**Date & Time:** Thursday, July 24, 2014, 16:30-17:30.

**Venue:** Ramanujan Hall

**Speaker:** Snigdhayan Mahanta, University of Münster

**Title:** Bivariant homology theories for noncommutative spaces

**Abstract:** In noncommutative geometry C*-algebras play the role of noncommutative spaces. Several problems in geometry and topology can be formulated (and solved) in terms of certain bivariant homology theories like KK-theory and periodic cyclic homology. The celebrated Baum-Connes Conjecture is a prime example, which is formulated in terms of KK-theory, and over the years it has emerged as one of the most successful techniques to prove the Strong Novikov Conjecture in topology. In the first part of the talk I am going to present an axiomatic framework for such bivariant homology theories. In the second part of the talk I am going to discuss some computations and applications focussing mainly on the universal example.