About me

I am a Postdoc 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 algebraic topology and differential geometry. In particular I am interested in the interplay of curvature conditions (mostly positive scalar curvature) and cobordism theory.

Publications and Preprints

• Georg Frenck: “Diffeomorphisms and positive curvature”, 2021; arXiv:2104.10595.
  Video abstract: Diffeomorphisms and positive curvature
• Georg Frenck, Jan-Bernhard Kordaß: “Spaces of positive intermediate curvature metrics”, 2020; arXiv:2011.11388.
• Georg Frenck, Jens Reinhold: “Spaces of metrics of positive Ricci curvature and bundles with non-multiplicative A-hat-genus”, 2020; arXiv:2010.04588, Int. Math. Res. Not., 2020.
  DOI: 10.1093/imrn/rnaa361
• 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”, 2020; arXiv:2004.01033.
• Georg Frenck: “The action of the mapping class group on metrics of positive scalar curvature”, 2019; arXiv:1912.08613.
• Johannes Ebert, Georg Frenck: “The Gromov-Lawson-Chernysh surgery theorem”, 2018; arXiv:1807.06311, Bol. Soc. Mat. Mex. (3), 2020.
  DOI: 10.1007/s40590-021-00310-w

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

• 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 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

You can contact me via math(at)frenck.net.

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.