Johan Commelin
I work parttime 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 ominimality to algebraic geometry/topology;
in particular, applications of ominimality to the theory of periods and motives.
I am actively involved in the Lean community.
In 20212022, 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
 Raphael Douglas Giles, Christian Merten, and Pim Otte started as PhD students at the math department in Utrecht. They are all working on topics related to formalization of mathematics.
 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 padic 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 ominimal geometry.
[arXiv:2108.11952]
 With Annette Huber and Philipp Habegger.
Exponential periods and ominimality.
[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, 25952603.
[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
p_{g} = q = 2
and maximal Albanese dimension.
Trans. Amer. Math. Soc. 373 (2020) 17491773.
[arXiv:1901.00193]

On compatibility of the ℓadic 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 ℓadic 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 Lfunctions, 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 webapp that makes it easy to suggest slogans for tags (results) in the Stacks Project.