Spring 2013, Thursdays, Milner 216, 4:00-4:50 PM

Date: April 4

"  Introduction to noncommutative geometry and the Baum-Connes conjecture "
  Jianchao Wu  Texas A&M and Vanderbilt University


Noncommutative geometry, first developed by Alain Connes as a result of his attempts to generalize the Atiyah-Singer index theorem, uses functional analytic or operator algebraic tools to study geometry and topology. A central problem and major driving force in the area is the Baum-Connes conjecture, which asserts a certain assembly map on K-theory is an isomorphism, and takes as consequences many long-standing conjectures, for instance, the Novikov conjecture in topology and Klapansky's idempotent conjecture in algebra. I will start from some basic notions in noncommutative geometry, and tell you why the Baum-Connes conjecture is important and what is known about it.