Project Details
Projekt Print View

Coordination Funds

Subject Area Mathematics
Term since 2017
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 358674704
 
This programme combines research in differential geometry, geometric topology, and global analysis. Crossing and transcending the frontiers of these disciplines it is concerned with convergence and limits in geometric-topological settings and with asymptotic properties of objects of infinite size. The overall theme can roughly be divided into the three cross-sectional topics convergence, compactifications, and rigidity.Examples of convergence arise in Gromov-Hausdorff limits and geometric evolution equations. The behaviour of geometric, topological and analytic invariants under limits is of fundamental interest. Often limit spaces are non-smooth so that it is desirable to generalize notions like curvature or spectral invariants appropriately. Limits can also be used to construct asymptotic invariants in geometry and topology such as simplicial volume or L2-invariants.Compactifications reflect asymptotic properties of geometric objects under suitable curvature conditions. Methods from topology, differential geometry, operator algebras and probability play a role in this study. Important issues are boundary value problems for Laplace or Dirac type operators, both in the Riemannian and Lorentzian setting, as well as spectral geometry and Brownian motion on non-compact manifolds.Besides continuous deformations rigidity is essential for many classification problems in geometry and topology. It appears in geometric contexts, typically in the presence of negative curvature, and in topological and even algebraic settings. Rigidity also underlies isomorphism conjectures relating analytic, geometric and homological invariants of infinite groups and more general coarse spaces.The priority programme supports individual research projects and coordinated research activities. These activities will ensure a coherence of research directions, identify promising lines of interdisciplinary research, encourage the establishment of new research cooperations, and realize gender equality measures.
DFG Programme Priority Programmes
 
 

Additional Information

Textvergrößerung und Kontrastanpassung