Abstracts

Prof. Bernd Ammann und Mitarbeiter, Zimmer 119

Sebastian Heller, Tübingen

Modulräume flacher Zusammenhänge und integrable Flächentheorie

In diesem Vortrag werde ich erläutern, wie man kompakte Flächen konstanter mittlerer Krümmung (CMC) in Raumformen mittels spezieller Kurven in den Modulraum flacher SL(2,C)-Zusammenhänge erhält. Dies führt dann zur Definition der Spektraldaten von (symmetrischen) CMC Flächen. Im zweiten Teil des Vortrags berichte ich über eine aktuellen Arbeit (mit L. Heller und N. Schmitt), in welcher wir eine Methode zur systematischen Konstruktion von Spektraldaten von CMC Flächen höheren Geschlechts einführen.

Stuart Hall

Canonical metrics in 4-dimensions - a tale of two surfaces

The complex surface CP^2#-CP^2 admits an Einstein metric due to Page, a Kähler-Ricci soliton due to Koiso and Cao and a one-parameter family of quasi-Einstein metrics due to Lü-Page-Pope. The surface CP^2#-2CP^2 admits an Einstein metric due to Chen-LeBrun-Weber and a Kähler-Ricci soliton due to Wang and Zhu. It is currently an open problem as to whether CP^2#-2CP^2 admits quasi-Einstein metrics analogous to the Lü-Page-Pope metrics. I'll talk about progress in answering this question including joint work with Wafaa Batat, Ali Jizany and Thomas Murphy.

Volker Branding

Dirac-harmonic maps, extensions and applications

In the first part of the talk we will give an introduction to the notion of Dirac-harmonic maps. These arise as critical points of a functional, that is motivated from the supersymmetric nonlinear sigma model in quantum field theory. However, the full supersymmetric nonlinear sigma model contains additional terms, that are not captured by the analysis of Dirac-harmonic maps. We will discuss several extensions of Dirac-harmonic maps, in particular geometric and analytic properties of the latter. If time permits, we will also point out a geometric application of Dirac-harmonic maps. hr>
Bernd Ammann, 4.6.2015 oder später