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.
01Hitchin components for orbifolds
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.
03Geometric operators on a class of manifolds with bounded geometry
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.
04Secondary invariants for foliations
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.
05Index theory on Lorentzian manifolds
The project will further develop Lorentzian index theory and, in particular, relax the assumption on spatial compactness.
06Spectral Analysis of Sub-Riemannian Structures
The project studies geometric aspects of sub-Riemannian structures and relations to the spectral analysis of induced differential operators, e.g. sub-Laplace operators.
07Asymptotic geometry of moduli spaces of curves
The project investigates the global geometry of Kodaira moduli spaces via twistor methods.
08Parabolics and invariants
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.
09Diffeomorphisms and the topology of positive scalar curvature
The project studies the action of the diffeomorphism group on the space of metrics of positive scalar curvature for a given smooth manifold.
10Duality and the coarse assembly map
The project studies questions related to the coarse Baum-Connes conjecture.
11Topological and equivariant rigidity in the presence of lower curvature bounds
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.
12Anosov representations and Margulis spacetimes
The project aims to study Margulis spacetimes via Anosov representations and, in particular, to investigate degenerations of Anosov structures.
13Analysis on spaces with fibred cusps
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.
14Boundaries of acylindrically hyperbolic groups and applications
The goal of the project is to study boundary amenability of acylindrically hyperbolic groups, isometric actions on Lp-spaces, and rigidity of cross ratios.
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.
16Minimizer of the Willmore energy with prescribed rectangular conformal class
The project aims at determining all tori in 3-space minimizing the Willmore functional with prescribed rectangular conformal type.
17Existence, regularity and uniqueness results of geometric variational problems
The project is concerned with area minimising currents in higher codimensions, p-harmonic maps and Willmore surfaces.
18Analytic L2-invariants of non-positively curved spaces
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.
19Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces
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.
20Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings
The project is concerned with rigidity, compactifications and local-to-global principles in CAT(0) geometry.
21Stability and instability of Einstein manifolds with prescribed asymptotic geometry
The project aims to improve the knowledge about the connection between linear stability, integrability and dynamical stability of Ricci solitons in the noncompact case.
22Willmore functional and Lagrangian surfaces
The objective of the project is to establish analytical tools to study the Willmore functional along Lagrangian surfaces.
23Spectral geometry, index theory and geometric flows on singular spaces
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.
24Minimal surfaces in metric spaces
The project is devoted to the investigation of minimal surfaces in metric spaces.
25The Willmore energy of degenerating surfaces and singularities of geometric flows
The project wants to study the behavior of immersed closed surfaces that degenerate in moduli space and of surfaces or curves that move under the volume preserving mean curvature flow.
26Projective surfaces, Segre structures and the Hitchin component for PSL(n,R)
The project aims to study conformal structures on projective surfaces, topological properties of projective surfaces, and the Hitchin component for PSL(3,R) and PSL(4,R).
27Invariants and boundaries of spaces
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.
28Rigidity, deformations and limits of maximal representations
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.
29Curvature flows without singularities
The project investigates whether for curvature flows like mean curvature flow there exist solutions with principal curvatures bounded in terms of the geometry.
30Nonlinear evolution equations on singular manifolds
The project concerns quasilinear parabolic problems on conic manifolds both with and without boundary and on edge manifolds via a maximal Lp-regularity approach
31Solutions to Ricci flow whose scalar curvature is bounded in Lp.
The aim of the project is to understand singularities of the Ricci flow in four dimensions under restrictions on the topology and geometry of the solutions.
32Asymptotic geometry of the Higgs bundle moduli space
The project aims at providing concrete asymptotic models for the ends of the moduli space of Higgs bundles with its hyperkähler metric.
33Gerbes in renormalization and quantization of infinite-dimensional moduli spaces
The project wants to apply new methods developed in string topology and higher category theory for an understanding of infinite-dimensional moduli spaces and renormalization.