Oberseminar Geometrie, Topologie und Analysis

H. Geiges, G. Marinescu, U. Semmelmann, G. Thorbergsson

Sommersemester 2010

Freitag, 10:30-11:30, Seminarraum 1

4.6.10 Prof. Emma Carberry (Sydney)
Bubble, bubble toil and trouble: constant mean curvature surfaces in Euclidean 3-space

Abstract: I will discuss constant mean curvature surfaces from several viewpoints, and explain how these different points of view are related. The integrable systems approach stems from considering the classical associated family of constant mean curvature surfaces and leads to a complete description of constant mean curvature tori in terms of a linear flow in an abelian variety. Using a generalisation of the classical Darboux transform, I will give a geometric interpretation of this, relate it to a more general construction stemming from work of Martin Schmidt and also explain geometric properties of the transformed surfaces. This is joint work with Katrin Leschke and Franz Pedit.
25.6.10 Prof. Uwe Semmelmann
Fast-komplexe Strukturen auf symmetrischen Räumen

2.7.10 Prof. José Carlos Díaz Ramos (Santiago de Compostela)
Homogeneous hyperpolar foliations on symmetric spaces of noncompact type

Abstract: I will begin this talk with a short introduction to polar and hyperpolar actions on Riemannian manifolds. Then I will focus on hyperpolar actions that induce foliations. I will present rather elementary examples of homogeneous hyperpolar foliations on Euclidean and hyperbolic spaces. These will be the building blocks of the more complicated examples that I will present later. Then I will discuss some of the concepts needed to study symmetric spaces of noncompact type, specially the Langlands decomposition of a noncompact semisimple Lie algebra. This decomposition and the elementary examples on Euclidean and hyperbolic spaces will fit together to produce the complete classification of homogeneous hyperpolar foliations on symmetric spaces of noncompact type.
9.7.10 Prof. Burglind Jöricke (MSRI)
Analytische Knoten, Satelliten und das 4-Ball-Geschlecht

H. Geiges, 5.4.02