Teaching

Since 2013 I have given lectures and seminars at the universities of Marburg, Cologne, Gießen and Stuttgart, for students of mathematics, physics and the natural sciences and for future mathematics teachers. I write all my lecture notes myself in LaTeX.

Current teaching

• Winter 2026/27
  Einführung in p-adische Zahlen
  Lecture (Wednesdays 12–14) and exercise class (Thursdays 8–10), Philipps-Universität Marburg. Dates, lecture notes and exercise sheets are on the course page.

Lectures and seminars

• Winter 2026/27
  Philipps-Universität Marburg

  • Lecture Einführung in p-adische Zahlen
• Winter 2024/25
  Justus-Liebig-Universität Gießen

  • Lecture Mathematik für Naturwissenschaftler (4 SWS)
    Contents

    Set theory, sequences and convergence, continuity, differentiability, integration, vector spaces, linear maps, eigenvalues, multivariable analysis, partial differential equations, numerical methods.

  • Lecture Morsetheorie (2 SWS)
    Contents

    Existence of Morse functions, gradient-like vector fields, Morse lemma, handle decompositions and their consequences.

• Summer 2024
  Universität zu Köln

  • Lecture Algebraische Topologie 2 (4 SWS)
    Contents

    Cup product, Künneth formulas, homotopy groups and their computation, Hurewicz theorem, fibre bundles, stable homotopy groups, Postnikov towers, obstruction theory.

• Summer 2023
  Philipps-Universität Marburg

  • Seminar Ricci flow (2 SWS)
    Contents

    Evolution of geometric quantities under the Ricci flow, maximum principle, parabolic PDEs and the Ricci flow, DeTurck trick, blow-ups, Perelman's W-functional, Uhlenbeck trick, Hamilton's theorem.

• Winter 2022/23
  Justus-Liebig-Universität Gießen

  • Lecture Mathematik für Physiker (4 SWS)
    Contents

    Complex numbers, sequences, series, power series, convergence, continuity, differentiation, integration, vector spaces, linear maps, matrices, diagonalisation, eigenvalues and eigenspaces, scalar products, determinants, matrix groups.

  • Lecture Dirac-Operatoren in der Riemannschen Geometrie (2 SWS)
    Contents

    Clifford algebras, spin representation, connections on principal bundles, Riemannian geometry, differential forms, Clifford bundles, Dirac operators, spin structures, spinor bundles, analytic properties of the Dirac operator, Weitzenböck formulas, harmonic spinors.

• Winter 2021/22
  Justus-Liebig-Universität Gießen

  • Lecture Mathematik für Physiker (4 SWS)
  • Seminar Morsetheorie (2 SWS)
    Contents

    Existence of Morse functions, gradient-like vector fields, Morse lemma, handle decompositions and their consequences.

• Summer 2021
  Philipps-Universität Marburg

  • Learning seminar Selected topics of Hirzebruch's work
• Summer 2020
  Universität zu Köln

  • Lecture Topologie (4 SWS)
    Contents

    Basics of topology, constructions of topological spaces, fundamental group, Seifert–van Kampen theorem, simplicial complexes, simplicial homology, Lefschetz fixed point theorem.

  • Seminar Knotentheorie (2 SWS)
    Contents

    Knots and links, link diagrams, Reidemeister moves, Kauffman and Jones polynomials, colourability of knots, Alexander polynomial, knot groups, Seifert surfaces, Seifert matrices and the Alexander polynomial.

• Winter 2019/20
  Universität zu Köln

  • Lecture Elementare Differentialgeometrie (4 SWS)
    Contents

    Curves in Rⁿ, plane curves, Frenet equations, surfaces in R³, Gauss and mean curvature, fundamental theorems of surface theory, Theorema egregium, global differential geometry, differentiable manifolds.

