The analysis group has a wide range of interests, including functional analysis, harmonic analysis, (partial) differential equations, dynamical systems, and ergodic theory. We are particularly fascinated by the connections between classical analysis and the noncommutaive world, such as mathematical physics, topological field theory. One of our group members has initiated research on noncomutative Fourier analysis, which establishes a link between Fourier analysis and noncommutative symmetries. We anticipate discovering even deeper intrinsic connections between analysis and other fields in the future.

The BIMSA Differential Geometers is a newly founded research group investigating a wide range of questions arising in differential geometry and applications thereof. There exist very natural interconnections to areas such as mathematical physics, algebraic geometry, computer graphics and analysis. The focus of our current members is on integrable geometric differential equations, minimal and Willmore surfaces, Riemann surfaces, Riemannian manifolds with special holonomies, geometric structures, hyperbolic geometry, derived C^∞-geometry, symplectic geometry and geometric analysis. If you want to know more, feel free to contact any of us or just drop by at our weekly seminar on Wednesday afternoons.

General relativity is one of the fundamental theories of modern physics. The gravitational field, described by the Einstein equation, governs phenomena from on all scales, from cosmology to the solar system. The tension between general relativity and quantum mechanics is one of the greatest mysteries of science. We carries out research on problems in geometry and physics motivated by questions in general relativity and related physical theories, using a wide range of techniques, including geometric analysis, as well as numerical simulations and symbolic calculations. Among the focus areas currently are quasi-local mass, the Penrose inequality, the black hole stability problem, and the problem of stability of Calabi-Yau compactified spacetimes.