# Prof. Dr. Siegfried Echterhoff, Mathematisches Institut

Member of CRC 1442 Geometry: Deformations and RigidityInvestigator in Mathematics Münster

Investigator in Mathematics Münster

Private Homepage | http://wwwmath.uni-muenster.de/u/echters |

Research Interests | Operatoralgebren und nichtkommutative Geometrie |

Project membershipMathematics Münster | B: Spaces and OperatorsB3: Operator algebras & mathematical physics |

Current Projects | • CRC 1442: Geometry: Deformation and Rigidity - D02: Exotic crossed products and the Baum–Connes conjecture The Baum–Connes conjecture on the K-theory of crossed products by group actions on C*-algebras is one of the central problems in noncommutative geometry. The conjecture holds for large classes of groups and has important applications in other areas of mathematics. However, there are groups for which the conjecture fails to be true and in this project we study a new formulation of the conjecture due to Baum, Guentner and Willett which avoids the known counterexamples for the classical one. This involves new exotic crossed product functors which differ from the classical maximal or reduced crossed products. online• 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 • EXC 2044 - B3: Operator algebras & mathematical physics The development of operator algebras was largely motivated by physics since they provide the right mathematical framework for quantum mechanics. Since then, operator algebras have turned into a subject of their own. We will pursue the many fascinating connections to (functional) analysis, algebra, topology, group theory and logic, and eventually connect back to mathematical physics via random matrices and non-commutative geometry. online |

E-Mail | echters@uni-muenster.de |

Phone | +49 251 83-33736 |

FAX | +49 251 83-32708 |

Room | 405 |

Secretary | Elke Enning Frau Elke Enning Telefon +49 251 83-33088 Fax +49 251 83-32708 Zimmer 402 |

Address | Prof. Dr. Siegfried Echterhoff Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |

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