Monday, November 7th, 2005
2:30pm - 3:30pm, in Science 2-065

Catalin Zara

Penn State Altoona and UMass Boston

Hamiltonian GKM Spaces: From Geometry To Combinatorics and Back

Abstract: This talk will provide a gentle introduction to some beautiful yet surprising connections between Symplectic Geometry and Combinatorics which show that the continuous world of compact Hamiltonian spaces with torus actions and the discrete world of polytopes and graphs are not as far apart as it may seem. For such spaces the Convexity Theorem of Atiyah-Guillemin-Sternberg states that the image of the moment map is a convex polytope, and it turns out that this polytope encodes a lot of geometric and topological information about the space. In fact, in some special cases, the polytope completely determines the space! The talk is intended for a general mathematical audience and will be as self-contained as possible.