I am a postdoc at EPFL in the group of Zsolt Patakfalvi.

Before I was a postdoc at the University of Toulouse, in the group of Stéphane Lamy.
I did my PhD in algebraic geometry under the supervision of Jérémy Blanc at the University of Basel.

Interests: Arithmetic questions on groups of birational transformations, classical algebraic geometry, Cremona groups, plane curve singularities, birational geometry, non-closed fields, turtles.

• Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank
(with Jérémy Blanc and Egor Yasinsky)

Abstract arXiv

Abstract arXiv

We describe the group of birational transformations of a non-trivial Severi-Brauer surface over a perfect field K, proving in particular that if it contains a point of degree 6, then it is not generated by elements of finite order as it admits a surjective group homomorphism to Z.
We then use this result to study Mori fibre spaces over the field of complex numbers, for which the generic fibre is a non-trivial Severi-Brauer surface. We prove that any group of cardinality at most the one of C is a quotient of any Cremona group of rank at least 4. As a consequence, this gives a negative answer to the question of Dolgachev of whether the Cremona groups of all ranks are generated by involutions. We also prove that the 3-torsion of the Cremona group of rank at least 4 is not countable.

The plane Cremona group over the finite field 𝔽

_{2}is generated by three infinite families and finitely many birational maps with small base orbits. One family preserves the pencil of lines through a point, the other two preserve the pencil of conics through four points that form either one Galois orbit of size 4, or two Galois orbits of size 2. For each family, we give a generating set that is parametrized by the rational functions over 𝔽_{2}. Moreover, we describe the finitely many remaining maps and give an upper bound on the number needed to generate the Cremona group. Finally, we prove that the plane Cremona group over 𝔽_{2}is generated by involutions.
The files are sagemath files for Jupyter notebook.

We prove that over any perfect field the plane Cremona group is generated by involutions.

Accepted in Algebraic Geometry.

• Algebraic subgroups of the plane Cremona group over a perfect field
(with Susanna Zimmermann)

Abstract arXiv Erratum

Abstract arXiv Erratum

EpiGA, vol. 5 (2021), no. 14

We show that any infinite algebraic subgroup of the plane Cremona group over a
perfect field is contained in a maximal algebraic subgroup of the plane Cremona group.
We classify the maximal groups, and their subgroups of rational points, up to conjugacy by a birational map.

Annales de l'Institut Fourier, Volume 72 (2022) no. 1, pp. 1-42.

For perfect fields k with algebraic closure L satisfying [L:k] > 2, we construct new normal subgroups of the plane Cremona group and provide an elementary proof of its non-simplicity, following the melody of the recent proof by Blanc, Lamy and Zimmermann that the Cremona group of rank n over (subfields of) the complex numbers is not simple for n ≥ 3.

North-W. Eur. J. of Math., vol 6, 2020, pages 45-89

We provide a tool how one can view a polynomial on the affine plane of bidegree (a,b) - by which we mean that its Newton polygon lies in the triangle spanned by (a,0), (0,b) and the origin - as a curve in a Hirzebruch surface having nice geometric properties. As an application, we study maximal A

_{k}-singularities of curves of bidegree (3,b) and find the answer for b ≤ 12.
PhD thesis: A birational journey: From plane curve singularities to the Cremona group over perfect fields

open access

open access

University of Basel, 2020