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 Matteo Penegini. In preparation:
On the cohomology of surfaces with
p_{g} = q = 2
and maximal Albanese dimension. arXiv:1901.00193.
[link]

The Mumford–Tate conjecture for products of abelian varieties.
(To appear in Algebraic Geometry.) arXiv:1804.06840.
[link]

On compatibility of the ℓadic realisations of an abelian motive.
(To appear in Annales de l'Institut Fourier.) arXiv:1706.09444v1.
[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
Course  Semester 
Algebra and Number Theory  Winter 18/19 
Seminar Algebraic Geometry  Winter 18/19 
Seminar Local Fields  Summer 2019 
Invited talks
 07 May 2019
 Berlin (HU) — TBA.
 11 Apr 2019
 Strasbourg — TBA.
 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 ℓadic realisations of abelian motives.
 27 Jul 2017

AVGA conference (Poznań) —
On compatibility of the ℓadic 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 ℓadic 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 coorganised).
Old teaching
As teaching assistent in Freiburg:
Course  Semester 
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 MumfordTate conjecture. Notes
 19 Jan 2016
 Faltings seminar — pdivisible 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 GL_{2} 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 Lfunctions
 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 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
 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 webapp that makes it easy to suggest slogans for tags (results) in the Stacks Project.