Since September 2020, I am an associate professor ("Maître de Conférences") at the Université Caen Normandie . I am a member of the team GRAAL (Géométrie, Représentations, Algèbre, Analyse, Logique) at the Laboratoire de Mathématiques Nicolas Oresme.
I am broadly interested in Functional Analysis. I started research by studying Operator Theory, and especially the beautiful theory of Schur multipliers and its applications in Perturbation theory. A Schur mutlipliers is simply the pointwise multplication of a matrix by a fixed matrix. The study of the norm of such mappings is an old problem, and even when the space of matrices is equipped with the usual operator norm, the answer is not easy and is a deep result by Grothendieck. These simple transformations are applied, for instance, in harmonic analysis and in perturbation theory. To study the latter, the notion of multiple operator integrals will come in handy. These objects are "continuous" generalizations of Schur multipliers and are a useful tool to study operator functions (that is, functions valued in a space of operators). With these tools in hand, we are able to give simple formulas for the derivative of functions valued in certain non-commutative Lp spaces.
More recently, I have been interested in the so-called Lipschitz free spaces. These Banach spaces are easy to define but certainly not easy to analyse. It is a convenient object which allows to "linearize" a given Lipschitz function. This research topic is quite active and many questions have no answer yet. I have been interested, more precisely, in the dynamical properties that can be transfered from the Lipschitz function to the linearized mapping.
- January 2020 - June 2024 : Member of the ANR project "Noncommutative analysis on groups and quantum groups" .
The project coordinator is Quanhua Xu (LMB, Besançon) and the team leader is Eric Ricard (LMNO, Caen).
- 2021 : Member of the INSMI PEPS JCJC project , "Linear and nonlinear dynamics in Lipschitz-free spaces", with Arafat Abbar and Colin Petitjean.
The arXiv versions of my papers are provided below.
Higher order S^p-differentiability: the unitary case, A pre-adjoint approach on weighted operators between spaces of Lipschitz functions, A note on the spectrum of Lipschitz operators and composition operators on Lipschitz spaces, Growth rate of eventually positive Kreiss bounded C_0-semigroups on L^p and C(K), Perturbation theory and higher order S^p-differentiability of operator functions, Compact and weakly compact Lipschitz operators, On the dynamics of Lipschitz operators, Complete boundedness of multiple operator integrals, When do triple operator integrals take value in the trace class?, Higher order S^2-differentiability and application to Koplienko trace formula, Schur multipliers on B(L^p, L^q), Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae: The unitary case, Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae, Between September 2014 and June 2017, I studied for my PhD, under the supervision of Christian Le Merdy, the so-called continuous multilinear Schur multipliers and their applications to perturbation theory. During these years, I had the opportunity to collaborate with various researchers : Denis Potapov, Anna Skripka, Fedor Sukochev and Anna Tomskova. I also had the chance to be invited by A. Skripka for two months at the University of New Mexico in Albuquerque (USA) where I worked on the higher order S^2 differentiability of operator functions. My PhD thesis :
Continuous linear and bilinear Schur multipliers and applications to perturbation theory The beamer of my PhD defense :
Beamer PhD defense Between November 2017 and August 2019, I did a Postdoc at the Central South University (in Changsha, Hunan province, China), under the supervision of Jiao Yong. I pursued the research activities I started during my pHD and worked mostly on the differentiability of operator functions.
The beamer of my postdoc defense :
Beamer postdoc defense
Fonctions opérateurs-Lipschitz sur les classes de Schatten,
Transformée de Hilbert,
Calcul fonctionnel dans les algèbres de Banach et Hypercyclicité,
La revanche de l’intégrale de Riemann, Here are a few of the talks I gave since I started doing research. The ones I mention here are the ones for which I made a beamer presentation and, most importantly, the ones for which I still have the pdf file.
12ème journée de la Fédération Normandie-Mathématiques ,
Université Caen Normandie, Caen, France (November 2020)
Autumn School "Multipliers in NC analysis and their applications" ,
Laboratoire de Mathématiques de Besançon, France (November 2019)
Conference ”Advanced Courses in Operator Theory and Complex Analysis” ,
Université Paris-Est Marne-la-Vallée, Champs-sur-Marne, France (June 2019)
Mini-Course ”Norms of Schur Multipliers and applications”, University of New Mexico, Albuquerque, USA (May 2019). Séminaire ”Probabilités, Analyse et Statistique”,
Université Clermont Auvergne, Clermont-Ferrand,
France (May 2017)
Maths colloquium,
University of New Mexico, USA (March 2017)
Maths seminar,
Seoul National University, South Korea (November 2016)
20th Conference of the International Linear Algebra Society,
Katholieke Universiteit Leuven, Leuven, Belgium (July 2016)
26th International Conference in Operator Theory ,
West University, Timisoara, Romania (June 2016)
GDR AFHP ,
Luminy - CIRM, Marseille, France (November 2015)
Mock oral exams ("Colles") ,
Second year students in advanced preparatory school for the French "Grandes Écoles" Mentoring.
