Teaching and supervision

Teaching: pictures, structure and useful confusion

My teaching sits at the same place as my research: algebra, topology, categories, computation, diagrams and examples.

This page collects lecture notes, course pages, supervision information, project ideas, and statements about teaching and EDI.

In plain language. Good mathematics teaching is not just explaining the answer. It is arranging enough examples, pictures, computations and wrong turns so that the structure becomes visible.
VisualMath Quantum topology notes teaching philosophy EDI philosophy

Supervision

Projects for students interested in representation theory, categories, topology, computation and diagrams.

Lectures

Course material ranging from foundations to algebraic topology, representation theory and quantum topology.

Resources

Notes, videos, project descriptions and teaching statements collected in one place.

Disclaimer

Videos of (some of) my lectures/seminars can be found here: https://www.youtube.com/c/VisualMath.
Notes for my lecture “Quantum topology without topology” can be found here: Click.

Supervision

Current primary PhD supervision: Katharina Arms, Super Cao, Daniel W. Collison and Willow Stewart.
Secondary and collaborative PhD supervision: Peter DeBello, Jensen O'Sullivan and Victor L. Zhang.
Bjarke Rasmussen starts in January 2027, jointly with Kevin Coulembier.

For my previous Ph.D. students see here: Click. You can write your bachelor’s, master’s or PhD thesis with me. Contact me by email or find me in my office.

  • Potential master or Ph.D. projects
    • Please contact me if you find them attractive.

    My teaching and EDI philosophy

  • Some thoughts on teaching and EDI (equality, diversity, inclusion)

    • My lectures

    Teaching list: available here.
    I have been/am/will be a lecturer/research assistant for the following courses.

    I am on teaching leave for my ARC Future Fellowship in 2024–2027. I plan to return to regular teaching in 2028.

  • In 2026
    • Voluntary teaching cover: MATH3061 Geometry and Topology, the first three lectures, August 2026.
  • In 2025
    • Teaching leave due to fellowship.
  • In 2024
    • Teaching leave due to fellowship, Spring Semester 2024.
    • Teaching leave due to fellowship, Fall Semester 2024.
  • In 2023
    • Geometry and topology, Spring Semester 2023. Click
    • Algebraic graph theory, Fall Semester 2023. Click
  • In 2022
    • Geometry and topology, Spring Semester 2022. Click
    • Representation theory, Fall Semester 2022. Click
    • Category theory, Fall Semester 2022. Click
  • In 2021
    • Algebraic topology, Spring Semester 2021. Click
    • Quantum topology without topology, Spring Semester 2021. Click
  • In 2020
    • Online seminar diagrammatic algebra: a prototypical example, Fall Semester 2020. Click
    • Quantum invariants of links, Spring Semester 2020. Click
    • Seminar: Representation theory of algebras, Spring Semester 2020. Click
  • In 2019
    • Foundations of Mathematics (in German), Fall Semester 2019. Click
    • Seminar: Representation theory of finite groups, Fall Semester 2019. Click
    • Seminar: Representation theory of \(\mathfrak{sl}_2\), Spring Semester 2019. Click
  • In 2018
    • Foundations of Mathematics (in German), Fall Semester 2018. Click
    • Seminar on 2D TQFTs, Fall Semester 2018. Click
    • Seminar on tensor categories, Spring Semester 2018. Click
  • In 2017
    • Seminar: Representation theory of finite groups (in German), SoSe 2017. Click
    • Oberseminar Darstellungstheorie, SoSe 2017. Click
    • Seminar: Representation theory of (tensor) categories, SoSe 2017. Click
    • Oberseminar Darstellungstheorie, WiSe 2016/2017. Click
    • Seminar: Affine Hecke algebras and their appearance in mathematics, WiSe 2016/2017. Click
  • In 2016
    • Oberseminar Darstellungstheorie, SoSe 2016. Click
    • Seminar: Categorification at roots of unity for pedestrians, SoSe 2016. Click
    • Oberseminar Darstellungstheorie, WiSe 2015/2016. Click
    • Seminar: Recent topics in representation theory, WiSe 2015/2016. Click
  • Before 2016
    • Assistant Calculus and Linear Algebra I - MATLAB, WiQu 2014/2015.
    • Lecturer: Introduction to categorification, SpQu 2014.
    • Assistant Calculus and Linear Algebra I - MATLAB, WiQu 2013/2014.
    • Assistant Calculus and Linear Algebra I - MATLAB, WiQu 2013.
    • Differential- und Integralrechnung I, Semester break in the summer 2013.
    • Differential- und Integralrechnung I, Semester break in the summer 2012.
    • Differential- und Integralrechnung II, SoSe 2012.
    • Seminar on Category Theory, WiSe 2011/2012 (slides of the introduction talk: German and English).
    • Differential- und Integralrechnung II, SoSe 2011.
    • Differential- und Integralrechnung I, WiSe 2010/2011.
    • Several courses before WiSe 2010/2011 as an undergraduate assistant.