| Private Homepage | https://www.uni-muenster.de/IVV5WS/WebHop/user/wiemelem/index.html |
| Topics in Mathematics Münster | T2: Moduli spaces in arithmetic and geometry T5: Curvature, shape, and global analysis |
| Current Publications | • Krishnan, Anusha M.; Wiemeler, Michael Positively curved 10-manifolds with T^3-symmetry. Communications in Contemporary Mathematics, 2025 online • Wiemeler, Michael Rigidity of elliptic genera for non-spin manifolds. Algebraic and Geometric Topology Vol. 25 (4), 2025 online • Kennard, Lee; Wiemeler, Michael; Wilking, Burkhard Positive curvature, torus symmetry, and matroids. Journal of the European Mathematical Society, 2025 online • Wiemeler, Michael On circle actions with exactly three fixed points. Journal of Fixed Point Theory and Applications Vol. 27 (3), 2025 online • Wiemeler, Michael On a conjecture of Stolz in the toric case. Proceedings of the American Mathematical Society Vol. 152 (8), 2024 online • 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 • Goertsches O.; Wiemeler M. Non-negatively curved GKM orbifolds. Mathematische Zeitschrift Vol. 300 (2), 2022, pp 2007-2036 online • Tuschmann W.; Wiemeler M. On the topology of moduli spaces of non-negatively curved Riemannian metrics. Mathematische Annalen Vol. 384, 2022, pp 1629-1651 online • Wiemeler, Michael Smooth classification of locally standard T^k-manifolds. Osaka Journal of Mathematics Vol. 59 (3), 2022 online |
| Current Projects | • EXC 2044 - T02: Moduli spaces in arithmetic and geometry The term “moduli space” was coined by Riemann for the space Mg parametrizing all one-dimensional complex manifolds of genus g. Variants of this appear in several mathematical disciplines. In arithmetic geometry, Shimura varieties or moduli spaces of shtukas play an important role in the realisation of Langlands correspondences. Diffeomorphism groups of high-dimensional manifolds and moduli spaces of manifolds and of metrics of positive scalar curvature are studied in differential topology. Moduli spaces are also one of the central topics in our research in mathematical physics, where we study moduli spaces of stable curves and of Strebel differentials. online • EXC 2044 - T05: Curvature, shape and global analysis Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global topological and analytical properties, which in general are strongly intertwined. For instance, it is well known that certain positivity assumptions on the curvature tensor (a local geometric object) imply topological obstructions of the underlying manifold. online • 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. • 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 | wiemelerm@uni-muenster.de |
| Phone | +49 251 83-32731 |
| FAX | +49 251 83-32711 |
| Room | 312 |
| Secretary | Sekretariat Huppert Frau Sandra Huppert Telefon +49 251 83-33748 Fax +49 251 83-32711 Zimmer 411 |
| Address | PD Dr. Michael Wiemeler Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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