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 Kostantâ€™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 |