Spaces and Moduli Spaces of Riemannian Metrics

Abstract:
Focusing on the case of lower curvature bounds, I will present recent results and open questions about the global topological properties of spaces and moduli spaces of Riemannian metrics on manifolds, explain why these also matter in geometric manifold learning, and discuss metric approaches to the study of suitable compactifications of the latter.

Biography:
Professor Wilderich Tuschmann holds the Differential Geometry Professorial Chair at Karlsruhe Institute of Technology (KIT). He is a geometer with research interests in global differential geometry and geometric topology and their applications in geometric data analysis, manifold learning, information geometry, mathematical physics, robotics, and biology. He co-authored a Birkhaeuser Oberwolfach Research Monograph on moduli spaces of Riemannian metrics and a scientific biography of the Russian mathematician Sofya Kovalevskaya, and co-edited geometry conference proceedings published by Cambridge University Press and Springer. His research works have been published in scientific journals including the Annals of Mathematics, Geometric and Functional Analysis (GAFA), Journal of Differential Geometry (JDG) and Mathematische Annalen. Currently, he is also co-authoring Birkhaeuser-Springer monographs on the geometry and topology of compact homogeneous spaces and canonical metrics in real and complex differential geometry and geometric analysis as well as a Springer monograph about mathematical foundations of machine learning.