Moduli Spaces of Riemannian Metrics

Part I: Positive scalar curvature

- The (moduli) space of all Riemannian metrics

- Clifford algebras and spin

- Dirac operators and index theorems

- Early results on the space of positive scalar curvature metrics

- Kreck-Stolz invariants

- Applications of Kreck-Stolz invariants

- The eta invariant and applications

- The case of dimensions 2 and 3

- The observer moduli space and applications

- Other topological structures

- Negative scalar and Ricci curvature

- Part II: Sectional curvature

- Moduli spaces of compact manifolds with positive or non-negative sectional curvature

- Moduli spaces of compact manifolds with negative and non-positive sectional curvature

- Moduli spaces of non-compact manifolds with non-negative sectional curvature

- Positive pinching and the Klingenberg-Sakai conjecture

Wilderich Tuschmann's general research interests lie in the realms of global differential geometry, Riemannian geometry, geometric topology, and their applications, including, for example, questions concerning the geometry and topology of nonnegative and almost nonnegative curvature, singular metric spaces, collapsing and Gromov-Hausdorff convergence, analysis and geometry on Alexandrov spaces, geometric finiteness theorems, moduli spaces of Riemannian metrics, transformation groups, geometric bordism invariants, information and quantum information geometry. After his habilitation in mathematics at the University of Leipzig in 2000 he worked as a Deutsche Forschungsgemeinschaft Heisenberg Fellow at Westfälische Wilhems-Universität Münster, and from 2005-2010 he held a professorship at Christian-Albrechts-Universität Kiel. In the fall of 2010 he was appointed professor of mathematics at Karlsruhe Institute of Technology (KIT), a position he currently holds. David Wraith's main mathematical interests concern the existence of Riemannian metrics satisfying various kinds of curvature conditions and their topological implications. Most of his work to date has focused on the existence of positive Ricci curvature metrics. He has worked at the National University of Ireland Maynooth since 1997.