Theoretical Statistics and Mathematics Unit, ISI 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.