Johan Commelin
I am a postdoc in the group of Stefan Kebekus. My main interest lies in algebraic geometry and algebraic number theory.
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: Hodge theory, Galois representations, motives, Mumford–Tate conjecture, periods.
News & Olds
Contact details
Publications/preprints
- With Kevin Buzzard and Patrick Massot.
Formalising perfectoid spaces
[arXiv:1910.12320]
[project webpage]
-
With Victoria Cantoral Farfán.
The Mumford–Tate conjecture implies the
algebraic Sato–Tate conjecture
of Banaszak and Kedlaya arXiv:1905.04086.
[link]
-
With Matteo Penegini.
On the cohomology of surfaces with
pg = q = 2
and maximal Albanese dimension.
(To appear in Transactions of the AMS.) arXiv:1901.00193.
[link]
-
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]
Current and upcoming teaching
Invited talks
- 17 Dec 2019
- Darmstadt — Formalising perfectoid spaces.
- 27 Nov 2019
- Leuven — The Mumford–Tate conjecture implies the algebraic Sato–Tate conjecture.
- 07 May 2019
- Berlin (HU) — On the cohomology of smooth projective surfaces with $p_g = q= 2$ and maximal Albanese dimension.
- 11 Apr 2019
- Strasbourg — On the cohomology of smooth projective surfaces with $p_g = q= 2$ and maximal Albanese dimension.
- 28 Jan 2019
- Nancy — The Mumford–Tate conjecture for products of abelian varieties.
- 08 Jan 2019
- Amsterdam — The perfectoid project (Lean Together; talk joint with Patrick Massot).
- 06 Dec 2018
- Triest — On the cohomology of smooth projective surfaces with $p_g = q= 2$ and maximal Albanese dimension.
- 15 Nov 2017
- Bielefeld — On the Mumford–Tate conjecture for products of abelian varieties.
- 05 Oct 2017
- Strasbourg — On compatibility of the ℓ-adic realisations of abelian motives.
- 27 Jul 2017
-
AVGA conference (Poznań) —
On compatibility of the ℓ-adic realisations of abelian motives.
- 30 Jun 2017
- Freiburg — The Mumford–Tate conjecture for products of K3 surfaces.
- 14 Jun 2017
- SCA seminar (Jussieu) — On compatibility of the ℓ-adic realisations of abelian motives.
- 28 Apr 2017
- SGA seminar (Heidelberg) — The Mumford–Tate conjecture for products of K3 surfaces.
- 26 Apr 2017
- SFB seminar (Mainz) — The Mumford–Tate conjecture for products of K3 surfaces.
Seminars
Seminars that I organised (or co-organised).
Old teaching
As teaching assistent in Freiburg:
| Course | Semester |
|---|
| Algebra and Number Theory | Winter 18/19 |
| Seminar Algebraic Geometry | Winter 18/19 |
| Algebraic Number Theory | Summer 2018 |
| Proseminar Quadratic Forms | Summer 2018 |
In Utrecht I supervised 4 students on a project for the course
Orientation in Mathematical Research.
The title of the project was:
Supersingular Isogeny Diffie–Hellman.
As teaching assistant in Nijmegen:
As teaching assistant in Leiden:
Other talks
- 9 Mar 2018
- 2018 Intercity Geometry Seminar — Birational Calabi–Yau varieties have the same Betti numbers. Notes
- 24 Nov 2017
- Derived Algebraic Geometry Seminar — Twisted sheaves. Notes
- 13 Oct 2017
- Derived Algebraic Geometry Seminar — A theorem of Bondal and Orlov. Notes
- 10 Apr 2017
- Seminar on Perverse Sheaves — The decomposition theorem. Notes
- 15 Dec 2016
- PhD colloquium — Chebotarev's density theorem.
- 7 Dec 2016
- Crystalline seminar (Amsterdam, UvA) — Comparing infinitesimal cohomology with de Rham cohomology I. Notes
- 13 Oct 2016
- PhD colloquium — Introduction to abelian varieties and the Mumford--Tate conjecture. Notes
- 19 Jan 2016
- Faltings seminar — p-divisible groups. Notes
- 30 Nov 2015
- PhD colloquium — Periods (and why the fundamental theorem of calculus conjecturely is a fundamental theorem). Notes
- 26 Nov 2015
- Diamant symposium — On the Mumford–Tate conjecture for the product of an abelian surface and a K3 surface. Slides
- 24 Nov 2015
- Faltings seminar — Gabber's lemma. Notes
- 27 Oct 2015
- GQT School — On the Mumford–Tate conjecture for surfaces with p_g = q = 2. Notes
- 27 May 2015
- Mixed Homotopy Theory — Motivic cohomology. Notes
- 6 May 2015
- Mixed Homotopy Theory — Smooth and étale morphisms. Notes
- 15 Apr 2015
- Mixed Homotopy Theory — Intro to schemes and their basic properties. Notes
- 11 Dec 2014
- Local Langlands seminar — Weil–Deligne representations. Notes
- 13 Nov 2014
- Local Langlands seminar — Functional equation for GL2 and cuspidal local constants. Notes
- 23 Oct 2014
- Abelian Varieties — Finite group schemes. Notes
- 3 Mar 2014
- PhD colloquium (RU) — What is a motive? Notes
- 3 Dec 2013
- Seminar on Étale Cohomology — Étale cohomology of fields. Notes
- 16 Jul 2013
- Master's thesis defense — Algebraic cycles, Chow motives, and L-functions
- 18 Mar 2013
- Topics in Algebraic Geometry — Good reduction. Notes
- 11 Feb 2013
- Topics in Algebraic Geometry — Projective and noetherian schemes.
- 26 Apr 2012
- Commutative Algebra seminar — Derivations and Differentials. Notes
- 26 Mar 2012
- Topics in Algebraic Geometry — The structure of [N] II. Notes
- 19 Mar 2012
- Topics in Algebraic Geometry — The structure of [N] I. Notes
Other writing
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
- 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. (A local clone with a more advanced UI.)
- Sloganerator. Together with Pieter Belmans I wrote a web-app that makes it easy to suggest slogans for tags (results) in the Stacks Project.
