Charles-Edouard Bréhier - Institut Camille Jordan

Charles-Edouard Bréhier
Curriculum Vitae
Contact
B [email protected]
Í http://math.univ-lyon1.fr/~brehier/
Í https://www.researchgate.net/profile/Charles_Edouard_Brehier
T +33 4 72 43 16 92.
Address:
Institut Camille Jordan
Université Claude Bernard Lyon 1
43 boulevard du 11 novembre 1918
69622 Villeurbanne cedex
France
Situation
Junior researcher, French National Center for Scientific Researh (CNRS).
Institut Camille Jordan – Université Claude Bernard Lyon 1.
Diplomas/Qualification
PhD in Mathematics of ENS Cachan - Bretagne. Obtained in 2012.
Teaching qualification (France): Agrégation de Mathématiques. Obtained in 2009. National rank: 24.
Allows me to teach at high-school level.
CNU Qualification: section 26, Applied Mathematics (2013).
Allows me to apply for teaching and research position in French Universities.
Fields of Research
In Probability:
Stochastic Partial Differential Equations
Slow-fast Systems, Averaging Principle
Algorithms for Rare Event Simulation, Metastability: interacting particle methods, adaptive biasing
methods.
Statistical properties: unbiasedness, asymptotic normality.
In Numerical Analysis:
Multiscale numerical scheme for slow-fast systems
Long-time convergence and approximation of invariant distributions
Monte-Carlo methods, simulation
Semi-Lagrangian methods
PhD Thesis
Intitulée:
Supervisors:
Institution:
Link:
Defence:
Numerical analysis of highly oscillatory Stochastic PDEs
Arnaud Debussche (ENS Rennes) and Erwan Faou(Inria)
ENS Cachan-Bretagne
http://tel.archives-ouvertes.fr/tel-00763340
11/27/2012. Grade: Très honorable (highest).
Referees: Sandra Cerrai (University of Maryland, USA)
Tony Lelièvre (Ecole des Ponts)
Examinators: Anne De Bouard (Ecole Polytechnique)
François Delarue (University of Nice Sophia-Antipolis), President
Florent Malrieu (University of Rennes 1)
Andreas Prohl (University of Tübingen, Germany)
Post-doctoral research
01.2015– University of Neuchâtel, (Switzerland).
08.2015 Supervisor: Michel Benaïm
09.2013– Inria Rocquencourt & Ecole des Ponts, Inria team Matherials & CERMICS.
12.2014 Supervisors: Tony Lelièvre and Mathias Rousset
01.2013– University of Warwick, (UK).
03.2013 Project with Martin Hairer and Andrew Stuart
Studies
09.2009– PhD, ENS Cachan-Bretagne.
11.2012 Preparation of a PhD Thesis under the supervision of Arnaud Debussche and Erwan Faou.
2009 "Agrégation de Mathématiques", Rank :24.
French high-level national competitive examination for the recruitment of teachers
2007–2009 Master of Mathematics, ENS Lyon & Université Lyon 1, Mention Très bien.
Internship: Laboratoire de Probabilités et Modèles Aléatoires - Paris 6 et 7, under the
supervision of François Delarue. Subject: Probabilistic Analsysis of the upwind scheme for
transport.
2006-2007 Licence of Mathematics, ENS Lyon, Mention Bien.
Internship: Université of Nantes, under the supervision of Xue-Ping Wang. Subject: Study of
quantum systems of particules.
2006–2010 ENS Lyon.
2004–2006 Classes Préparatoires aux Grandes Ecoles, Lycée Clemenceau, Nantes.
Undergraduate courses to prepare for entry competitive exams to top universities
2004 Baccalauréat S.
High-school degree in France
Foreign languages
Native Language: French.
English, Spanish (Written and Spoken).
Softwares
Computing Matlab/Scilab/Octave, Maple, R
Programmaing C++, Python
Publications and preprints
PhD Thesis
Analyse numérique d’EDP Stochastiques hautement oscillantes.
