Teaching

Fall 2026

Computer-assisted mathematics (An introduction to Lean), UiT The Arctic University of Norway. Lecture notes and other materials will also be made available on Canvas.

Spring 2025

Algebraic geometry, UiT The Arctic University of Norway. Following Cox, Little, O’Shea: Ideals, varieties and algorithms.

Spring 2023

April to June (Period V): Real algebraic geometry, Aalto University (MyCourses). Lecture notes and exercises:
- Chapter 1: Ordered and real-closed fields
- Chapter 2: Semialgebraic sets
- Chapter 3: Quantifier elimination and projection
- Chapter 4: Applications of quantifier elimination
- Chapter 5: Stellensätze and non-negativity
- Appendix A: Review of commutative algebra
- Appendix B: Concepts from model theory
- Bibliography

Student supervision

M.Sc. thesis of Emil Verkama on Repairing the Universality Theorem for 4-Polytopes at Aalto Univerity (2022).
- Emil won the 2024 Ernst Lindelöf prize from the Finnish Mathematical Society for this thesis. Congratulations!