Boris Okun, z. Z. MPIM Bonn
"Action Dimension and L2-homology"
The action dimension of a group G, actdim(G) is the least dimension of a contractible manifold which admits a proper G-action. The action dimension conjecture states that L^2-homology of any group G vanishes above actdim(G)/2.
I will explain the equivalence of this conjecture to the classical Singer conjecture. I will also explain a computation of actdim for the right-angled Artin groups.
This is based on a joint work with Kevin Schreve, and also with Grigori Avramidi, and Mike Davis.