Together with Rudolf Zeidler I am organizing a reading seminar this winter on generalized soap bubbles and positive scalar curvature. The goal of it is to read the corresponding preprint by Chodosh-Li (arXiv:2008.11888). The two main results we want to understand are the following:
No closed aspherical manifold of dimension 4 or 5 admits a Riemannian metric with positive scalar curvature.
Let n≤7 and let X be any n-dimensional manifold (without boundary). Then Tn#X does not admit any complete Riemannian metric with positive scalar curvature.
The proofs use the minimal hypersurface technique to obstruct positive scalar curvature metrics. The original approach to this was developed by Schoen and Yau and in fact, we will also discuss as a gentle starter into the seminar their classical proof that the n-torus does not admit any metric with positive scalar curvature.
The reading seminar will be held via zoom and is open to participants from outside of Münster. The concrete programme may be found here: link. The tentative date and time is Wednesdays 10-12 with the first talk on November 4th. If you wish to participate actively, please send an E-Mail either to me (email@example.com) or to Rudolf Zeidler (firstname.lastname@example.org) until October 26th indicating which parts from the programme you are willing to cover.