Home Contact Chinese CAS
Home  About Us    Research     People   International Cooperation   News     Papers   Education & Training  Join Us
Location: Home > Research > Colloquia & Seminars

Functional integration and index theory Jean-Michel Bismut
【2013.10.9 4:00pm,S703】

 Date:03-12-2013 Page Views:
Print
Text Size: A A A
Close

 2013-9-30 

  Colloquia & Seminars 

  Speaker

 

Prof.Jean-Michel Bismut,University Paris-Sud

  Title

       

   Functional integration and index theory Jean-Michel Bismut  

  Time

      

    2013.10.9 4:00pm   

  Venue

  S703

  Abstract

In the first part of the talk, I will explain the connections between the heat equation proof of the index theorem for Dirac operators, and the localization formulas of Duistermaat-Heckman. In particular, I will show how to pass from integration with respect to the Brownian measure on the loop space of a Riemannian manifold to integration of differential forms on this loop space.

In the above situation, the geometry of the loop space is associated with its L2-Riemannian metric. In a second part of the talk, I will show how replacing the L2-metric by a H1-metric determines a new measure on the loop space, which corresponds to a geometric Langevin process, whose generator is a hypoelliptic operator on the total space of the tangent bundle.

I will naturnally explain how the above suggests the possibility of deforming the elliptic Dirac operator to a family of hypoelliptic Dirac operators.

  Affiliation

     

[ Close ]  [ Top ]
  Copyright © 2012, All Rights Reserved, National Center for Mathematics and Interdisciplinary Sciences, CAS
Tel: 86-10-62613242 Fax: 86-10-62616840 E-mail: ncmis@amss.ac.cn