extend this notion to arbitrary subsets of Euclidean space and arbitrary subfields of coefficients (in the convex combinations). We then use this to find and classify faces'' of the set of lattice points inside weight polytopes attached to finite-dimensional modules over complex semisimple Lie algebras.