#### Room 326

#### The formulation of the Baum-Connes conjecture

#### Ruben Martos

##### University of Paris 7

*The Baum-Connes conjecture, formulated in 1982 by Paul Baum and Alain Connes,*

is one of the most active topic of research in noncommutative geometry and despite of the

relevant developments after his formulation, the conjecture is still unsolved.

If it is satisfied, then it will allow to prove other well known conjectures of different

areas of mathematics like in geometry (Novikov conjecture) or in analysis (Kadison-

Kaplansky conjecture).

In this talk, we are going to introduce in a simple way the tools used for being able to

formulate the Baum-Connes conjecture in a proper way. More precisely, we’ll define the

classifying space of proper actions of a group G, the G-quivariant K-homology with compact

supports and we’ll show an explicit way of constructing the assembly map. Finally, we’ll do

an overview of the current situation of the conjecture.

Done