For more information about this meeting, contact Ping Xu, Mathieu Stienon, Nigel Higson.

Title: | A Lefschetz number theorem for differential operators |

Seminar: | GAP Seminar |

Speaker: | Ajay Ramadoss, Cornell University |

Abstract: |

Let $X$ be a compact, complex manifold and let $E$ be a holomorphic vector bundle on $X$. Let $ Diff^{\bullet}(E)$ be the Dolbeault resolution of the sheaf of holomorphic differential operators on $E$. A construction due to Feigin, et. al , gives a linear functional on the $0$-th Hochschild homology of $Diff^{\bullet}(E)$. This functional "extends" to a linear functional on the "completed" $0$-th Hochschild homology of $Diff^{\bullet}(E)$ ,thereby giving a linear functional $I_E$ on the top cohomology $\text{H}^{2n} (X,\mathbb C)$ of $X$ with complex coefficients. The main result is that $I_E$ is just integration over $X$. As a consequence, one obtains a Lefschetz number formula for a global holomorphic differential operator on $E$. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 27 / 2009 |

Time: | 02:30pm - 03:30pm |