SPP 1154:  Global Differential Geometry

• Subject Area: Mathematics
• Term: from 2003 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5471954

The Priority Programme supports projects in Global Riemannian Geometry, Geometric Analysis and Symplectic Geometry with a particular emphasize on interaction between these research areas.Global Riemannian Geometry covers global problems concerning geometric structures: for instance existence and obstruction results for metrics with prescribed curvature or geometric structures on low-dimensional manifolds. Typical methods used include geometric limits, asymptotic symmetry and homotopy principles. Also, extending the frame of smooth Riemannian geometry, the geometry of singular spaces with curvature bounds is part of the project. The main topics of the Geometric Analysis part of the programme are the spectral geometry of elliptic operators in Riemannian geometry (including applications in differential topology), the geometry and analysis on (and related to) Lorentzian manifolds and the analysis of submanifolds of constant mean curvature. Symplectic Geometry treats questions related to symplectic invariants, Hamiltonian dynamical systems, Lagrangian submanifolds and contact structures on odd-dimensional manifolds.

• DFG Programme: Priority Programmes
• International Connection: Australia, Canada, Italy, New Zealand, Switzerland, USA

Projects

• Analysis of Floer Homology, its Natural Ring Structure and its S1-equivariant version, in Relation with the Free Loop Space and Symplectic Invariants (Applicant Schwarz, Matthias )
• Analysis of singularities of the Lagrangian mean curvature flow with pseudo-holomorphic curves (Applicant Smoczyk, Knut )
• Analysis of singularities of the Lagrangian mean curvature flow with pseudo-holomorphic curves (Applicant Schwarz, Matthias )
• Analytic aspects of almost Kähler manifolds (Applicant Wang, Guofang )
• Asymptotic Invariants of Manifolds (Applicant Kotschick, Ph.D., Dieter )
• Asymptotic limits of SCFTs and their relation to corresponding geometric structures, combining techniques from SCFT, noncommutative geometry, and algebraic geometry (Applicant Wendland, Katrin )
• Classification of isoparametric hypersurfaces (Applicant Kramer, Linus )
• Conformal Geometry of Generalized Brinkmann Spaces (Applicant Kühnel, Wolfgang )
• Conformal Geometry of semi-Riemannian Manifolds (Applicant Rademacher, Hans-Bert )
• Constrained Willmore surfaces (Applicant Bobenko, Alexander I. )
• Constrained Willmore surfaces (Applicants Pedit, Franz ;  Pinkall, Ulrich )
• Construction of Functoriality for Floer Homology together with its Ring Structure and Applications for Symplectic Invariants and Lagrangian Intersections (Applicant Schwarz, Matthias )
• Coordination (Applicant Lohkamp, Joachim )
• Deformations of 3-dimensional cone-manifold structures (Applicant Weiß, Hartmut )
• Differential geometric study of conformal and CR invariant theory via the ambient metric construction due to Fefferman and Graham (Applicant Leitner, Felipe )
• Differential geometric study of conformal and CR invariant theory via the ambient metric construction due to Fefferman and Graham (Applicant Leitner, Felipe )
• Differential Geometry of Singular Spaces (Applicant Bernig, Andreas )
• Differential operators and relations between G-structures (Applicant Belgun, Florin )
• Ergodic geometry in nonpositive curvature (Applicant Link, Gabriele )
• Families of contact structures on 3-manifolds; surgery descriptions and open book decompostions of contact manifolds (Applicant Geiges, Hansjörg )
• Finsler Metrics and Closed Geodesics (Applicant Rademacher, Hans-Bert )
• Fortführung und Erweiterung des Projektes `Functoriality for Floer homology` und Erlernen der neuen Techniken entwickelt von H. Hofer (Applicant Albers, Peter )
• Geodesic flows and billiards in the presence of magnetic fields (Applicant Siburg, Karl Friedrich )
• Geometric Formality (Applicant Kotschick, Ph.D., Dieter )
• Geometric problems in semi-Riemannian manifolds (Applicant Gerhardt, Claus )
• Geometric structures on aspherical manifolds (Applicants Baues, Oliver ;  Cortés, Vicente )
• Geometrische Indextheorie für Faserbündel mit Ecken (Applicant Bunke, Ulrich )
• Geometrische und getwistete algebraische Topologie (Applicant Bunke, Ulrich )
• Geometrisierung in Dimension 3 und Geometrie singulärer Räume (Applicant Leeb, Bernhard )
