The world's simplest index theorem and noncommutative topology
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
Time: 2:30pm - 3:30pm