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.

- In WS19/20 I am organising a seminar on Condensed Mathematics.
- Together with Stefan Kebekus and Annette Huber-Klawitter, I organised a summer school (09–13 Sept 2019): o-Minimal Structures in Algebraic Geometry.

@: | initials (funny symbol) `math.uni-freiburg.de`
(initials = `jmc` ) — PGP keys: [public] [private] |
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A: |
Room 425 Albert–Ludwigs-Universität Freiburg Mathematisches Institut Ernst-Zermelo-Straße 1 79104 Freiburg im Breisgau Deutschland |

- 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*(To appear in`p`=_{g}`q`= 2 and maximal Albanese dimension.*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]

Course | Semester |
---|---|

Seminar Local Fields | Summer 2019 |

Linear Algebra 2 | Summer 2019 |

- 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.

Seminar | Semester |
---|---|

Derived Algebraic Geometry Seminar (with Salvatore Floccari) | Fall 2017 |

Motivic Homotopy Theory Seminar (with Joost Nuiten) | Spring 2015 |

Local Langlands Microsymposium (with Milan Lopuhaä) | 27 January 2015 |

Local Langlands Seminar (with Milan Lopuhaä) | Autumn 2014 |

PhD Colloquium | Spring 2014 – Spring 2016 |

Basic Notions Reading Group | Autumn 2013 |

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:

Course | Semester |
---|---|

Rings and Fields | Autumn 2016 |

Algebraic Topology 2 | Spring 2016 |

Introduction to Algebraic Curves | Autumn 2015 |

Calculus 3&4 | Spring 2015 |

Abelian Varieties | Autumn 2014 |

Rings and Fields | Spring 2014 |

As teaching assistant in Leiden:

Course | Semester |
---|---|

Algebra 1 | Spring 2013 |

Algebra 3 | Spring 2013 |

Seminar on Commutative Algebra | Spring 2012 |

Algebra 1 | Spring 2012 |

Projective Geometry | Spring 2012 |

Analysis 3 (physics) | Autumn 2011 |

- 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 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
`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

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.

- 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.