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.

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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.

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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

• 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).

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CV

You may find my academic CV here.

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Contact

You can contact me via math(at)frenck.net.
orcid: 0000-0002-4260-7797
ResearchGate

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Miscellanous

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.