Lucas Lagarde

Address :

Laboratoire Analyse, Géométrie et Applications
Institut Galilée – Université Sorbonne Paris Nord
99 avenue Jean-Baptiste Clément
93430 Villetaneuse
France

E-mail address : lagarde[at]math.univ-paris13.fr
Office : A307
Research group : Arithmétique et Géométrie Algébrique

I am a PhD student in the Laboratoire Analyse, Géométrie et Applications (LAGA) of Université Paris 13, under the supervision of Olivier Wittenberg. Before that, I was an ALGANT student at Universiteit Leiden and Université de Bordeaux.
I am mainly interested in (arithmetic) algebraic geometry, notably cohomological methods for rational points (Brauer-Manin, fppf descent) and algebraic cycles, and related topics (unramified cohomology, algebraic K-theory, motivic cohomology, motives, motivic homotopy theory).

Research :

Cycle class maps for zero-cycles over higher local fields.

In preparation.

Higher Beauville components of Ceresa cycles and modified diagonals (with M. Moakher, M. Porzio, J. Rawson, and F. Trejos).

In preparation.

Degree three unramified cohomology of homogeneous spaces with finite stabilisers.

In preparation.

Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem. arXiv:2506.02600.

41 pages, June 2025 (preprint).

Documents :

There might (surely) be a wide variety of errors hidden in these notes, reader beware.

Master's Thesis : Unramified cohomology, cycles, and integral Hodge classes

Notes :

Toric reduction of modular Jacobians

Galois categories , following SGA1, §§4--6 (in French, unfinished)

Modular curves over ℚ

On the cotangent complex (in French)

Model structure on simplicial categories , following Quillen's "Homotopical Algebra" (in French)

Left and right fibrations, joins and slices , following Cisinski's "Higher Categories and Homotopical Algebra"

Model structures ex nihilo , following Cisinski's "Higher Categories and Homotopical Algebra"

Brauer, Manin, and rational points (in French)

Teaching :

Représentations linéaires des groupes finis, M1 Mathématiques Fondamentales, Institut Galilée (Spring 2025).

Seminars and study groups :

Learning seminar on perverse sheaves, IMJ-PRG.

Study group on Mazur's torsion theorem, Online.

[Last update : 03/06/25]