# Prof. Dr. Burkhard Wilking, Mathematisches Institut

Member of CRC 1442 Geometry: Deformations and RigidityMember of Mathematics Münster

Investigator in Mathematics Münster

Member of Mathematics Münster

Investigator in Mathematics Münster

Private Homepage | https://www.uni-muenster.de/Diffgeo/burkhardwilking.html |

Project membershipMathematics Münster | B: Spaces and OperatorsC: Models and ApproximationsB1: Smooth, singular and rigid spaces in geometry C4: Geometry-based modelling, approximation, and reduction |

Current Publications | • Bamler R.H.; Cabezas-Rivas E.; Wilking B. The Ricci flow under almost non-negative curvature conditions. Inventiones Mathematicae Vol. 217 (1), 2019, pp 95-126 online• Grove K.; Wilking B.; Yeager J.; Halperin S. Almost non-negative curvature and rational ellipticity in cohomogeneity two. Annales de l’Institut Fourier Vol. 69 (7), 2019, pp 2921-2939 online |

Current Projects | • CRC 1442: Geometry: Deformation and Rigidity - B01: Curvature and Symmetry The question of how far geometric properties of a manifold determine its global topology is a classical problem in global differential geometry. Building on recent breakthroughs we investigate this problem for positively curved manifolds with torus symmetry. We also want to complete the classification of positively curved cohomogeneity one manifolds and obtain structure results for the fundamental groups of nonnegatively curved manifolds. Other goals include structure results for singular Riemannian foliations in nonnegative curvature and a differentiable diameter pinching theorem. • CRC 1442: Geometry: Deformation and Rigidity - Geometric evolution equations Hamilton's Ricci flow is a (weakly parabolic) geometric evolution equation, which deforms a given Riemannian metric in its most natural direction. Over the last decades, it has been used to prove several significant conjectures in Riemannian geometry and topology (in dimension three). In this project we focus on Ricci flow in higher dimensions, in particular on heat flow methods, new Ricci flow invariant curvature conditions and the dynamical Alekseevskii conjecture. • EXC 2044 - B1: Smooth, singular and rigid spaces in geometry Many interesting classes of Riemannian manifolds are precompact in the Gromov-Hausdorfftopology. The closure of such a class usually contains singular metric spaces. Understanding thephenomena that occur when passing from the smooth to the singular object is often a first step toprove structure and finiteness results. In some instances one knows or expects to define a smoothRicci flow coming out of the singular objects. If one were to establishe uniqueness of the flow, thedifferentiable stability conjecture would follow. If a dimension drop occurs from the smooth to thesingular object, one often knows or expects that the collapse happens along singular Riemannianfoliations or orbits of isometric group actions.Rigidity aspects of isometric group actions and singular foliations are another focus in this project.For example, we plan to establish rigidity of quasi-isometries of CAT(0) spaces, as well as rigidity oflimits of Type III Ricci flow solutions and of positively curved manifolds with low-dimensional torusactions.We will also investigate area-minimising hypersurfaces by means of a canonical conformal completionof the hypersurface away from its singular set. online • EXC 2044 - C4: Geometry-based modelling, approximation, and reduction In mathematical modelling and its application to the sciences, the notion of geometry enters in multiple related but different flavours: the geometry of the underlying space (in which e.g. data may be given), the geometry of patterns (as observed in experiments or solutions of corresponding mathematical models), or the geometry of domains (on which PDEs and their approximations act). We will develop analytical and numerical tools to understand, utilise and control geometry, also touching upon dynamically changing geometries and structural connections between different mathematical concepts, such as PDE solution manifolds, analysis of pattern formation, and geometry. online |

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

Phone | +49 251 83-33732 |

FAX | +49 251 83-32711 |

Room | 410 |

Secretary | Sekretariat Huppert Frau Sandra Huppert Telefon +49 251 83-33748 Fax +49 251 83-32711 Zimmer 411 |

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

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