# 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.

## 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

## 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.