"`Positive scalar curvature"'

Question: given a smooth compact manifold M (without boundary), is it possible to put a Riemannian metric with positive scalar curvature on M. If yes, how does the space of such metrics look like. This question has a number of fascinating answers, relating it to algebraic topology, index theory, "coarse" geometry. During this semester, quite a few people who have looked at this problem (and are still working at it's further advancement) are present in Goettingen. We will, starting from the beginning, look at the different facets of the problem. Program (dvi). Literatur: