| Private Homepage | http://wwwmath.uni-muenster.de/u/jeber_02/johannesebert.html |
| Topics in Mathematics Münster | T1: K-Groups and cohomology T2: Moduli spaces in arithmetic and geometry T5: Curvature, shape, and global analysis |
| Current Publications | • Ebert, Johannes; Wiemeler, Michael On the homotopy type of the space of metrics of positive scalar curvature. Journal of the European Mathematical Society Vol. 26 (9), 2024 online |
| Current Projects | • CRC 1442 - B03: Moduli spaces of metrics of positive curvature We will develop a family version of coarse index theory which encompasses all existing index invariants for the understanding of spaces of positive scalar curvature (psc) metrics—the higher family index and index difference—as well as new ones such as family rho-invariants. This will enable the detection of new non-trivial elements in homotopy groups of certain moduli spaces of psc metrics. We will also further study the concordance space of psc metrics together with appropriate index maps. • EXC 2044 - B2: Topology We will analyse geometric structures from a topological point of view. In particular, we will study manifolds, their diffeomorphisms and embeddings, and positive scalar curvature metrics on them. Via surgery theory and index theory many of the resulting questions are related to topological K-theory of group C*-algebras and to algebraic K-theory and L-theory of group rings. Index theory provides a map from the space of positive scalar curvature metrics to the K-theory of the reduced C*-algebra of the fundamental group. We will develop new tools such as parameterised coarse index theory and combine them with cobordism categories and parameterised surgery theory to study this map. In particular, we aim at rationally realising all K-theory classes by families of positive scalar curvature metrics. Important topics and tools are the isomorphism conjectures of Farrell-Jones and Baum-Connes about the structure of the K-groups that appear. We will extend the scope of these conjectures as well as the available techniques, for example from geometric group theory and controlled topology. We are interested in the K-theory of Hecke algebras of reductive p-adic Lie groups and in the topological K-theory of rapid decay completions of complex group rings. Via dimension conditions and index theory techniques we will exploit connections to operator algebras and coarse geometry. Via assembly maps in algebraic K- and L-theory we will develop index-theoretic tools to understand tangential structures of manifolds. We will use these tools to analyse the smooth structure space of manifolds and study diffeomorphism groups. Configuration categories will be used to study spaces of embeddings of manifolds. online |
| johannes dot ebert at uni-muenster dot de | |
| Phone | +49 251 83-33092 |
| FAX | +49 251 83-38370 |
| Room | 506 |
| Secretary | Sekretariat AG Topologie Frau Claudia Rüdiger Telefon +49 251 83-35159 Fax +49 251 83-38370 Zimmer 516 |
| Address | Prof. Dr. Johannes Ebert Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
| Diese Seite editieren |