Positive scalar curvature, index theory, and the minimal surfaces:
(a counterexample to the Gromov-Lawson-Rosenberg conjecture)

Abstract:
We adress the question which closed manifolds admit a metric with
positive scalar curvature.

The talk describes obstructions which use the Atiyah-Singer index
formula (and refinements where the obstruction lives in the K-theory
of the reduced C*-algebra of the fundamental group). For some time,
the "Gromov-Lawson-Rosenberg"-conjecture stated that these are the
only obstructions.
We give a counterexample to this conjecture, using the minimal
surfaces and geometric measure theory.