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Arbeitsgruppe Differentialgeometrie

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 1.003
Ute Peters

Adresse
Institut für Algebra und Geometrie
Englerstr. 2
76131 Karlsruhe

Öffnungszeiten:
Mo-Fr 09:00-15:00
Für Studierende:
Mo-Fr 09:15-11:15

Tel.: 0721 608 43943

Fax.: 0721 608 46909

AG Differentialgeometrie (Sommersemester 2019)

Dozent: Prof. Dr. Wilderich Tuschmann
Veranstaltungen: Seminar (0176100)
Semesterwochenstunden: 2


Termine
Seminar: Donnerstag 15:45-17:15 SR 2.66
Dozenten
Seminarleitung Prof. Dr. Wilderich Tuschmann
Sprechstunde:  n. V.
Zimmer 1.002 Kollegiengebäude Mathematik (20.30)
Email: tuschmann@kit.edu

Vorträge


25.4.2019

Georg Frenck (Universität Münster)

The action of Diff(M) on the space of psc metrics

In 1974, Nigel Hitchin showed that the orbit map associated to the action of the diffeomorphism group of the d-dimensional sphere on the space of its positive scalar curvature metrics induces a nontrivial map on components provided that d = 0,1 mod 8. Hence, this map detects non-isotopic psc metrics.

In this talk, I will present a rigidity result for this action. Among other applications, it implies that the orbit map for the sphere is trivial in every other high enough dimension, so Hitchin’s detection result is the only possible one of this kind for high-dimensional spheres.



9.5.2019

Oliver Goertsches (Philipps-Universität Marburg)

Biquotients in symplectic geometry

Biquotients are generalizations of homogeneous spaces that naturally occur in Riemannian geometry, mostly in regards to questions concerning positive and nonnegative curvature. In this talk we will explain why they are also of interest in symplectic and Kähler geometry, by constructing many such structures on equal rank biquotients. Particular emphasis will be put on Eschenburg's twisted flag manifold SU(3)//T, which we will compare to Tolman's and Woodward's examples of symplectic manifolds admitting Hamiltonian non-Kähler torus actions. (This is joint work with Panagiotis Konstantis and Leopold Zoller.)




16.5.2019

Joachim Lohkamp (Universität Münster)

Hyperbolic unfoldingss of minimal hypersurfaces

Minimal Hypersurfaces may carry delicate singularities and both the regular
part of the surface but also the elliptic analysis on such surfaces degenerate towards these
singularities. Nevertheless, we get a surprisingly fine control over the asymptotic analysis of
elliptic equations on these surfaces. This is owing to canonical conformal deformations of the
regular part of the surface to complete Gromov hyperbolic spaces of bounded geometry,
the hyperbolic unfoldings. We introduce to these unfoldings and explain some striking
geometro-analytic applications in potential theory and in scalar curvature geometry.



27.6.2019

Artem Nepechiy (Universität Köln)

Toward canonical convex functions in Alexandrov spaces

For a point $p$ in a Riemannian manifold all small metric balls around $p$ are convex. This is no longer true in the realm of Alexandrov spaces. In particular it might happen that the distance squared function at $p$ is not convex in any neighborhood around $p$.

In this talk I will explain how to construct for every point $p$ in a finite-dimensional Alexandrov space a function in a small neighborhood around p, which approximates the distance squared function at $p$ up to second order and has convexity properties as we would expect it from Euclidean space. Moreover, the function $f$ can be lifted to Gromov-Hausdorff close Alexandrov spaces of the same dimension.