Abstract: Groupoids are a natural setting to deal with non proper (semi) group actions. Their convolution algebras can be viewed as a natural generalization of the quotient space of a proper action. A topological groupoid, equipped with a closed cocycle, gives rise to a metric structure on the convolution algebra, in the form of an unbounded KK-cycle. Such cycles are central in noncommutative geometry, and give rise to index maps in K-theory. I will discuss these concepts and explain the philosophy of noncommutative geometry. Then I will discuss how the Patterson-Sullivan measure on the limit set of a Kleinian group gives rise to a field of noncommutative geometries parametrized by the hyperbolic manifold uniformized by the group.


Here is a link to the slides of Mesland’s talk.

Location: room 611 of the Wiskunde building (campus De Uithof) Budapestlaan 6, Utrecht.

Date and time: Thursday, October 1, 2009 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.