TN

Courses · Materials · Student projects

Teaching

How I teach

In my courses, I aim to give you a clear conceptual overview together with careful attention to definitions, proofs, and examples. I take students seriously. This means that while I ask you to engage with difficult and meaningful material, I also offer the conceptual orientation, guidance, and support needed to do so. Questions and discussion are always welcome and are, for me, among the most important aspects of a course. Lecture notes and problem sheets are available for almost all of my courses.

My courses range from foundational undergraduate mathematics to advanced topics close to current research. At the beginning of each course, I try to give you a map of the subject—its central questions, conceptual goals, and why the material is worth learning. As the course develops, I encourage you to explore examples, formulate questions of your own, and become increasingly independent in approaching unfamiliar mathematics.

Current teaching

Winter term 2026/27

Lecture course

Algebraic Geometry I

Upcoming teaching

Linear Algebra

Winter term 2027/28

Linear Algebra I

Summer term 2028

Linear Algebra II

Course materials

Lecture notes

Courses 2021–23 Algebraic Geometry I–III Open PDF → Courses 2024–26 Topology I–III Open PDF → Course 2017 Spectral Sequences Open PDF → Courses 2023–24 Sheaves on Manifolds Open PDF → Course 2021 Einführung in die Algebra Open PDF → Course 2018 Funktionentheorie Open PDF → Course 2016 Rational and p-adic Homotopy Theory Open PDF → Course 2020/21 Topological Cyclic Homology Open PDF → Course 2020 Stable ∞-categories and Algebraic Surgery Open PDF →

Video

Recorded lectures

Recorded lectures Homotopy Theory Münster View channel ↗ Course recordings · 2020 Stable ∞-categories and Algebraic Surgery View lectures →

Previous semesters

Course archive

Select a course to view available information, notes, and materials.

University of Münster

Winter term 25/26: Seminar on almost mathematics (w. Franziska Jahnke)
Winter term 25/26: Topologie III
Summer term 25: Topologie II
Winter term 2024/25: Topologie I
Summer term 2024: Sheaves on manifolds II
Winter term 2023/24: Sheaves on manifolds
Winter term 2022/23: Algebraic Geometry III
Summer term 2022: Algebraic Geometry II
Winter term 2021/22: Algebraic Geometry I
Winter term 2021/22: Seminar Kompakte Lie Gruppen (with J.Ebert)
Summer term 2021: Einführung in die Algebra
Winter term 2020/21: Topological Cyclic Homology (with A. Krause)
Summer term 2020: Stable infinity-categories and algebraic surgery
Summer term 2020: Seminar on condensed mathematics (with A. Krause)
Winter term 19/20: Homotopietheorie

    Vorlesung, Di 8-10 und Fr 8-10
    Webpage mit weiteren Informationen und Übungen:
    Homotopietheorie

Winter term 19/20: Sheaves in Geometry and Logic
Summer term 2019: Topologie II

    Vorlesung, Mo 10-12 and Do 10-12
    Die Vorlesung beginnt erst in der zweiten Semesterwoche!
    Webpage mit weiteren Informationen und Übungen:
    Topologie II

Summer term 2019: Einfache Homotopietheorie
Winter term 18/19: Topologie I

    Vorlesung, Mo 10-12 and Do 10-12
    Webpage with further information and exercises:
    Topologie I

Winter term 18/19: Derived algebraic geometry and elliptic cohomology

    Lunchseminar, Di 12-2

Winter term 18/19: Oberseminar Topologie

    Vorlesung, Mo 10-12 and Do 10-12
    Webpage with further information and list of talks:
    Oberseminar

Summer term 2018: Funktionentheorie
Summer term 2018: Topological Hochschild homology and Hodge-de Rham degeneration

University of Bonn

Winter term 17/18: Work Group Seminar Homotopy Theory

    Do 10-12, MPIM Seminar room
    Webpage with further information and schedule:
    Seminar program

Summer term 2017: Algebraic topology II
Summer term 2016: Rational and p-adic homotopy theory
Summer term 2016: Work Group Seminar Homotopy Theory
Winter term 15/16: Work Group Seminar Homotopy Theory
Summer term 2015: Topology II

    Lecture course (V3D2), 4 hrs, Mo 10-12, Wed 8-10. Assistent: Markus Land.
    Webpage with further information und excercises sheets.

Summer term 2015: Differential Topology
Winter term 14/15: Topology I

    Lecture course (V3D1), 4 hrs, Mo 10-12, Wed 8-10. Assistent: Markus Land.
    Webpage with further information und excercises sheets.

Winter term 14/15: Characteristic classes'

University of Regensburg

Summer term 2014: Funktionentheorie auf Riemannschen Flaechen
Summer term 2014: TMF and logarithmic structures
Summer term 2013: Fraktal Geometry
Summer term 2013: Factorization Algebras in Quantum Field Theory
Winter term 13/14: Mathematical Foundations of Physics
Winter term 13/14: Chromatic stable homotopy theory
Summer term 2013: Cryptography with elliptic curves
Summer term 2013: Orientations of ring spectra
Winter term 12/13: Differential Geometry I
Winter term 12/13: Topological Modular Forms