Joaquín Rodrigues Jacinto

joaquin.rodrigues-jacinto at univ-amu.fr

Welcome!

I am a Maître de Conférences at the Université Aix-Marseille. My main research areas are Algebraic Number Theory and Arithmetic Geometry. I am interested in the construction of p-adic L-functions, and in their connection to the p-adic Langlands correspondence. I also work in the study of special values of L-function framed in the setting of Deligne-Beilinson and Tate conjectures. Lately, I have been working on the applications of condensed mathematics to p-adic representation theory.

Articles and preprints

p-adic interpolation of Gauss-Manin connections on nearly overconvergent modular forms and p-adic L-functions (with A. Graham and V. Pilloni), Preprint 2023, 45 pages.
An introduction to p-adic L-functions (with Chris Williams), Preprint 2023, 66 pages.
Solid locally analytic representations (with J. E. Rodríguez Camargo), Preprint 2023, 51 pages.
Tempered currents and Deligne cohomology of Shimura varieties, with an application to GSp6 (with J. I. Burgos Gil, A. Cauchi and F. Lemma), Preprint 2022, 47 pages.
On higher regulators of Siegel varieties (with A. Cauchi and F. Lemma), Preprint 2019 (revised in 2022), 30 pages.
Algebraic cycles and functorial lifts from G2 to PGSp6 (with A. Cauchi and F. Lemma), to appear in Algebra & Number Theory.
Solid locally analytic representations of p-adic Lie groups (with J.E. Rodríguez Camargo), Representation Theory 26 (2022), 962–1024 (journal).
Norm-compatible systems of Galois cohomology classes for GSp6 (with A. Cauchi), Documenta Mathematica 25 (2020), 911-954 (journal).
Arithmetic families of (φ,Γ)-modules and locally analytic representations of GL2(Qp), (with I. Gaisin) Documenta Mathematica 23 (2018), 1313-1404 (journal).
La conjecture ε locale de Kato en dimension 2, Mathematische Annalen 372-3 (2018), 1277--1334 (journal).
(φ,Γ)-modules de de Rham et fonctions L p-adiques, Algebra & Number Theory 12-4 (2018), 885--934 (journal).
(φ,Γ)-modules de de Rham et fonctions L p-adiques, Ph.D. Thesis.

Teaching

2023-2024 :

Théorie algorithmique des nombres (M2 IMD) : Lecture notes.
Analyse 2.

Algèbre 3.

2022-2023 :

Représentations des groupes finis (USPN M1 Mathématiques) : TD1, TD2, TD3, TD4, TD5.
Cryptographie (USPN M2 Mathématiques des données) : TD1., TD2, TD3, TD4, TD5, TD6.

Other writings

Cohomology of Arithmetic Groups, Notes for a study group on derived structures in the Langlands program at UCL.
Torema de Krein-Milman, Concurso de monografías UMA.
Teorema de Stokes en variedades (with Ramiro Lafuente), Concurso de monografías UMA.