Spaces and moduli spaces of Riemannian metrics with curvature bounds - A-Fri-Ka

Jan 23, 2020, 12:30 PM → Jan 24, 2020, 2:00 PM Europe/Berlin

2.058

Georg Frenck (KIT), Wilderich Tuschmann (KIT)

A short workshop on spaces and moduli spaces of Riemannian metrics.

Thursday, January 23

12:30 PM → 2:30 PM Lunch, 'Il Caminetto'

2:30 PM → 3:15 PM Bundles with negatively curved fibers

Speaker: Tom Farrell (KIT)

3:30 PM → 4:15 PM Contractible 3-manifolds and Positive scalar curvature

It is not known whether a contractible 3-manifold admits a complete metric of positive scalar curvature. For example, the Whitehead manifold is a contractible 3-manifold but not homeomorphic to $R^3$. In this talk, we will present my proof that it does not have a complete metric of non-negative scalar curvature. I will further explain that a contractible genus one 3-manifold, a notion introduced by McMillan, does not have a complete metric of non-negative scalar curvature.

Speaker: Jian Wang (Universität Augsburg)

4:15 PM → 5:00 PM Coffee Break

5:00 PM → 5:45 PM Curvature bounds for regularized riemannian metrics

Speaker: Jan-Bernhard Kordaß (University of Fribourg)

6:00 PM → 6:45 PM H-Space multiplications on metrics of positive scalar curvature

Speaker: Georg Frenck (KIT)

6:45 PM → 9:45 PM Dinner, 'La Casa do José

Friday, January 24

9:30 AM → 10:15 AM Moduli spaces of metrics of nonnegative sectional curvature on homotopy RP^7

Speaker: Jonathan Wermelinger (University of Fribourg)

10:30 AM → 11:15 AM Moduli Spaces of Ricci-Flat Metrics on K3 Surfaces

Speaker: David Degen (KIT )

11:30 AM → 12:15 PM Scalar positive immersions

As shown by Gromov-Lawson and Stolz the only obstruction to the existence of positive scalar curvature metrics on closed simply connected manifolds in dimensions at least five appears on spin manifolds, and is given by the non-vanishing of the alpha-genus of Hitchin.

When unobstructed we shall realise a positive scalar curvature metric by an immersion into Euclidean space whose dimension is uniformly close to the classical Whitney upper bound for smooth immersions.
Our main tool is an extrinsic counterpart of the well-known Gromov-Lawson surgery procedure for constructing positive scalar curvature metrics.

Speaker: Bernhard Hanke (Universität Augsburg)

12:30 PM → 2:00 PM Lunch, ‘Kleiner Ketterer’