[Video] Character Formulas

In this expository talk, we will give a simple formula, with a simple proof, for the equivariant euler characteristic of an equivariant vector bundle on on complete, smooth variety with a torus action. On homogeneous varieties this gives Weyl's character formula, and on toric varieties it gives Brion's formula for lattice points in polytopes. This is based on ideas of George Quart in the 1970s and recent conversations with Bill Graham.