For more information about this meeting, contact John Roe, Dmitri Burago.

Title: | Integrality and divisibility of the Witten genus |

Seminar: | Geometry Luncheon Seminar |

Speaker: | Stephan Stolz, Notre Dame |

Abstract: |

It is well-known that the A-roof genus A(M) of a closed spin manifold M is integral, and in fact divisible by 2 if the dimension of M is 8k+4. First proved via K-theory, this is the consequence of the Atiyah-Singer Index Theorem which interprets A(M) as the index of the Dirac operator on M. A higher analog of A(M) is the Witten genus W(M) which heuristically can be interpreted as the equivariant index of the (only heuristically defined) "Dirac operator" on the free loop space LM. Work of Mike Hopkins and collaborators on "Topological Modular form theory" (a cohomology theory) implies divisibility results for
W(M) for string manifolds M. An analytic interpretation of these results is an open question. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 04 / 14 / 2010 |

Time: | 12:15pm - 01:30pm |