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Current position

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.


Research interests

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.


Contact informations

Université Caen Normandie
Département de Mathématiques
UFR des Sciences - Campus 2
F14032 Caen Cedex
Bureau : S3 321
clement.coine (at) unicaen.fr

Research activities


Publications

The arXiv versions of my papers are provided below.

About Dynamics on Lipschitz-Free spaces

On the dynamics of Lipschitz operators,
with Arafat Abbar and Colin Petitjean, preprint (2020), arXiv:2011.10800. To Appear in Integral Equations and Operator Theory.

About differentiability for the Schatten p-norms

Perturbation theory and higher order S^p-differentiability of operator functions,
To appear in Revista Matemática Iberoamericana.

Higher order S^2-differentiability and application to Koplienko trace formula,
with Christian Le Merdy, Anna Skripka and Fedor Sukochev, Journal of Functional Analysis, Volume 276, Issue 10 (2019), 3170-3204.

Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae: The unitary case,
with Christian Le Merdy, Denis Potapov, Fedor Sukochev and Anna Tomskova, Journal of Functional Analysis, Volume 271, Issue 7 (2016), 1747-1763.

Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae,
with Christian Le Merdy, Denis Potapov, Fedor Sukochev and Anna Tomskova, Proc. London Math. Soc.(3) 113 (2016), 113-139.

About the boundedness of Schur multipliers/Multiple operator integrals

Complete boundedness of multiple operator integrals,
Canadian Mathematical Bulletin, 64(2) (2021), 474-490. doi:10.4153/S0008439520000570

Schur multipliers on B(L^p, L^q),
J. Operator Theory 79:2(2018), 301-326.

When do triple operator integrals take value in the trace class?,
with Christian Le Merdy and Fedor Sukochev, To appear in Annales Institut Fourier.



PhD Thesis

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



Postdoc 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



Selected talks

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)
Régularité des fonctions d’opérateurs

Autumn School "Multipliers in NC analysis and their applications" , Laboratoire de Mathématiques de Besançon, France (November 2019)
Differentiability of operator functions in Schatten norms

Conference ”Advanced Courses in Operator Theory and Complex Analysis” , Université Paris-Est Marne-la-Vallée, Champs-sur-Marne, France (June 2019)
Differentiability of operator functions in Schatten norms

Mini-Course ”Norms of Schur Multipliers and applications”, University of New Mexico, Albuquerque, USA (May 2019).
Invited by Anna Skripka for the "Workshop on Positivity". One day I will write a pdf of my notes for the mini-course, but meanwhile, here is the abstract for those who are interested in this topic.

Séminaire ”Probabilités, Analyse et Statistique”, Université Clermont Auvergne, Clermont-Ferrand, France (May 2017)
Opérateurs intégraux multiples et théorie de la perturbation

Maths colloquium, University of New Mexico, USA (March 2017)
Triple operator integrals valued in trace class operators

Maths seminar, Seoul National University, South Korea (November 2016)
S1-boundedness of triple operator integrals

20th Conference of the International Linear Algebra Society, Katholieke Universiteit Leuven, Leuven, Belgium (July 2016)
Application of Schur multipliers to a problem of perturbation

26th International Conference in Operator Theory , West University, Timisoara, Romania (June 2016)
Perturbation of second order for functional calculus

Teaching

What I teached

2020-2021 (Université Caen Normandie, Caen)

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

2019-2020 (Université Gustave Eiffel, Marne-la-Vallée)

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

2014-2017 (Lycée Victor Hugo, Besançon)

Mock oral exams ("Colles") , Second year students in advanced preparatory school for the French "Grandes Écoles"

2016-2017 (UFRST Besançon)

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

2015-2016 (UFRST Besançon)

Analysis, course and exercise sessions , First year science students

Analysis, exercise sessions , First year biology students

2014-2015 (UFRST Besançon)

Analysis, course and exercise sessions , First year science students

Analysis, exercise sessions , First year biology students

2013-2014 (UFRST Besançon)

Analysis, course and exercise sessions , First year science students

Analysis, course and exercise sessions (Differential calculus) , First year biology students

2012-2013 (UFRST Besançon)

Analysis, exercise sessions , First year biology students

2011-2012 (UFRST Besançon)

Tutoring , First year science students

Other things

Popularization

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.

CV

Curriculum vitae

English version

CV Clément Coine

French version

CV Clément Coine