Research Group Differential Geometry

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 1.003
Ute Peters

Institut für Algebra und Geometrie
Englerstr. 2
D-76131 Karlsruhe

Office hours:
Mo-Fr 09:00-15:00
Für Studierende:
Mo-Fr 09:15-11:15

Tel.: +49 721 608 43943

Fax.: +49 721 608 46909

# AG Differentialgeometrie (Summer Semester 2015)

 Lecturer: Prof. Dr. Wilderich Tuschmann (speaker of the institute) Seminar (0176100) 2

 Seminar: Wednesday 11:30-13:00 SR 2.58 Wednesday 11:30-13:00 Z 2
 Lecturer Prof. Dr. Wilderich Tuschmann (speaker of the institute) Office hours: by appointment; during lecture period: Thu. 10:15 - 11:15 Room 1.002 Kollegiengebäude Mathematik (20.30) Email: tuschmann@kit.edu

# 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 di erential equations. Furthermore, I introduce
new techniques to finding solutions of these boundary value problems and discuss several
interesting examples.

# 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.