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.
Publications and Preprints
-
: "Positive scalar curvature with point singularities", 2024.
arXiv: 2407.20163 -
: "Characteristic numbers of manifold bundles over spheres and positive curvature via block bundles", 2021.
Journal: Forum of Mathematics, Sigma, 2025.
DOI: 10.1017/fms.2025.10054
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) -
: “Spaces of Positive Scalar Curvature metrics on totally nonspin Manifolds with spin boundary”, 2022.
arXiv: 2204.11512.
Journal: Mathematische Zeitschrift, 2023.
DOI: 10.1007/s00209-023-03270-1
Video abstract: Spaces of Positive Scalar Curvature metrics on totally nonspin Manifolds with spin boundary
-
: “Spaces of positive intermediate curvature metrics”
Journal: Geometriae Dedicata, 2021.
DOI: 10.1007/s10711-021-00635-w
arXiv: 2011.11388 -
: “Spaces of metrics of positive Ricci curvature and bundles with non-multiplicative A-hat-genus”
Journal: International Mathematics Research Notices, 2020.
DOI: 10.1093/imrn/rnaa361 (free access article link )
arXiv: 2010.04588 -
: “Cohomogeneity One Manifolds and Homogeneous Spaces of Positive Scalar Curvature”
Journal: Bulletin of the London Mathematical Society, 2022.
DOI: 10.1112/blms.12557
arXiv: 2009.13142 -
: “H-Space structures on spaces of metrics of positive scalar curvature”
Journal: Transactions of the American Mathematical Society, 2021.
DOI: 10.1090/tran/8505
arXiv: 2004.01033 -
: “The action of the mapping class group on metrics of positive scalar curvature”
Journal: Mathematische Annalen, 2021.
DOI: 10.1007/s00208-021-02235-1
arXiv: 1912.08613 -
: “The Gromov-Lawson-Chernysh surgery theorem”
Journal: Boletín de la Sociedad Matemática Mexicana, 2020.
DOI: 10.1007/s40590-021-00310-w
arXiv: 1807.06311
Theses
- PhD-Thesis: The action of the mapping class group on spaces of metrics of positive scalar curvature, 2019.
- Master's Thesis: On the Gromov-Lawson surgery theorem, 2015.
CV
You may find my academic CV here.
Contact
You can contact me via math(at)frenck.net.
orcid: 0000-0002-4260-7797
ResearchGate
Miscellanous
On my YouTube channel you may find occasional video abstracts, a playlist of my zoom-talks and (possibly) other stuff.
I occasionally do a bit of coding. Here's a whiteboard-like tool that can be used for online presentations or teaching using a reMarkable tablet. It's a modification of Pipes-and-Paper.