Thomas Lanard

About

Ph.D. student at IMJ-PRG
Supervisor: Jean-François DAT
Team: Formes Automorphes

Research Areas: Representation theory, Number theory, Algebra
Current interests: Representations of p-adic groups, Langlands program

Publications

  • Sur les \(\ell\)-blocs de niveau zéro des groupes \(p\)-adiques, Compos. Math. 154 (2018), no. 7 (pdf)
    Let \(G\) be a \(p\)-adic group that splits over an unramified extension. We decompose \(Rep_{\Lambda}^{0}(G)\), the abelian category of smooth level \(0\) representations of \(G\) with coefficients in \(\Lambda=\overline{\mathbb{Q}}_{\ell}\) or \(\overline{\mathbb{Z}}_{\ell}\), into a product of subcategories indexed by inertial Langlands parameters. We construct these categories via systems of idempotents on the Bruhat-Tits building and Deligne-Lusztig theory. Then, we prove compatibilities with parabolic induction and restriction functors and the local Langlands correspondence.
  • Sur les \(\ell\)-blocs de niveau zéro des groupes \(p\)-adiques II (pdf,arXiv:1806.09543)
    Let \(G\) be a \(p\)-adic group which splits over an unramified extension and \(Rep_{\Lambda}^{0}(G)\) the abelian category of smooth level 0 representations of \(G\) with coefficients in \(\Lambda=\overline{\mathbb{Q}}_{\ell}\) or \(\overline{\mathbb{Z}}_{\ell}\). We study the finest decomposition of \(Rep_{\Lambda}^{0}(G)\) into a product of subcategories that can be obtained by the method introduced by Lanard, which is currently the only one available when \(\Lambda=\overline{\mathbb{Z}}_{\ell}\) and \(G\) is not an inner form of \(GL_n\). We give two descriptions of it, a first one on the group side à la Deligne-Lusztig, and a second one on the dual side à la Langlands. We prove several fundamental properties, like for example the compatibility to parabolic induction and restriction or the compatibility to the local Langlands correspondence. The factors of this decomposition are not blocks, but we show how to group them to obtain "stable" blocks. Some of these results support a conjecture given by Dat.

  • Thesis : Sur les \(\ell\)-blocs de niveau zéro des groupes \(p\)-adiques (pdf)

    CV

    Education

    2015–

    PhD in Mathematics,
    Advisor : Jean-François Dat,
    Université Pierre et Marie Curie, IMJ-PRG, Paris

    Subject: Blocks of p-adic groups and Langlands functoriality

    2014-2015

    Master (M2) of Mathematics,
    École Normale Supérieure de Lyon

    Subject: Introduction to the theory of L and zeta functions and their applications

    2013-2014
    Agrégation of Mathematics,
    École Normale Supérieure de Lyon
    Rank : 1st
    2012-2013
    Master (M1) of Mathematics, ERASMUS,
    Imperial College London / École Normale Supérieure de Lyon
    2011-2012
    Bachelor of Mathematics,
    École Normale Supérieure de Lyon

    Talks

    February 2018
    Sur les l-blocs des groupes p-adiques,
    Séminaire Groupes Réductifs et Formes Automorphes de l’IMJ-PRG, Paris
    November 2017
    Sur les l-blocs des groupes p-adiques,
    Séminaire Groupes, Représentations et Géométrie, Paris

    Research Internships

    2015
    Institut Mathématique de Jussieu, Jean François Dat
    Representations of p-adic groups and Langlands conjectures
    2013
    Imperial College London, Kevin Buzzard
    The Modularity Theorem
    2012
    École Polytechnique, Centre de Mathématiques Laurent Schwartz, Alain Plagne
    Waring’s Problem

    Teaching

    2015-2019
    Mathematics in continuing education
    L3, Autonomous
    Polytech’ Paris
    2018-2019
    Group theory
    L3, Teaching assistant of B. Stroh
    Sorbonne Université
    2018-2019
    Arithmetic
    L2, Teaching assistant of S. Chemla
    Sorbonne Université
    2015-2018
    Fourier analysis and Distributions
    L3, Teaching assistant of L. Lazzarini
    Polytech’ Paris