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.

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.

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!

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).