PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Nigel Higson.

Title:A Lie-algebraic approach to the local index theorem on a flag variety
Seminar:Noncommutative Geometry Seminar
Speaker:Seunghun Hong, Penn State
Abstract:
Let G be a compact Lie group and let T be a maximal torus in G (more generally we could consider any connected closed subgroup). Using a K-theory point of view, Bott related the Atiyah-Singer index theorem for elliptic operators on G/T to the Weyl character formula. In this talk we shall explain how to prove the local index theorem on G/T using Lie algebra methods. Our method follows in outline the proof of the local index theorem due to Berline and Vergne. But our use of Kostant’s cubic Dirac operator in place of the Riemannian Dirac operator leads to substantial simplifications. An important role is also played by the quantum Weil algebra of Alekseev and Meinrenken.

Room Reservation Information

Room Number:MB106
Date:11 / 17 / 2011
Time:02:30pm - 03:30pm