Numerical Analysis of highly oscillatory Stochastic PDEs.
http://tel.archives-ouvertes.fr/tel-00763340
Publications
{ Strong and Weak orders in Averaging for SPDEs, Stochastic Processes and their Applications, 122(7), 2253-2293, 2012.
http://www.sciencedirect.com/science/article/pii/S0304414912000683
{ Analysis of a HMM time-discretization scheme for a system of Stochastic PDEs, Siam
Journal on Numerical Analysis, 51(2), 1185-1210, 2013.
http://epubs.siam.org/doi/abs/10.1137/110853078
{ Approximation of the invariant measure with an Euler scheme for Stochastic PDEs
driven by Space-Time White Noise, Potential Analysis, 40(1), 1-40, 2014.
http://link.springer.com/article/10.1007/s11118-013-9338-9
{ Analysis of Adaptive Multilevel Splitting algorithms in an idealized case, with T. Lelièvre,
M. Rousset. ESAIM: PS, 19 (2015) 361-394.
http://www.esaim-ps.org/articles/ps/abs/2015/01/ps140029/ps140029.html
{ Analysis and simulation of rare events for SPDEs, with M. Gazeau, L. Goudenège, M. Rousset. ESAIM: PROCEEDINGS AND SURVEYS, January 2015, Vol. 48, p. 364–384, 2015.
http://www.esaim-proc.org/articles/proc/abs/2015/01/proc144817/proc144817.html
{ Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme, with E. Faou.
Applied Mathematics Research Express, 10.1093/amrx/abv001, 2015.
http://amrx.oxfordjournals.org/content/early/2015/04/28/amrx.abv001.short?rss=1
{ Recent advances in various fields of numerical probability, with P.E. Chaudru de Raynal,
V. Lemaire, F. Panloup, C. Rey. ESAIM: Proc., 51 (2015) 272-292
http://www.esaim-proc.org/articles/proc/abs/2015/04/proc145115/proc145115.html
{ Large deviations principle for the Adaptive Multilevel Splitting Algorithm in an idealized setting. ALEA, Lat. Am. J. Probab. Math. Stat. 12, 717–742, 2015.
http://alea.impa.br/articles/v12/12-27.pdf
{ Convergence of Adaptive Biaising Potential methods for diffusions, avec M. Benaïm.
Comptes Rendus de l’Académie des Sciences.
http://www.sciencedirect.com/science/article/pii/S1631073X1630084X
{ Approximation of the invariant law of SPDEs: error analysis using a Poisson equation
for a full-discretization scheme, avec M. Kopec. IMA Journal of Numerical Analysis.
http://imajna.oxfordjournals.org/content/early/2016/07/08/imanum.drw030
{ Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized
Setting, avec L. Goudenège, L. Tudela. Monte Carlo and Quasi-Monte Carlo Methods. Volume
163 of the series Springer Proceedings in Mathematics & Statistics pp 245-260
http://link.springer.com/chapter/10.1007%2F978-3-319-33507-0_10
{ High-order integrator for sampling the invariant distribution of a class of parabolic
SPDEs with additive space-time noise, avec G. Vilmart. Siam Journal of Scientific Computing.
http://epubs.siam.org/doi/abs/10.1137/15M1021088
Preprints
Submitted, under review
{ Unbiasedness of some Generalized Adaptive Multilevel Splitting algorithms, with M. Gazeau,
L. Goudenège, T. Lelièvre, M. Rousset. Accepted, Annals of Applied Probability.
arxiv: http://arxiv.org/abs/1505.02674
HAL: https://hal.archives-ouvertes.fr/hal-01142704
{ Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization,
with M. Hairer, A. M. Stuart. Accepted, Journal of Computational Mathematics – Special issue on
“Numerics for SPDEs”.
arxiv: http://arxiv.org/abs/1602.04057
HAL: https://hal.archives-ouvertes.fr/hal-01273500v1
Notes
A short introduction to Stochastic PDEs. Introductory lecture given at Cermics, 2014.
