Université Sorbonne Paris Nord
Institut Galilée, LAGA, UMR 7539

Case C-3
Ave J.-B. Clément
F-93430, Villetaneuse
France
Email : declercq∅math.univ-paris13.fr

• with Mathieu Florence, we introduced the notion of smooth profinite groups, whose purpose is to try to deduce from an enhancement of Kummer theory for fields lifting theorems for mod p Galois representations, aiming at providing a proof of a generalized version of the Norm Residue Isomorphism Theorem, proved by Rost, Suslin, Voevodsky and Weibel (also known as the Bloch-Kato conjecture).

• I study motives and upper motives of projective homogeneous varieties for reductive algebraic groups. I introduced motivic equivalence for these groups, constructed the discrete invariants (the higher Tits p-indexes) which control it, providing a complete classification of reductive groups of (p-)inner type in terms of the motives of their twisted flag varieties. We also extended these result for all absolutely simple groups (except groups of type ⁶D₄), developping the theory of A-upper motives (joint work with Nikita Karpenko and Anne Quéguiner-Mathieu). More recently, inspired by these techniques, I'm developping the theory of mixed initial motives with Fabio Tanania.

• I've been recently working on new developments for a more sustainable and efficient Artificial Intelligence, notably on geometric approaches to LLM and World Models in Université Sorbonne Paris Nord and in the industry (see the dedicated page).