Georg Frenck

About me

I am a Postdoc in the differential geometry group at the Mathematical Institute of the University of Augsburg. Before, I was in the differential geometry group at the Institute for Algebra and Geometry of the KIT. I obtained my PhD in Münster under the supervision of Johannes Ebert.


Activities

Seiberg-Witten Theory -- Seminar

I am currently organizing an online seminar on Seiberg--Witten Invariants (Programme) together with Rudi Zeidler. If you are interested in participating, you are very welcome to contact me!

IX. Bavarian Geometry and Topology Meeting

Together with Artiom Nepechiy, we organized the IX. Bavarian Geometry and Topology Meeting.


Research

My research interest lies in geometric topology and differential geometry. In particular I am interested in studying spaces of Riemannian metrics with curvature bounds like positive scalar curvature through topological methods.

Publications and Preprints

  • Georg Frenck: “Sphericity of kappa-classes and positive curvature via block bundles”, 2021.
    arXiv: 2109.10306.
    (This article is a major upgrade to its previous version to be found here: arXiv:2104.10595. Video abstract: Diffeomorphisms and positive curvature)
  • Georg Frenck, Jan-Bernhard Kordaß: “Spaces of positive intermediate curvature metrics”
    Geometriae Dedicata, 2021.
    DOI: 10.1007/s10711-021-00635-w
    arXiv: 2011.11388
  • Georg Frenck, Jens Reinhold: “Spaces of metrics of positive Ricci curvature and bundles with non-multiplicative A-hat-genus”
    International Mathematics Research Notices, 2020.
    DOI: 10.1093/imrn/rnaa361
    arXiv: 2010.04588
  • Georg Frenck, Fernando Galaz-Garcia, Philipp Reiser: “Cohomogeneity One Manifolds and Homogeneous Spaces of Positive Scalar Curvature”, 2020.
    arXiv: 2009.13142
  • Georg Frenck: “H-Space structures on spaces of metrics of positive scalar curvature”
    Transactions of the American Mathematical Society, 2021.
    DOI: 10.1090/tran/8505
    arXiv: 2004.01033
  • Georg Frenck: “The action of the mapping class group on metrics of positive scalar curvature”
    Mathematische Annalen, 2021.
    DOI: 10.1007/s00208-021-02235-1
    arXiv: 1912.08613
  • Johannes Ebert, Georg Frenck: “The Gromov-Lawson-Chernysh surgery theorem”
    Boletín de la Sociedad Matemática Mexicana, 2020.
    DOI: 10.1007/s40590-021-00310-w
    arXiv: 1807.06311

Theses

Talks

Slides

  • The action of the Diff(M) on metrics of positive scalar curvature, from my colloquium talk in Maynooth (2019).
  • H-Space structures on metrics of positive scalar curvature, from my OberZOOMinar talk in Göttingen (2020).