# AG Differentialgeometrie (Summer Semester 2015)

Lecturer: | Prof. Dr. Wilderich Tuschmann |
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Classes: | Seminar (0176100) |

Weekly hours: | 2 |

Seminar: | Wednesday 11:30-13:00 | SR 2.58 |
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Wednesday 11:30-13:00 | Z 2 |

Lecturer | Prof. Dr. Wilderich Tuschmann |
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Office hours: by appointment; during lecture period: Thu. 10:15 - 11:15 | |

Room 1.002 Kollegiengebäude Mathematik (20.30) | |

Email: tuschmann@kit.edu |

# Future talks

# Thursday, 25.6.2015

# SR 2.58, 15:45–17:15.

**Speaker:** Anna Siffert (University of Pennsylvania)

**Title:** Harmomic maps of cohomogeneity one manifolds

**Abstract:** In my talk I present a method for reducing the problem of constructing harmonic

self-map of cohomogeneity one manifolds to solving non-standard singular boundary

value problems for non-linear ordinary dierential equations. Furthermore, I introduce

new techniques to finding solutions of these boundary value problems and discuss several

interesting examples.

# Previous talks

# Wednesday, 3.6.2015

**Speaker:** Matthias Franz (University of Western Ontario/Augsburg)

**Title:** Big polygon spaces and syzygies in equivariant cohomology

**Abstract:** Polygon spaces are configuration spaces of polygons with prescribed edge lengths. We present a related family of compact orientable manifolds, called big polygon spaces. They come with a canonical torus action, whose fixed point set is a polygon spaces. Big polygon spaces are particularly interesting because they provide the only known examples of maximal syzygies in equivariant cohomology. I will therefore start by reviewing the theory of syzygies in equivariant cohomology for actions of compact connected Lie groups as well as its relation to the equivariant Poincaré pairing and the "GKM method"

# Thursday, 28.5.2015

**Speaker:** Michael Wiemeler (Universität Augsburg)

**Title:** Invariant metrics of positive scalar curvature on S^1-manifolds

**Abstract:** In this talk we will discuss the construction of invariant metrics of positive scalar curvature on manifolds $M$ with circle actions. We will discuss two cases. First the case where there is a fixed point component of codimension two. Then there is always an invariant metric of positive scalar curvature on $M$.

The case where the fixed point set has codimension at least four is more complicated. In this case the answer to the question if there is an invariant metric of positive scalar curvature on $M$ depends on the class of M in a certain equivariant bordism group. We will discuss the case, where the maximal stratum of $M$ is simply connected and all normal bundles to the singular strata are complex vector bundles, in more detail. In this case there is an $l\in \mathbb{N}$ such that the equivariant connected sum of $2^l$ copies of $M$ admits an invariant metric of positive scalar curvature if and only if a $\mathbb{Z}\frac{1}{2}$-valued bordism invariant of $M$ vanishes.

# Wednesday, 27.5.2015

**Speaker:** Martin Kell (IHES)

**Title:** Heat, Entropy and Curvature

**Abstract:** In this talk I will present how the interplay of the heat and entropy flow, more precisely the viewpoint of one and the same flow, helps to naturally combine geometry and analysis of a spaces.