Georg Frenck

About me

I am a Postdoc in the differential geometry group at the Mathematical Institute of the University of Augsburg.

From October 2024 to September 2025 I was a substitute Professor at the University of Göttingen.

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 application of surgery techniques in Riemannian geometry, for example in studying spaces of Riemannian metrics with curvature bounds like positive scalar curvature.

Publications and Preprints

Georg Frenck: “Surgery and total mean curvature”, 2026.
arXiv: 2601.10617.
Georg Frenck: “Positive scalar curvature with point singularities”, 2024.
to appear in Duke Mathematical Journal.
arXiv: 2407.20163.
Georg Frenck: “Sphericity of kappa-classes and positive curvature via block bundles”.
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)
Georg Frenck: “Spaces of Positive Scalar Curvature metrics on totally nonspin Manifolds with spin boundary”, 2022.
Mathematische Zeitschrift, 2023.
DOI: 10.1007/s00209-023-03270-1
arXiv: 2204.11512.
Video abstract: Spaces of Positive Scalar Curvature metrics on totally nonspin Manifolds with spin boundary
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 (free access article link )
arXiv: 2010.04588
Georg Frenck, Fernando Galaz-Garcia, Philipp Reiser: “Cohomogeneity One Manifolds and Homogeneous Spaces of Positive Scalar Curvature”
Bulletin of the London Mathematical Society, 2022.
DOI: 10.1112/blms.12557
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

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.

Talks

2021 Curvature and Global Shape, Universität Münster:
Diffeomorphisms and positive curvature.
2021 Workshop on Geometry, Analysis and Topology of positive scalar curvature, Mathematisches Forschungsinstitut Oberwolfach:
Diffeomorphisms and positive curvature.
2021 Topology/Geometry Zoom Seminar, University of Oregon:
Diffeomorphisms and positive curvature.
2021 Topology and Geometry seminar, University of Toronto:
Diffeomorphisms and positive curvature.
2020 Oberseminar Geometrie, Ludwig-Maximiliansuniversität München:
The action of Diff(M) on metrics of positive scalar curvature.
2020 Oberseminar AG Differentialgeometrie, KIT:
The space of positive Ricci curvature metrics.
2020 Oberseminar Global Analysis and Geometry, Universität Regensburg:
The space of positive Ricci curvature metrics.
2020 Geometry and Topology Seminar, Durham University:
The space of positive Ricci curvature metrics, available on Youtube.
2020 Topology/Geometry Zoom Seminar, University of Oregon:
The space of positive Ricci curvature metrics.
2020 Oberseminar Topologie, Georg-August-Universität Göttingen:
H-Space multiplications on metrics of positive scalar curvature.
2020 Spaces and moduli spaces of Riemannian metrics with curvature bounds - A-Fri-Ka:
H-Space multiplications on metrics of positive scalar curvature.
2019 Department of Mathematics & Statistics Colloquium, Maynooth University:
The action of Diff(M) on metrics of positive scalar curvature.
2019 Oberseminar Differentialgeometrie, Universität Augsburg:
The action of Diff(M) on metrics of positive scalar curvature.
2019 Oberseminar AG Differentialgeometrie, KIT:
The action of Diff(M) on metrics of positive scalar curvature.
2019 Oberseminar Topologie, Georg-August-Universität Göttingen:
The action of Diff(M) on metrics of positive scalar curvature.
2019 Research Seminar on Topology, University of Fribourg:
The action of Diff(M) on metrics of positive scalar curvature.
2018 Young Topologist's meeting:
Topology and Positive Scalar Curvature.
2016 Surgery and Geometry (16w2689):
Surgery and Positive Scalar Curvature.

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).

CV

You may find my academic CV here.

Contact

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.