HAL: https://hal.archives-ouvertes.fr/hal-00973887
Teaching
Currently
2016 − 2017: Tutorial classes of Probability and Statistics.
At University Lyon 1
2015-2016: oral mock exams, second year of undergraduate. Université Lyon 1.
Supervision
2014: Research internship of Loïc Tudela (ENSAI), Master Degree, July-September. Co-supervision
with L. Goudenège (CNRS, Centrale Paris).
Suject: Central Limit Theorem for Adaptive Multilevel Splitting.
Lessons in Engineer Schools:
{ 2013 − 2014, 2014 − 2015: Introduction to stochastic processes, Esiea, 4th year, 18h.
As a teaching assistant
September 2010- June 2013: ENS Cachan-Bretagne, 64 hours a year.
In the first year of the "Magistère" (third year of undergraduate):
{ Practicals of Numerical Linear Algebra (scilab): 2010 − 2011, 2011 − 2012. With B. Boutin.
Associated with lessons of R. Texier-Picard.
{ Practicals of Differential Equations (scilab): 2012 − 2013. With B.Boutin. Associated with lessons
of P. Chartier.
{ Tutorial classes of Probability: 2010 − 2011, 2011 − 2012. Associated with lessons of M. Gradinaru.
{ Practicals of Probability (scilab): 2010 − 2011, 2011 − 2012. Associated with lessons of M. Gradinaru.
{ Supervisor for a project (2 students): 2011 − 2012. Subject: random walks on Z d .
Interventions for the preparation of "Agrégation":
{ Oral mock exams (Analysis and Probability, Mathematics for computer science; modelling: probability and statistics, computer science).
{ Correction of a written mock exam and associated lessons: 2012 − 2013.
Oral mock exams in classes préparatoires aux grandes écoles, for the preparation
of competitive exams for French engineer schools:
2009-2010: mathématiques spéciales (2nd year), Lycée Chateaubriand, Rennes.
2008-2009: mathématiques supérieures et spéciales (1st and 2nd year), Lycée Aux Lazaristes, Lyon.
2007-2008: mathématiques spéciales (2nd year), Lycée Aux Lazaristes, Lyon.
Research activities
Short projects
03–2016 Participation to a project BOUM, SMAI, With: Oriane Blondel, Clément
Érignoux, Cyril Labbé, Éric Luçon, Christophe Poquet, Julien Reygner, Marielle
Simon.
Subject: Fluctuations de systèmes de particules en interaction.
07/08–2013 Participation to CEMRACS (Summer Center in Mathematics for Advanced Research in Scientific Comuting), Marseille.
Collaboration with M. Gazeau, L. Goudenège, D. Iampietro, M. Rousset, on the simulation of
rare events for SPDEs.
01/03–2013 Visit at University of Warwick, Mobility grant from Region Bretagne.
Project with Martin Hairer and Andrew Stuart, on the weak approximation of SPDEs
Participations to conferences, with oral communication
08/10–2017 ICTS Workshop on Large deviation Theory in Statistical Physics, Bangalore
(Inde).
07–2017 Stochastic Processes and their Applications Conference, Moscou (Russie).
12–2016 Workshop Numerics for SPDEs and its applications, Linz (Autriche).
Special semester on Computational Methods in Science and Engineering
07–2016 Symposium Extreme events in Earth and planetary sciences, Warwick (UK).
06–2016 Conference on SPDEs and Applications X, Trento (Italie).
03–2016 RESIM (Rare event simulation) workshop, Eindhoven (Pays-Bas).
07–2015 10th IMACS Seminar on Monte Carlo Methods, Linz (Austria).
Session "SPDEs"
08–2014 Journées MAS (Modélisation aléatoire et statistique), Toulouse.
