## About

**Postdoc** at Vienna University, Austria

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

## Publications

**Unipotent \(\ell\)-blocks for simply connected \(p\)-adic groups**(pdf)

Let \(F\) be a non-archimedean local field and \(G\) the \(F\)-points of a connected simply-connected reductive group over \(F\). In this paper, we construct the unipotent \(\ell\)-blocks of \(G\). To do that we introduce the notion of d-1-series for finite reductive groups. These series form a partition of the irreducible representations and are defined using Harish-Chandra theory and d-Harish-Chandra theory. The \(\ell\)-blocks are then constructed using these d-1-series, with d the order of q modulo \(\ell\), and consistent systems of idempotents on the Bruhat-Tits building of \(G\).

**Équivalence de catégories entre systèmes de coefficients et d'idempotents**(pdf,arXiv:1912.06566)

The consistent systems of idempotents of Meyer and Solleveld allow to construct Serre subcategories of \(Rep_{R}(G)\), the category of smooth representations of a \(p\)-adic group \(G\) with coefficients in \(R\). In particular, they were used to construct level 0 decompositions when \(R=\overline{\mathbb{Z}}_{\ell}\), \(\ell \neq p\), by Dat for \(GL_n\) and the author for a more general group. Wang proved in the case of \(GL_n\) that the sub-category associated with a system of idempotents is equivalent to a category of coefficient systems on the Bruhat-Tits building. This result was used by Dat to prove an equivalence between an arbitrary level zero block of \(GL_n\) and a unipotent block of another group. In this paper, we generalize Wang's equivalence of category to a connected reductive group on a non-archimedean local field.

**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.

**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.

## CV

## Education

- 2019–
**Post-Doc in Mathematics,**

*University of Vienna, Austria*- 2015-2019
**PhD in Mathematics,**

Advisor : Jean-François Dat,

*Université Pierre et Marie Curie, IMJ-PRG, Paris*Subject: On the l-locks of p-adic groups

- 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

- December 2019
- London Number Theory Seminar, London, United-Kingdom
- February 2019
- Colloquium GDR TLAG, Poitiers, France
- February 2019
- Seminare of the University of East Anglia, Norwich, United-Kingdom
- December 2018
- Seminare of the University of Vienna, Vienna, Austria
- November 2018
- Seminare of the Laboratoire de Mathématiques de Versailles, Versailles, France
- February 2018
- Seminare Groupes Réductifs et Formes Automorphes de l’IMJ-PRG, Paris, France
- November 2017
- Seminare Groupes, Représentations et Géométrie, Paris, France

## 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

- 2019-2029
**Algebraic Number Theory**

Master, Teaching assistant of A. Mínguez

*University of Vienna*- 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*

## Computer science

- 2011-2012
**Programming Theory,**

*École Normale Supérieure de Lyon*

Validated with 19/20- 2011
- TIPE : Ant colony optimization algorithms

*Lycée Michel-Montaigne, Bordeaux, France* - 2010
- TIPE : Artificial intelligence for the game of Go

*Lycée Michel-Montaigne, Bordeaux, France*

**Programming language :** C++, Python, Pascal, HTML, CSS, JavaScript