Johan Commelin
I work part-time as universitair docent (assistant professor) at Utrecht University,
and part time at the Lean FRO.
My main interests lie in arithmetic geometry and formalization of mathematics.
From 2018 till 2023 I was a postdoc in the group of Stefan Kebekus in Freiburg (DE).
From 2017 till 2018 I was a postdoc of Carel Faber in Utrecht (NL).
From 2013 till 2017 I was a PhD student in Nijmegen (NL), supervised by Ben Moonen.
Current research topics include:
formalization of algebraic geometry, homological algebra, and condensed mathematics;
categorical logic and applications of o-minimality to algebraic geometry/topology;
in particular, applications of o-minimality to the theory of periods and motives.
I am actively involved in the Lean community.
In 2021-2022, I have lead the Liquid Tensor Experiment
following up on a challenge by Peter Scholze.
If you want to learn more about Lean,
here's a great place to find guides/resources/tutorials/chat/etc.
I greatly appreciate (anonymous) feedback on my lectures, talks, and other activities.
News & Olds
- Jiang Jiedong is visiting the math department in Utrecht for a 6 month internship (Jun–Nov 2024). He will work work on formalization of foundations of p-adic Hodge theory.
- Corentin Cornou is visiting the math department in Utrecht for a 3 month internship (May–Jul 2024). He will work work on formalization of finite groups of Lie type.
- Together with Sander Dahmen (VU), I am setting up the Informal Formalization Seminar.
The second installment was on March 8, 2024.
- On April 16, 2024, I coorganized a Dutch Formal Methods Day.
Contact details
Preprints
- With Reid Barton.
Model categories for o-minimal geometry.
[arXiv:2108.11952]
- With Annette Huber and Philipp Habegger.
Exponential periods and o-minimality.
[arXiv:2007.08280]
Publications
- With Adam Topaz.
Abstraction boundaries and spec driven development in pure mathematics.
Bull. Amer. Math. Soc.
DOI: https://doi.org/10.1090/bull/1831
Published electronically: February 15, 2024
[PDF]
- With Victoria Cantoral Farfán.
The Mumford–Tate conjecture implies the
algebraic Sato–Tate conjecture
of Banaszak and Kedlaya.
Indiana Univ. Math. J. 71 (2022), no. 6, 2595--2603.
[arXiv:1905.04086]
- With Robert Y. Lewis.
Formalizing the Ring of Witt Vectors.
Certified Programs and Proofs 2021, 264–277.
[arXiv:2010.02595]
[project webpage]
This paper was accepted with a Distinguished Paper Award.
- With Kevin Buzzard and Patrick Massot.
Formalising perfectoid spaces
Certified Programs and Proofs 2020, 299–312.
[offprint]
[arXiv:1910.12320]
[project webpage]
-
With Matteo Penegini.
On the cohomology of surfaces with
pg = q = 2
and maximal Albanese dimension.
Trans. Amer. Math. Soc. 373 (2020) 1749-1773.
[arXiv:1901.00193]
-
On compatibility of the ℓ-adic realisations of an abelian motive.
Annales de l’Institut Fourier.
Volume 69 (2019) no. 5, p. 2089–2120.
[link]
-
The Mumford–Tate conjecture for products of abelian varieties.
Algebraic Geometry (6) 6 (2019) 650–677.
[link]
-
The Mumford–Tate Conjecture for the Product of an Abelian Surface and a K3 Surface.
Documenta Math. 21 (2016) 1691–1713.
[link]
Past teaching
| Course | Semester |
|---|
| Assistent for Funktionentheorie | Summer 2021 |
| Teaching: Coxeter Groups and Lie Algebras | Winter 20/21 |
| Assistent for Introduction to Algebraic Curves | Summer 2020 |
| Assistent for Mathematics for Natural Scientists II | Summer 2020 |
| Assistent for Cohomology of Algebraic Varieties | Winter 19/20 |
| Assistent for Mathematics for Natural Scientists I | Winter 19/20 |
| Seminar Local Fields | Summer 2019 |
| Linear Algebra 2 | Summer 2019 |
Other writing
MacLane's Q'-construction and Breen–Deligne resolutions (draft). An unpublished note written as part of the Liquid Tensor Experiment.
My PhD thesis: On ℓ-adic compatibility for abelian motives & the Mumford–Tate conjecture for products of K3 surfaces [Erratum]. Completed in the summer of 2017 under the supervision of Ben Moonen.
I wrote my master's thesis, titled Algebraic cycles, Chow motives, and L-functions, in the spring of 2013 under the supervision of Robin de Jong.
I wrote my bachelor's thesis, titled Tannaka Duality for Finite Groups, in the spring of 2011 under the supervision of Lenny Taelman.
Side projects
- Lean and its mathematical library.
I am one of the maintainers of the mathematical library of the Lean theorem prover.
- Superficie algebriche. (Together with Pieter Belmans.) le superficie algebriche is a tool for studying numerical invariants of minimal algebraic surfaces over the complex numbers. We implemented it in order to better understand the Enriques–Kodaira classification, and to showcase how mathematics can be visualised on the web.
- Sloganerator. Together with Pieter Belmans I wrote a web-app that makes it easy to suggest slogans for tags (results) in the Stacks Project.