Oberseminar Geometrie, Topologie und Analysis

H. Geiges, A. Lytchak, G. Marinescu, G. Thorbergsson

Wintersemester 2013/14

Freitag, 10:30-11:30, Seminarraum 2 (Raum 204)

18.10.13 Michael Brandenbursky (MPI Bonn)
Braids and invariant metrics on groups of area-preserving diffeomorphisms of surfaces

Abstract: We survey results on the large-scale metric properties of groups area-preserving diffeomorphisms of surfaces endowed with the hydrodynamic L2-metric (or more generally the Lp-metric). We prove that every finite dimensional vector space admits a quasi-isometric embedding into these groups, and in particular these groups are unbounded w.r.t. these metrics. Our methods involve quasi-morphisms on braid groups and configuration space integrals. No previous knowledge of the subject will be assumed.
8.11.13 NRW Topology Meeting, MPI Bonn

15.11.13 Calin Martin (Wien)
Local bifurcation and regularity for capillary gravity water waves with constant vorticity

Abstract: We give a local existence result for capillary-gravity water waves at the free surface of water in a flow with constant non-zero vorticity over a flat bed. We will describe how to model the physical problem and the free boundary value problem we will be working with. To study the free boundary problem we will reformulate it as a quasilinear equation in fixed domain for a periodic function of one variable. We will apply for the obtained quasilinear equation bifurcation tools in the spirit of Crandall-Rabinowitz.
13.12.13 Bochum-Köln-Münster-Seminar in Bochum

10.1.14 Simone Diverio (Paris 6)
Kobayashi hyperbolicity and positivity properties of the canonical bundle

Abstract: Let X be a smooth projective manifold. In this talk we will describe the conjectural equivalence (due, among others, to Lang) between the analytic property of being Kobayashi hyperbolic and the algebraic property for X of being of general type together with all its subvarieties. We shall try then to give some evidences toward this equivalence, possibly in both directions, describing some recent results. If time permits, we will see the limits of a classical approach (degeneracy of the Green-Griffiths locus) to prove the sufficiency part of the conjecture.
17.1.14 Stefan Wenger (Fribourg)
Lipschitz homotopy groups of the Heisenberg groups

Abstract: The n-th Heisenberg group Hn, when endowed with its sub-Riemannian metric, is homeomorphic to Euclidean space R2n+1, however not even locally biLipschitz homeomorphic to it. We study the question for which integers k Lipschitz maps from the Euclidean k-sphere to Hn extend to Lipschitz maps on the (k+1)-ball. When k < n such extensions always exist. When k = n, however, no "non-trivial" Lipschitz map from Sn to Hn admits an extension. The situation is more complicated and not yet well understood for k > n. In this talk I will describe what is known about this problem. In particular, I will answer in the negative the following question, recently raised by DeJarnette-Hajlasz-Lukyanenko-Tyson: is it true that the composition of a homotopically non-trivial Lipschitz map from Sk to Sn with a biLipschitz embedding of Sn into Hn does not admit a Lipschitz extension to the (k+1)-ball? Based on considerations involving Sard's theorem, one would expect a positive answer to this question. This talk is based on joint work with Robert Young.
24.1.14 Christoph Böhm (Münster)
Long-time behaviour of homogeneous Ricci flows

31.1.14 Hugues Auvray (ENS Cachan)
Asymptotic properties of extremal Kähler metrics of Poincaré type

H. Geiges, 5.4.02