# Sanaz Pooya: The Baum-Connes conjecture via explicit examples

**Time: **
Wed 2019-03-20 13.15 - 15.00

**Lecturer: **
Sanaz Pooya (SU)

**Location: ** Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Abstract: The Baum-Connes conjecture, generalising the Atiyah-Singer index theorem, suggests a link between operator algebras and topology/geometry. The link is provided via the so-called assembly map and the conjecture is that this map is an isomorphism of two abelian groups; equivariant K-homology and K-theory of specific objects constructed from a group. The conjecture is formulated for all second countable groups. Up to date, it is known that the conjecture holds true for large classes of groups, including amenable groups and free groups however it is still open for linear groups. In this talk, I will take a different perspective and provide an alternative proof for bijectivity of the assembly map for one specific class of groups. I will also give a brief account of the development of the theory around this conjecture since its birth 1982.