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

Europe/Berlin
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Description

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

Registration
Participants
Participants
• Anand Dessai
• Bernhard Hanke
• David Degen
• Georg Frenck
• Jan-Bernhard Kordaß
• Jian Wang
• Jonathan Wermelinger
• Martin Günther
• Thomas Farrell
• Wilderich Tuschmann
• Thursday, 23 January
• 12:30 14:30
Lunch, 'Il Caminetto' 2h
• 14:30 15:15
Bundles with negatively curved fibers 45m 2.058

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Speaker: Tom Farrell (KIT)
• 15:30 16:15
Contractible 3-manifolds and Positive scalar curvature 45m 2.058

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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)
• 16:15 17:00
Coffee Break 45m 1.058

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• 17:00 17:45
Curvature bounds for regularized riemannian metrics 45m 2.058

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Speaker: Jan-Bernhard Kordaß (University of Fribourg)
• 18:00 18:45
H-Space multiplications on metrics of positive scalar curvature 45m 2.058

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Speaker: Georg Frenck (KIT)
• 18:45 21:45
Dinner, 'La Casa do José 3h
• Friday, 24 January
• 09:30 10:15
Moduli spaces of metrics of nonnegative sectional curvature on homotopy RP^7 45m 0.019

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Speaker: Jonathan Wermelinger (University of Fribourg)
• 10:30 11:15
Moduli Spaces of Ricci-Flat Metrics on K3 Surfaces 45m 0.019

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Speaker: David Degen (KIT )
• 11:30 12:15
Scalar positive immersions 45m 0.019

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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 14:00
Lunch, ‘Kleiner Ketterer’ 1h 30m
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