Bachelor and Master students. Preparation for the writing and oral exams of the "Agrégation de Mathématiques", and knowledge enhancement in Analysis,
Fifth year science students Integration and probability,
Third year science students Differential Calculus, exercise sessions,
Second year science students Mock oral exams ("Colles"),
First year science students Analysis ,
First year science students Probability and statistics, exercise sessions,
Second year science students Mentoring.
Third year science student following a lab research training. Bachelor thesis about the approximation of Hölder continuous functions by Bernstein polynomials. Preparation for the writing and oral exams of the "Agrégation de Mathématiques", and knowledge enhancement in Analysis,
Fifth year science students Differential Calculus, exercise sessions,
Second year science students Sequences and series of functions,
Second year science students Analysis ,
First year science students Probability, exercise sessions,
First year science students Preparation for the writing and oral exams of the "Agrégation de Mathématiques",
Fifth year science students preparing for a national competitive examination to teach mathematics in secondary and post-secondary education Analysis, course about complex analysis and operators on a Hilbert space, and exercise sessions ,
Fifth year science students Differential Calculus, exercise sessions,
Second year science students Linear Algebra, course and exercise sessions ,
First year science students Probability, exercise sessions,
First year science students Linear Algebra, exercise sessions ,
Second year economics students Probability and Statistics, exercise sessions ,
Second year economics students Statistics, exercise sessions ,
First year economics students Analysis, exercise sessions ,
First year economics students Mock oral exams ("Colles") ,
Second year students in advanced preparatory school for the French "Grandes Écoles" Practice oral examinations of the "Agrégation de Mathématiques" , Fifth year science students Probability, exercise sessions ,
Second year computer science students Analysis, course and exercise sessions ,
First year science students Analysis, exercise sessions ,
First year biology students Analysis, course and exercise sessions ,
First year science students Analysis, exercise sessions ,
First year biology students Analysis, course and exercise sessions ,
First year science students Analysis, exercise sessions ,
First year biology students Analysis, course and exercise sessions ,
First year science students Analysis, course and exercise sessions (Differential calculus) ,
First year biology students Analysis, exercise sessions ,
First year biology students Tutoring ,
First year science students
Presentation of the profession of Associate professor during the "Journée des métiers des mathématiques" (2023). Held in Besançon (the talk was online). Animation of a popularization workshop during the ”Journée de Découverte de la Recherche Mathématiques", about the "Infinity in Mathematics",
with Marine Rougnant. Two sessions, one in french in front of highschool students, and one in english in front of PhD students. Here is the beamer of the french version.
Département de Mathématiques
UFR des Sciences - Campus 2
F14032 Caen Cedex
Bureau : S3 321
Research papers
2024
with Arup Chattopadhyay, Saikat Giri and Chandan Pradhan, arXiv:2404.08253.
with Arafat Abbar and Colin Petitjean, Results Math 79, 85 (2024).2023
with Arafat Abbar and Colin Petitjean. Arxiv:2310.08965.
with Loris Arnold. J. Evol. Equ. 23, 7 (2023). https://doi.org/10.1007/s00028-022-00860-0. 2022
Revista Matemática Iberoamericana, 38 (2022), 189-221.
with Arafat Abbar and Colin Petitjean. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 153(3), 1002-1020. doi:10.1017/prm.2022.29.2021
with Arafat Abbar and Colin Petitjean, Integral Equations Operator Theory 93 (2021), no. 4, Paper No. 45, 27 pp.
Canadian Mathematical Bulletin, 64(2) (2021), 474-490.
with Christian Le Merdy and Fedor Sukochev, Ann. Inst. Fourier, Grenoble 71, 4 (2021) 1393-1448.2019
with Christian Le Merdy, Anna Skripka and Fedor Sukochev, Journal of Functional Analysis, Volume 276, Issue 10 (2019), 3170-3204.2018
J. Operator Theory 79:2(2018), 301-326.2016
with Christian Le Merdy, Denis Potapov, Fedor Sukochev and Anna Tomskova, Journal of Functional Analysis, Volume 271, Issue 7 (2016), 1747-1763.
with Christian Le Merdy, Denis Potapov, Fedor Sukochev and Anna Tomskova, Proc. London Math. Soc.(3) 113 (2016), 113-139.
Selected talks
Régularité des fonctions d’opérateurs
Differentiability of operator functions in Schatten norms
Differentiability of operator functions in Schatten norms
Opérateurs intégraux multiples et théorie de la perturbation
Triple operator integrals valued in trace class operators
S1-boundedness of triple operator integrals
Application of Schur multipliers to a problem of perturbation
Perturbation of second order for functional calculus
Application of Schur multipliers to a problem of perturbation
Teaching
2021-2024 (Lycée Victor Hugo, Caen)
2022-2024 (Université Caen Normandie, Caen)
2021-2022 (Université Caen Normandie, Caen)
2020-2021 (Université Caen Normandie, Caen)
2019-2020 (Université Gustave Eiffel, Marne-la-Vallée)
2014-2017 (Lycée Victor Hugo, Besançon)
2016-2017 (UFRST Besançon)
2015-2016 (UFRST Besançon)
2014-2015 (UFRST Besançon)
2013-2014 (UFRST Besançon)
2012-2013 (UFRST Besançon)
2011-2012 (UFRST Besançon)