  • Seminar Differentialtopologie (2 SWS)
    Contents

    Submersions and transversality, Sard's theorem, Whitney embedding theorem, manifolds with boundary, Brouwer fixed point theorem, intersection numbers mod 2, Jordan–Brouwer separation theorem, Borsuk–Ulam theorem, intersection numbers, Lefschetz fixed point theorem.

• Summer 2019
  Philipps-Universität Marburg

  • Lecture Grundlagen der Mathematik (2 SWS)
    Contents

    Propositional logic, set theory, relations, maps, construction of the natural, integer and rational numbers, elementary group theory.

• Winter 2018/19
  Universität Stuttgart

  • Seminar Biquotienten (2 SWS)
    Contents

    Lie groups and invariant metrics, special metrics on biquotients, cohomology of biquotients, classification results.

  • Open tutorial Lernwerkstatt (2 SWS)
    Contents

    For first-year mathematics students: a supplementary course on topics from the introductory lectures, chosen by the students themselves.

• Summer 2018
  Philipps-Universität Marburg

  • Seminar Einführung in die Homotopietheorie (2 SWS)
    Contents

    Singular homology and cohomology, path fibrations, homotopy groups, Hurewicz theorem, Hopf invariant, Eilenberg–MacLane spaces, Postnikov towers.

• Summer 2017
  Philipps-Universität Marburg

  • Seminar h-Kobordismussatz und exotische Sphären (2 SWS)
    Contents

    Morse theory, Milnor's proof of the h-cobordism theorem, existence of exotic spheres after Milnor and Brieskorn, the group structure of exotic structures on spheres.

• Winter 2015–2017
  Philipps-Universität Marburg

  • Lecture Elementargeometrie (3 SWS), winter 2015/16 and 2016/17
    Contents

    For future teachers. Intercept theorems, Pappus' theorem, theorems on triangles, Euler line, nine-point circle, theorems on quadrilaterals, hyperbolic geometry, isometries of the hyperbolic plane, geodesics, angle sums of hyperbolic triangles.

• Summer 2015
  Philipps-Universität Marburg

  • Lecture Analysis III (4 SWS)
    Contents

    Submanifolds of Rⁿ, differential forms, integral theorems, de Rham cohomology.

• Winter 2014/15
  Philipps-Universität Marburg

  • Proseminar Darstellungstheorie endlicher Gruppen (2 SWS)
    Contents

    Elements of group theory, Euclidean motions, dihedral groups, lattices, symmetry groups of Platonic solids, three-dimensional crystallographic groups, Schur's lemma and representations, characters, representations of the symmetric group.

• Summer 2014
  Philipps-Universität Marburg

  • Lecture Funktionentheorie (4 SWS)
    Contents

    Complex differentiability, Cauchy–Riemann equations, basics of curves, holomorphic and meromorphic functions, Laurent series, residue theorem and applications.

Supervised theses

• Bachelor
  Fundamentalgruppen von Torusknoten, Universität zu Köln
• Diplom
  Gauge invariant quantities in general relativity, Universität Tübingen (with Prof. Frank Loose)
• Diplom
  Dynamische Systeme in der Kosmologie, Universität Tübingen (with Prof. Frank Loose)
• Staatsexamen
  Die 3-Sphäre in Dantes Universum, Universität Tübingen (with Prof. Rainer Nagel)

As teaching assistant

• Summer 2019
  Differentialoperatoren auf Mannigfaltigkeiten (Universität Stuttgart)
• Summer 2018
  Funktionentheorie und Vektoranalysis (Marburg)
• Winter 2017/18
  Analysis II (Marburg)
• Summer 2017
  Analysis I (Marburg)
• Winter 2014/15
  Partielle Differentialgleichungen (Marburg)
• Summer 2014
  Analysis 3 (Marburg)
• Winter 2013/14
  Analysis 2; Geometrie von Kurven und Flächen (Marburg)
• Summer 2013
  Analysis 1; Differentialgeometrie 2 (Marburg)
• Winter 2012/13
  Automorphe Formen; Funktionalanalysis (Marburg)