On June 29, 2026 the Colloquium of the CRC-TRR 358 will take place at the Department of Mathematics, Paderborn. The speakers are Hans-Joachim Hein (University Münster) and Wolfgang Lück (University Bonn).
Program:
15:00 - 16:00 1. talk: Hans-Joachim Hein
16:00 - 16:45 coffee break
16:45 - 17:45 2. talk: Wolfgang Lück
17:45 reception
Location:
The talks will be held in lecture room D1, the coffee break and reception will take place in room J2.138.
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Hans-Joachim Hein (University Münster)
Title: Riemannian geometry of Kähler manifolds
Abstract: Kähler manifolds are a class of Riemannian manifolds generalizing Riemann surfaces to higher dimensions. The most natural examples are complex projective algebraic manifolds together with the restriction of the Fubini-Study metric from CP^N. I will review the classical Uniformization Theorem for compact Riemann surfaces and its extension to higher-dimensional Kähler manifolds due to Calabi, Aubin and Yau in the 1970s. Then I will discuss some recent results aimed at understanding the geometric meaning of the Ricci curvature of a Kähler manifold, including work on the Positive Mass Theorem as well as some aspects of negative Kähler-Einstein manifolds generalizing the Teichmüller theory of hyperbolic Riemann surfaces.
Wolfgang Lück (University Bonn)
Title: An introduction to L^2-invariants
Abstract: Betti numbers of closed manifolds or finite simplicial complexes are classical invariants in algebraic topology.
Atiyah proposed an L^2-version obtained from the universal covering and the action of the fundamental group
using von Neumann algebras. We will present the basic properties of these L^2-Betti numbers
and discuss applications to topology, algebra, group theory, and geometry which are both interesting and not hard to explain.
Finally we give an outlook on the current research problems about L^2-invariants.
