# Meeting Details

For more information about this meeting, contact Sergei Tabachnikov.

Title: Finiteness for Tamagawa numbers Department of Mathematics Colloquium Brian Conrad, Stanford University ndre Weil introduced an "adelic" method for describing vector bundles on compact Riemann surfaces in terms of a certain double coset space, and analogues of such double coset spaces can be associated to any linear algebraic group over arithmetically interesting fields. In such cases, it makes sense to assign a certain canonical volume, called the Tamagawa number, which arises in settings as varied as the arithmetic of quadratic forms and counting connected components of certain moduli spaces of bundles over curves over finite fields. The finiteness of such volumes for all reductive groups was proved by Borel and Harder long ago. The finiteness in general can then be easily deduced in general in characteristic zero, but the case of positive characteristic needs completely different ideas and was settled only very recently. We discuss some of the highlights of this story.

### Room Reservation Information

Room Number: MB114 09 / 09 / 2010 04:00pm - 05:00pm