Invariants and Boundaries of Spaces

• Applicant: Privatdozent Dr. Andreas Ott
• Subject Area: Mathematics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 340014991

The project aims to study invariants and geometric objects arising in the context of spaces of non-positive curvature. It focuses on two main themes.(1) Developing new techniques for the explicit computation of the bounded cohomology of Lie groups and the simplicial volume of locally symmetric spaces. The methods are from analysis, geometry and homological algebra, involving partial differential equations, the geometry of Lie groups, and polylogarithm functions.(2) Investigating the interplay between gauge-theoretic and geometric compactifications of the moduli space of representations of surface groups into Lie groups. The methods are from global analysis and hyperbolic geometry, involving Higgs bundles, harmonic maps, and pleated surfaces.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity