Vorträge in der Woche 01.02.2016 bis 07.02.2016

Montag, 01.02.2016: Moduli spaces in Geometry and Physics

Dr. Jan Swoboda (LMU München / Universität Heidelberg)

In this talk, I aim to give an overview of some known results and several open questions concerning geometric, analytical and topological properties of some wellknown moduli spaces in geometry and physics, such as the Teichm¨uller moduli space T of hyperbolic metrics and the moduli spaceMk,d of stable Higgs bundles (of rank k and degree d) on a closed surface of genus larger than one. Concerning the latter, I shall in particular discuss the construction ofMk,d as the space of gauge equivalence classes of solutions to Hitchin’s self-duality equations. Some recent results (obtained jointly with Rafe Mazzeo, Hartmut Weiß and Frederik Witt) concerning the structure of ends ofM2,d as well as the large scale geometry of a naturally defined hyperk¨ahler metric will be presented. If time permits, I will also discuss a gluing construction which allows to compareM2,d with its counterpart comprising singular solutions on a noded Riemann surface.

Dienstag, 02.02.2016: Limits and degenerations of the Higgs bundle moduli space

Dr. Jan Swoboda (LMU München / Universität Heidelberg)

Dienstag, 02.02.2016: Local zeta functions of T-groups of class 2

Julien Sessler

Donnerstag, 04.02.2016: Regularity of stable CMC hypersurfaces

Prof. Neshan Wickramasekera (University of Cambridge)

I will describle joint work with Costante Bellettini (Cambridge) in which we develop a regularity theory for a class of hypersurfaces of a smooth Riemannian manifold that are stationary and stable for area with respect to volume preserving ambient deformations. The hypersurfaces (codimension 1 integral varifolds) in this class are required to satisfy two structural conditions: (1) they have no classical singularities. A classical singularity is a point about which there is a neighborhood in which the hypersurface is supported on three or more embedded sheets coming smoothly and transversely together along a common boundary. (2) if $y$ is a touching singularity---i.e. a point where the hypersurface locally is supported on two distinct $C^{1, alpha}$ graphs touching at that point---then there is a neighborhood of $y$ in which the set of points with density equal to the density at $y$ has zero $n$-dimensional Hausdorff measure, where $n$ is the dimension of the hypersurface. We show that such a hypersurface, away from a closed set of codimension at least 7, locally is supported on a smooth graph or two smooth graphs touching. Easy examples show that (1) and (2) are necessary. If the hypersurface is the boundary of a Caccioppoli set, then (2) is automatically satisfied. We also show that a collection of such hypersurfaces satisfying uniform volume and mean curvature bounds is compact in the varifold topology.

Donnerstag, 04.02.2016: Almost non-negative curvature, what's new?

Prof. Dr. Esther Cabezas-Rivas (Goethe-Universität Frankfurt)

We will review some classical problems in Differential Geometry, which lead us to work with manifolds with almost non-negative curvature. In particular, we will explain during the talk why it is natural to wonder weather for these manifolds a topological invariant called Â-genus vanishes (this question was proposed by John Lott in 1997). We will provide a positive answer by investigating sequences of spin manifolds with lower sectional curvature bound, upper diameter bound and the property that the Dirac operator is not invertible. As a key ingredient of the proof we prove a generalization (under weaker curvature assumptions) of the renowned theorem by Gromov about almost flat manifolds. This is joint work with Burkhard Wilking.

Donnerstag, 04.02.2016: Mathematische Experimente: Von realem Tun zu mathematischen Einsichten

Prof. Dr. Albrecht Beutelspacher (Universität Gießen)

In dem Vortrag wird gezeigt, wie man mit technisch sehr einfachen Experimenten mathematische Vorstellungen entwickeln und Erkenntnisse erzielen kann. Die Experimente können unmittelbar im Unterricht umgesetzt werden. Ein Vortrag, der Erkenntnisgewinn und Vergnügen an der Sache kombiniert.

Freitag, 05.02.2016: Zum Zusammenhang von annealed und quenched Lyapunov-Exponenten für die einfache symmetrische Irrfahrt

Gundelinde Wiegel (Universität Tübingen)

Freitag, 05.02.2016: Starke Transienz von stochastischen Prozessen

Thomas Jakob (Universität Tübingen)