• Geometry and analysis of semi-algebraic sets (Applicant Grieser, Daniel )
• Geometry of Engel structures (Applicant Vogel, Thomas )
• Global analysis and geometry of Lorentzian manifolds (Applicant Bär, Christian )
• Global Ricci and scalar curvature problems in semi-Riemannian geometry (Applicant Finster, Felix )
• Global theory of geodesically equivalent metrics (Applicant Matveev, Vladimir )
• Globale Geometrie von singulären Riemannschen Blätterungen (Applicant Töben, Dirk )
• Hamiltonian chords of quantized action (Applicant Frauenfelder, Urs )
• Harmonic spaces in Riemannian geometry (Applicant Knieper, Gerhard )
• Harmonic spaces in Riemannian geometry (Applicant Heber, Jens )
• Higher Torsion Invariants and Applications to Smooth Maps, Bundles and Foliations (Applicant Goette, Sebastian )
• Index theoretic approaches to the classification of positive scalar curvature (Applicant Schick, Thomas )
• Index theoretic approaches to the classification of positive scalar curvature (Applicant Hanke, Bernhard )
• L2-invariants (Applicant Schick, Thomas )
• Lagrangean Isotopy Problem and Special Lagrangian Submanifolds in Symplectic Geometry (Applicant Shevchishin, Vsevolod )
• Lie transformation groups in Riemannian geometry (Applicant Thorbergsson, Gudlaugur )
• Lorentzian and conformal manifolds with special holonomy (Applicants Baum, Helga ;  Leitner, Felipe )
• Lorentzian and conformal manifolds with special holonomy (Applicant Leitner, Felipe )
• Manifolds with Nonnegative and Almost Nonnegative Curvature (Applicant Tuschmann, Wilderich )
• Minimal surfaces, constant mean curvature surfaces, and the isoperimetric problem (Applicant Abresch, Uwe )
• Mirror symmetry, affine geometry and Gromov-Hausdorff limits (Applicant Siebert, Bernd )
• Nearly Kähler geometry (Applicant Semmelmann, Uwe )
• Noncommutative Geometry and Geometric Structures (Applicant Bär, Christian )
• Polygons in symmetric spaces and buildings with applications to algebra (Applicant Leeb, Bernhard )
• Positive scalar curvature at the intersection of global analysis, geometric topology and coarse geometry (Applicants Hanke, Bernhard ;  Schick, Thomas )
• Punctured Holomorphic Curves in Symplectic Geometry (Applicants Cieliebak, Kai ;  Mohnke, Klaus )
• Punctured Holomorphic Curves in Symplectic Geometry (Applicant Mohnke, Klaus )
• Representations whose orbit spaces have boundary (Applicant Wilking, Burkhard )
• Restrictions on scalar curvature and first Dirac eigenvalue of closed manifolds (Applicant Goette, Sebastian )
• Riemannian metrics with lower curvature bounds. Special symplectic connections and symplectic realizations. (Applicant Schwachhöfer, Lorenz )
• Scalar Curvature Contents (Applicant Lohkamp, Joachim )
• Selfsimilar solutions of the mean curvature flow (Applicant Smoczyk, Knut )
• Singular Riemannian foliation (Applicant Töben, Dirk )
• Smooth extensions of generalized cohomology theories (Applicant Bunke, Ulrich )
• Special Geometries and Fermionic Field Equations (Applicant Friedrich, Thomas )
• Spectral theory of Dirac and Laplace operators (Applicant Müller, Werner )
• Stability of non-compact manifolds under curvature flows (Applicants Schnürer, Oliver ;  Schulze, Felix )
• Stratifications of spaces with nonnegative sectional curvature and their relation to global structures and invariants (Applicants Abresch, Uwe ;  Püttmann, Thomas )
• Surface Geometry and Integrable Systems: Theory and Experiment (Applicant Pedit, Franz )
• Surfaces of constant mean curvature, harmonic tori, and pluriharmonic maps (Applicant Eschenburg, Jost-Hinrich )
• Surfaces of constant mean curvature with non-trivial topology and pluriharmonic maps (Applicants Dorfmeister, Josef ;  Eschenburg, Jost-Hinrich )
• Surfaces with prescribed curvature in theory and application (Applicant Grosse-Brauckmann, Karsten )
• Symmetric spaces of Kac-Moody type (Applicant Heintze, Ernst )
• Symplectic and complex geometry (Applicant Siebert, Bernd )
• The geometry of moduli space and the mapping class group (Applicant Hamenstädt, Ursula )
• The structure of pseudo-Riemannian symmetric spaces and holonomy groups (Applicant Kath, Ines )
• The symplectic vortex equations and applications (Applicant Cieliebak, Kai )
• Topology of positively curved manifolds with symmetry (Applicant Dessai, Anand )
• Transformations on harmonic maps and Willmore surfaces (Applicant Leschke, Katrin )

• Spokesperson: Professor Dr. Joachim Lohkamp