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Rademacher Lectures

Thursday, April 12, 2018 - 3:30pm

Paul Baum

Pennsylvania State University

Location

University of Pennsylvania

A4 DRL

Tea will be served at 3:00pm in 4E17 DRL

Lecture 4. BEYOND ELLIPTICITY or K-HOMOLOGY AND INDEX THEORY ON CONTACT MANIFOLDS

K-homology is the dual theory to K-theory. The BD (Baum-Douglas) isomorphism of Atiyah-Kasparov K-homology and K-cycle K-homology provides a framework within which the Atiyah-Singer index theorem can be extended to certain differential operators which are hypoelliptic but not elliptic. This talk will consider such a class of differential operators  on compact contact manifolds. These operators have been studied by a number of mathematicians (e.g. C.Epstein and R.Melrose).
 Operators with similar analytical properties have also been studied (e.g. by Alain Connes and Henri Moscovici  --- also Michel Hilsum and Georges Skandalis).  Working within the BD framework, the index problem will be solved for these differential operators on compact contact manifolds. This is joint work with Erik van Erp.