Paul Mitchener (University of Sheffield)
We describe the coarse category, and look at the coarse version of a homology theory. We then look at an isomorphism conjecture for coarse homology theories, called the coarse Baum-Connes conjecture, and prove it for finite-dimensional coarse cellular complexes; another concept we shall describe in the talk.
To conclude, we formulate the Gromov-Lawson conjecture on the existence of positive scalar curvature metrics on certain manifolds, and indicate how the coarse Baum-Connes conjecture implies it.
The talk is intended to be elementary, and suitable for a general mathematical audience with interest in geometry and topology.