**Date & Time:** Monday, January 26, 2009, 15:30-16:30.

**Venue:** Ramanujan Hall

**Title:** K-Theory of Homogeneous Spaces -I

**Speaker:** Parameswaran Sankaran, IMSc Chennai

**Abstract:** We consider smooth compact manifolds on which a compact connected Lie group *G* acts transitively. The problem of determining the K-ring of such a homogeneous space *G/H* is closely related to the complex representation ring of *G* and that of the isotropy subgroup *H*. The result is well-known and goes back to the work of Atiyah and Hirzebruch in the case when *G* is classical and *H* connected of maximal rank. We shall discuss this as well as the case where *H* is not of maximal rank and possibly not even connected. Some applications to topology of certain homogeneous spaces will be discussed.