Session "Numerical Probability"
04–2014 MCQMC Conference(Monte Carlo and quasi-Monte Carlo Methods), Leuven (Belgium).
Session "Mathematical aspects of Monte Carlo methods for molecular dynamics"
01–2014 Conference SPDEs and Applications IX, Trento (Italie).
09–2013 NASPDE Conference (Numerical Analysis of Stochastic PDEs), Rennes,
Lebesgue Center.
08–2012 Journées MAS (Modélisation aléatoire et statistique), Clermont-Ferrand.
Session "Stochastic PDEs"
07–2011 Foundations
(Hungary).
of
Computational
Mathematics
Conference,
Budapest
06–2011 Journées de probabilités, Nancy.
05–2011 Smai Conference (Applied and Intustrial Mathematics Society), Guidel.
09–2010 Summer School "Simulation of hybrid dynamical systems and applications
to molecular dynamics", Paris, Institut Henri Poincaré.
07–2010 Communication during Saint-Flour Summer school..
Talks in Seminars and Workgroups
11–2016
10–2016
10–2016
09–2016
06–2016
Applied Analysis Seminar, Marseille.
Applied Mathematics Seminar, Nantes.
Working seminar Applications of Mathematics, ENS Rennes.
Numerical Analysis Seminar, Genève (Suisse).
Meeting on AMS and rare events, Paris, Ecole des Ponts.
11-2015
11-2015
10-2015
01-2015
Seminar, Loeben (Austria).
Probability ant Statistics Seminar, Lyon.
Numerical analysis Seminar, Lyon.
Probability Seminar, Neuchâtel (Switzerland).
11-2014
10–2014
10–2014
06–2014
02–2014
01–2014
Probability ant Statistics Seminar, Bordeaux.
Numerical Analysis Seminar, Genève (Switzerland).
Workgroup on PDE and Probability, Marseille, Université de Provence.
Probability Seminar, Rennes.
Seminar on Numerical, mechanical and mathematical modeling, Caen.
Seminar of the Inria "TOSCA" Team,, Nice, Inria Nice Sophia-Antipolis.
08–2013 Communication during CEMRACS, Marseille.
01–2013 Stochastic Analysis Seminar, Warwick (UK).
04–2012 Workgroup on Numerical Analysis, Orsay.
01–2012 ANR Day "Systèmes stochastiques en mathématiques et physique mathématique", Cergy-Pontoise.
05–2011 Probability Seminar, Rennes.
Participations without talk
07–2016 International Conference on Monte Carlo techniques, Paris.
02-2016 COSMOS Conference (Computational Statistics and Molecular Simulation), Paris.
09-2015 NASPDE Conference (Numerical Analysis of Stochastic PDEs), Nice
Sophia-Antipolis).
10-2014 Workshop "Stochastic and multiscale inverse problems", Paris, Ecole des
Ponts.
09–2014 NASPDE Conference (Numerical Analysis of Stochastic PDEs), Lausanne
(Switzerland).
06–2013 Summer school "KPZ equations and rough paths",, Rennes, Lebesgue Center.
04–2013 Inaugural Conference of Lebesgue Center, Rennes, Lebesgue Center.
09–2012 Workshop "SPDEs Follow-up meeting", Cambridge (UK), Isaac Newton
Institute.
06–2012 Journées de probabilités, Rennes.
01–2012 Workshop "Recent developments in Stochastic Analysis". Stochastic Analysis and its Applications Program, Lausanne (Switzerland), EPFL.
Referee
Advances in Difference Equations, Annals of Applied Probabilty, Applied Numerical Mathematics,
Communications in Statistics - Theory and Methods, IMA Journal of Numerical Analysis, Journal
of Differential Equations, Journal of Scientific Computing, Nonlinearity, Potential Analysis, Siam
Journal on Numerical Analysis
AMS reviews