### AG Differentialgeometrie (Summer Semester 2018)

- Lecturer: Prof. Dr. Wilderich Tuschmann
- Classes: Seminar (0176100)
- Weekly hours: 2

Schedule | ||
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Seminar: | Thursday 15:45-17:15 | SR 2.66 |

Lecturers | ||
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Lecturer | Prof. Dr. Wilderich Tuschmann | |

Office hours: by appointment - please contact me by email; | ||

Room 1.002 Kollegiengebäude Mathematik (20.30) | ||

Email: tuschmann@kit.edu |

**Talks**

** 25.4.2018**

**Diego Corro (KIT)**

* Manifolds with singular Riemannian foliations by aspherical leaves*

** 17.5.2018**

**Anand Dessai (Université de Fribourg)**

*Moduli space of metrics of nonnegative sectional/positive Ricci curvature on homotopy real projective spaces *

We show that the moduli space of metrics of nonnegative sectional curvature on a smooth closed manifold homotopy equivalent to RP5 has infinitely many connected components. We also discuss corresponding results in higher dimensions for the moduli space of metrics of positive Ricci curvature. The proof uses eta invariants.

** 24.5.2018**

**Ruobing Zhang (State University of New York, Stony Brook)**

*Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces*

We exhibit sequences of Ricci-flat K ähler metrics on K3 surfaces which collapse to an interval. There is a corresponding singular fibration from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds, while each singular fiber is a singular circle bundle over a torus.

** 5.7.2018**

**Mauricio Bustamante (Universität Augsburg)**

*Bundles with fiberwise negatively curved metrics*

A smooth M-bundle is said to be negatively curved if its fibers are equipped with Riemannian metrics of negative sectional curvature, varying continuously from fiber to fiber. The difference between negatively curved M-bundles and smooth M-bundles is measured by the space of all negatively curved metrics on M. In this talk I will show that the latter space has non-trivial rational homotopy groups, provided certain dimension constraints are satisfied. Hence the two bundle theories may differ. The results extend to other spaces of metrics without conjugate points. This is joint work with F.T. Farrell and Y. Jiang.

** 12.7.2018**

**Michael Wiemeler (Universität Münster)**

*Applications of the work of Chang and Skjelbred to manifolds
with positive curvature*

I will report on ongoing joint work with Lee Kennard and

Burkhard Wilking on the cohomology of manifolds with positive sectional

curvature and isometric torus actions. If the dimension of the acting

torus is high enough and the action is equivariantly formal we can

compute the rational cohomology ring of the manifold.