

Private Homepage | https://www.uni-muenster.de/Diffgeo/burkhardwilking.html |
Selected Publications | • Bamler, Richard H.; Cabezas-Rivas, Esther; Wilking, Burkhard The Ricci flow under almost non-negative curvature conditions. Inventiones Mathematicae Vol. 217 (1), 2019, pp 95-126 online • Böhm, Christoph; Wilking, Burkhard Manifolds with positive curvature operators are space forms. Annals of Mathematics Vol. 167 (3), 2008 online • Cabezas-Rivas, Esther; Wilking, Burkhard How to produce a Ricci flow via Cheeger-Gromoll exhaustion. Journal of the European Mathematical Society Vol. 17 (12), 2015, pp 3153-3194 online • Grove, Karsten; Wilking, Burkhard A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry. Geometry and Topology Vol. 18 (5), 2014, pp 3091-3110 online • Grove, Karsten; Wilking, Burkhard; Ziller, Wolfgang Positively curved cohomogeneity one manifolds and 3-Sasakian geometry. Journal of Differential Geometry Vol. 78 (1), 2008, pp 33--111 online • Lytchak, Alexander; Wilking, Burkhard Riemannian foliations of spheres. Geometry and Topology Vol. 20 (3), 2016 online • Radeschi, Marco; Wilking, Burkhard On the Berger conjecture for manifolds all of whose geodesics are closed. Inventiones Mathematicae Vol. 210 (3), 2017 online • Wilking, Burkhard Torus actions on manifolds of positive sectional curvature. Acta Mathematica Vol. 191, 2003 online • Wilking, Burkhard A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities. Journal für die reine und angewandte Mathematik Vol. 679 (1), 2013, pp 223-247 online • Wilking, Burkhard; Ziller, Wolfgang Revisiting homogeneous spaces with positive curvature. Journal für die reine und angewandte Mathematik Vol. 738, 2018 online |
Topics in Mathematics Münster | T1: K-Groups and cohomology T5: Curvature, shape, and global analysis |
Current Publications | • Bamler, Richard H.; Cabezas-Rivas, Esther; Wilking, Burkhard 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 • Wilking, Burkhard; Ziller, Wolfgang Revisiting homogeneous spaces with positive curvature. Journal für die reine und angewandte Mathematik Vol. 738, 2018 online |
Current Projects | • CRC 1442 - 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 - B02: 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 | 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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