Johan Commelin
I am a PhD student under supervision of Ben Moonen. My main interest lies in algebraic geometry and algebraic number theory. I am funded by NWO project 613.001.207 (Arithmetic and motivic aspects of the Kuga–Satake construction).
Current research topics include: Hodge theory, Galois representations, motives, Mumford–Tate conjecture, periods.
PhD defense
On Friday, the 7th of July, 2017, I hope to defend my PhD thesis.
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More information]
Contact details
Publications/preprints

The Mumford–Tate Conjecture for the Product of an Abelian Surface and a K3 Surface.
Documenta Math. 21 (2016) 1691–1713.
[link]

On compatibility of the ℓadic realisations of an abelian motive.
Preprint. arXiv:1706.09444v1.
[link]
Invited talks
 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).
Teaching
As teaching assistant in Nijmegen:
As teaching assistant in Leiden:
Other talks
 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. 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.