Teaching

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!