MEMBERS SEMINAR | |

Topic: | The Regularized Determinant of a Four-Manifold |

Speaker: | Matt Gursky |

Affiliation: | University of Notre Dame and Member, School of Mathematics |

Date: | Monday, March 30 |

Time/Room: | 2:00pm - 3:00pm/S-101 |

I will give an overview of a variational problem in conformal geometry/spectral theory. Beginning with a formula for the determinant of the laplacian for a surface and the work of Osgood-Phillips-Sarnak, I will explain some attempts to generalize this work to four dimensions based on a formula of Branson-Orsted. The talk will be aimed at a general audience, and will be mostly a survey. Towards the end of the lecture I will briefly mention some work in progress, and indicate various technical issues that arise in 4-d that are absent in 2-d.