Research interests/Forschungsinteressen

Differential Geometry and Topology, Transformation Groups, Toric Topology, Equivariant Bordism, Positive and Non-negative Curvature

Differentialgeometrie und Differentialtopologie, Transformationsgruppen, torische Topologie, äquivarianter Bordismus, positive und nicht-negative Krümmung

Selected Publications/Ausgewählte Veröffentlichungen

  • (mit Johannes Ebert) On the homotopy type of the space of metrics of positive scalar curvature, J. Eur. Math. Soc. (2023), veröffentlichte Version: DOI:10.4171/JEMS/1333, Preprint Version: arXiv:2012.00432
  • (mit Wilderich Tuschmann) On the topology of moduli spaces of non-negatively curved Riemannian metrics, Math. Ann. 384 (2022) No. 3-4, 1629-1651, veröffentlichte Version: DOI:10.1007/s00208-021-02327-y, Preprint Version: arXiv:1712.07052
  • (mit Oliver Goertsches) Non-negatively curved GKM orbifolds, Math. Z. 300 (2022) No. 2, 2007-2036, veröffentlichte Version: DOI:10.1007/s00209-021-02853-0, Preprint Version: arXiv:1802.05871
  • On moduli spaces of positive scalar curvature metrics on highly connected manifolds, Int. Math. Res. Not. IMRN 2021 (2021) No. 11, 8698-8714, veröffentlichte Version: DOI:10.1093/imrn/rnz386, Preprint Version: arXiv:1610.09658
  • S^1-equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera, J. Topol. Anal. 12 (2020) No. 4, 1103-1156, veröffentlichte Version: DOI:10.1142/S1793525319500766, Preprint Version: arXiv:1506.04073
  • (mit Bernhard Hanke) An equivariant Quillen theorem, Adv. Math. 340 (2018), 48-75, veröffentlichte Version: DOI:10.1016/j.aim.2018.10.009, Preprint Version: arXiv:1711.02399
  • (mit Fernando Galaz-Garcia, Martin Kerin und Marco Radeschi) Torus orbifolds, slice-maximal torus actions and rational ellipticity, Int. Math. Res. Not. IMRN 2018 (2018) No. 18, 5786-5822, veröffentlichte Version: DOI:10.1093/imrn/rnx064, Preprint Version: arXiv:1404.3903
  • Circle actions and scalar curvature, Trans. Amer. Math. Soc. 368 (2016), No. 4, 2939-2966, veröffentlichte Version: DOI:10.1090/tran/6666, Preprint Version: arXiv:1305.2288
  • Torus manifolds and non-negative curvature, J. Lond. Math. Soc., II. Ser. 91 (2015), No. 3, 667-692, veröffentlichte Version: DOI:10.1112/jlms/jdv008, Preprint Version: arXiv:1401.0403
  • (mit Oliver Goertsches) Positively curved GKM-manifolds, Int. Math. Res. Not. IMRN, 2015 (2015), No. 22, 12015-12041, veröffentlichte Version: DOI:10.1093/imrn/rnv046, Preprint Version: arXiv:1402.2397
  • Torus manifolds with non-abelian symmetries Trans. Amer. Math. Soc., 364 (2012), No. 3, 1427-1487, veröffentlichte Version: DOI:10.1090/S0002-9947-2011-05463-2, Preprint Version: arXiv:0911.4936

Accepted Papers/Angenommene Arbeiten

  • On a conjecture of Stolz in the toric case, arXiv:2310.08456, erscheint in Proc. Amer. Math. Soc.
  • Rigidity of elliptic genera for non-spin manifolds, arXiv:2212.01059, erscheint in Algebr. Geom. Topol.

Recent Preprints/Aktuelle Preprints

  • (mit Anusha M. Krishnan) 10-dimensional positively curved manifolds with T^3-symmetry, arXiv:2310.12689, 2023
  • On circle actions with exactly three fixed points, arXiv:2303.15396, 2023
  • (mit Lee Kennard und Burkhard Wilking) Positive curvature, torus symmetry, and matroids, arXiv:2212.08152, 2022
  • (mit Lee Kennard und Burkhard Wilking) Splitting of torus representations and applications in the Grove symmetry program, arXiv:2106.14723, 2021

Selected Talks/Ausgewählte Vorträge

  • Positive Curvature, Symmetries, and Matroids, International Polyhedral Products Seminar, Princeton University, USA, 7. Oktober 2021
  • Positively curved manifolds with isometric torus actions, SPP 2026 Geometry at Infinity Conference, Münster, 4. April 2019
  • Equivariant bordism and applications in differential geometry, Augsburger Mathematisches Kolloquium, Universität Augsburg, 12. Januar 2016, Slides
  • Invariant metrics of positive scalar curvature on S^1-manifolds, Workshop on Curvature and Global Shape, Münster, 30. Juli 2015
  • Invariant metrics of positive scalar curvature on S^1-manifolds, Geometry and Topology, A conference in honor of Martin Bendersky's 70th birthday and in commemoration of our friend and colleague Sam Gitler, Princeton, 18. März 2015, Slides
  • Circle actions and positive scalar curvature, Oberwolfach Workshop: Analysis, Geometry and Topology of Positive Scalar Curvature Metrics, Oberwolfach, 6. August 2014
  • Non-negatively curved torus manifolds, Mathematical Congress of the Americas 2013, Special Session on Toric Geometry and Topology, Guanajuato, Mexico, 9. August 2013, Slides
  • Non-negatively curved torus manifolds, Workshop on Curvature and Global Shape, Münster, 23. Juli 2013