L^2-invariants, homology growth and embedding theory, II

For a closed manifold M with contractible universal cover, the Singer conjecture predicts that the L^2-Betti numbers of M are concentrated in the middle dimension. In this minicourse I will introduce L^2-Betti numbers and discuss the history of Singer's conjecture, its reinterpretation as a question about rational homology growth in finite covers, and how variations involving torsion and F_p homology growth can be addressed with the help of some very classical embedding theory.