Teaching

(Synthetic) algebraic geometry / algebraic function fields

Course in the winter term 2024 at the University of Antwerp. The lecture notes, exercise sheets and other course material is here.

Also: Antwerp Logic Adventures

Sheaves and logic

My course on sheaves and logic in the winter term 2017/2018 was recorded.

• Recordings of the lectures (in German)
• Lecture notes (in English)
• Exercise sheets (in German)

Lecture notes for pizza seminars

I organized several pizza seminars, seminars by students for students. Lecture notes and exercise sheets are available in German:

• Category theory (with a focus on motivating examples)
• Constructive mathematics (including a discussion of Hilbert’s program and the Bohr topos)

Related: QED course on metamathematics and topos theory (mostly in German)

Construction, realisability, double negation

Master minicourse at the University of Verona

Expository notes

• A quickstart guide to derived functors
• A one-page self-contained proof of a baby version of Kaplansky’s theorem without Noetherian hypotheses (a module is finitely generated and projective if and only if it is locally finite free)
• Fun with the little Zariski topos (in German)
• The Picard group and the Riemann–Roch theorem (in German)
• Higher direct images for dummies (joint with Pascuale Zenobio de Rossi, work in progress)
• On the Jordan canonical form (in German)
• A primer on automatic differentiation
• Modules over principal ideal domains: the Smith normal form approach

Talks for general mathematical or compsci audiences

• Exploring hypercomputation with the effective topos (Joint Philosophy/Mathematics Seminar in Warwick)
• The double negation translation and the CPS transformation (Computer Science Seminar at the KU Leuven)
• Konstruktive Mathematik, die Doppelnegationsübersetzung und Continuations (HAL2015)
• Introduction to homotopy type theory

Previous courses

Exercise sheets for courses where I coordinated the tutorials (in German):

• Galois theory I & II
• Homological algebra I & II
• Model categories
• Commutative algebra
• Algebraic number theory
• Complex analysis

Teaching statement

My teaching statement is online. I’d love to hear about your favorite teaching strategies by mail.