On this site you find the list of projects supported by the DFG priority programme „Geometry at Infinity“. The pages of the individual projects provide information on their research goals, publications, members, and activities.
The project belongs to higher Teichmüller Theory, it aims to define Hitchin components for orbifolds and analyze its topological and geometric properties, to study the degeneration of Hitchin representations for small orbifolds in order to understand general surface groups, and to parametrize Hitchin components for orbifolds.
The project focuses on studying geometric properties for sofic approximations of discrete groups and manifolds. It consists of three interacting themes: sofic boundary actions, study of analytic/geometric properties of groups using actions at infinity, and sofic manifolds.
The project studies, for Riemannian manifolds whose geometry at infinity is compatible with a Lie structure at infinity, the spectrum and the spectral density of geometric operators, emphasizing on the classical Dirac operator.
The project investigates local index theory and secondary invariants of foliations on a closed manifold, in particular eta and torsion forms for foliations both in the Haefliger setting and in the noncommutative one, and large time estimates for heat operators associated to Bismut superconnections.
The project aims to obtain new insights into certain asymptotic topological and homological invariants of groups, specifically the Sigma-invariants introduced by Bieri-Neumann-Strebel and Bieri-Renz, universal L2-torsion introduced by Friedl-Lück, and higher generation introduced by Abels-Holz.
The project aims at applying and developing equivariant topological methods in the context of Riemannian manifolds with a lower sectional curvature bound, and at studying closed Alexandrov spaces of cohomogeneity one.
The project aims to develop analytic tools for analyzing natural geometric differential operators associated to fibred cusp metrics and to apply these tools to problems in global analysis and spectral theory.
15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds
The project aims to construct non-zero classes in higher homotopy groups of the space of complete metrics of uniformly positive scalar curvature, to investigate when there exists a smoothly varying family of metrics satisfying some specific curvature bounds on the fibres of a smooth bundle, and to construct new examples of manifolds with disconnected moduli spaces of metrics of nonnegative sectional curvature and / or positive Ricci curvature.
The project studies analytic L2-invariants and compares them to combinatorial L2-invariants of suitable compactifications of the manifold in a variety of situations. Moreover it intends to initiate a study of twisted L2-torsions as a function on representation varieties.
The project will study the interplay between geometric properties of the Dirichlet space, spectral features of the generator of the Dirichlet form and stochastic features of the associated Markov process.
The project will be devoted to treatment of spectral geometric questions, index theory and geometric flows using the currently available microlocal methods on simple edge spaces with constant indicial roots.
The project studies a PDE approach to the computation of the continuous bounded cohomology of Lie groups, and constructs a Higgs bundle refinement of the Morgan-Shalen compactification of SL(2,C) character varieties.
The project is planned to explore structures of locally symmetric spaces associated to maximal representations, both generalizing the classical structure of Teichmüller theory and discovering new higher rank phenomena.
The aim of this project is to further investigate the types of finite time singularities that occur for the Ricci flow in four dimensions in the real case, and higher dimensions in the Kaehler case, when the scalar curvature is bounded in the L^p norm.
The project aims at completing our picture of the asymptotic geometry of the moduli space of Higgs bundles with its hyperkähler metric. The methods and expected results will crucially be used to answer questions concerning the asymptotic structure of the nonabelian Hodge correspondence and its relationship with representation varieties. In a related but different direction, the subclass of parabolic Higgs bundle moduli spaces which give rise to four-dimensional hyperkähler manifolds is given particular attention, where one goal is to gain a better understanding of various spaces of gravitational instantons from this point of view.