The world's simplest index theorem and noncommutative topology

GAP Seminar

Meeting Details

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

Speaker: Erik Van Erp,

Abstract: I present an index theorem for a class of scalar differential operators on closed 3-manifolds. The index is expressed as a sum of explicit winding numbers. These Fredholm differential operators, however, are not elliptic, and the formula will appear strange to those familiar with the Atiyah-Singer index theorem. Nevertheless, we will explain how our formula can be derived from the theorem of Atiyah-Singer, using techniques from noncommutative topology. A crucial modification is a re-interpretation of the notion of "symbol", and its associated K-theory class.

Room Reservation Information

Room Number: 106 McAllister

Date: 03/23/2010

Time: 2:30pm - 3:30pm