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AG Differentialgeometrie (Winter Semester 2018/19)

Seminar: Thursday 17:30-19:00 SR 2.67
Lecturer Prof. Dr. Wilderich Tuschmann (Spokesman of the Institute)
Office hours: by appointment - please contact me by email;
Room 1.002 Kollegiengebäude Mathematik (20.30)
Email: tuschmann@kit.edu



Martin Günther (KIT): An introduction to Lorentz geometry

In this talk, I will give a fairly low-level introduction to pseudo-Riemannian, and esp. Lorentzian geometry. I will discuss some differences to the Riemannian setting, introduce the basics of causality theory, and discuss the generalization of the Cheeger-Gromoll splitting theorem to the Lorentzian setting by Newman. This is an extended version of the talk I gave at the PhD-Seminar in Simonswald.

15.11.2018 (2 Talks)

Adam Moreno (University of Notre Dame): The Boundary Conjecture for Leaf Spaces

The boundary conjecture asks "Is the boundary of an Alexandrov space itself an Alexandrov space?" Attacking this problem is messy general. However, quotients of singular Riemannian foliations (with closed leaves), called leaf spaces, are a particularly nice type of Alexandrov space with a more approachable geometry. In this talk, we will use this geometry to prove the boundary conjecture for this special case. Given this generality, we see that the boundary conjecture also holds for orbit spaces of isometric group actions by compact Lie groups.

Jackson Goodman (University of Pennsylvania): Spin^c Dirac operators and moduli spaces of metrics.

The Kreck-Stolz s invariant is used to distinguish connected components of the moduli space of positive scalar curvature metrics. We use the Spin^c Dirac operator to generalize a formula of Kreck and Stolz for the s invariant of S^1 invariant metrics with positive scalar curvature. We then apply it to show that the moduli spaces of metrics with nonnegative sectional curvature on certain 7-manifolds have infinitely many path components. These include certain positively curved Eschenburg and Aloff-Wallach spaces. Furthermore, we use a Spin^c version of the s invariant to discuss moduli spaces of metrics of positive scalar and twisted scalar curvature on Spin^c manifolds.


Johannes Riesterer (TECO): Stochastische Regressionsmodelle auf Basis heterogener Messnetzwerke

Wir stellen ein Verfahren vor, das verbesserte, stochastische Vorhersagen unter Hinzunahme unsicherer Sensoren unbekannter Qualität ermöglicht. Grundlage hierfür ist die Kombination eines Qualitätsmodells mit einem Gauß-Prozeß-Regressionsverfahren in Form von Hyperparameter, welche durch einen genetischen Algorithmus optimiert werden. Innerhalb des Vortrages wird auch auf geometrische Aspekte und Konzepte des maschinellen Lernens eingegangen.


David González Álvaro (University of Fribourg): Open manifolds with positively curved souls

As Cheeger and Gromoll showed, an open manifold with a metric of non-negative sectional curvature is diffeomorphic to the normal bundle of certain totally convex closed submanifold, called the soul. It is possible to construct open manifolds with two or more such metrics whose souls are "different": we will review previous examples and we will construct open manifolds with non-homeomorphic positively curved souls. To do that we will study some properties of Eschenburg spaces, an infinite family of positively curved manifolds.