Fabien CaubetUniversité Paul Sabatier

Institut de Mathématiques de Toulouse118 route de Narbonne

31062 Toulouse Cedex 9, FranceT +335.61.55.61.18

B fabien.caubet@math.univ-toulouse.frÍ www.math.univ-toulouse.fr/∼fcaubet

born on the 1st of October 1986(30 years old)

in Pau (France)French citizenship

Assistant Professor in Applied MathematicsInstitut de Mathématiques de Toulouse

"Mathématiques pour l’Industrie et la Physique" team

Diplomas and studies2013– Assistant professor (maître de conférences), Université Toulouse III – Paul Sabatier

(Toulouse, France), IMT, "Mathématiques pour l’Industrie et la Physique" team.2012–2013 Associate member of the "DéFI" team, École Polytechnique (Palaiseau, France),

CMAP.2012–2013 ATER (full time) in applied mathematics, UTC (Compiègne, France), LMAC, "Inverse

Problems, Approximation and Control" team.2009–2012 PhD thesis in applied mathematics, UPPA (Pau, France), LMAP, "PDE Analysis and

Optimization" team, supervised by Marc Dambrine and Mehdi Badra.Subject: Detecting an obstacle immersed in a fluid.Thesis defended on June 29, 2012. Defence committee: M. Badra (Supervisor), C. Conca (Re-viewer), M. Dambrine (Supervisor), A. Munnier (Examinator), É. Oudet (Reviewer), J.P. Raymond(Examinator). Mention très honorable.

2007–2009 Master’s degree in mathematical research (Mathematics, Modeling and Simula-tion), UPPA (Pau, France), research option. Mention bien.Report: Sensitivity with respect to the shape of the solution of the Stokes equations

2004–2007 Licence’s degree in mathematics, UPPA (Pau, France). Mention très bien.2004 Baccalaureate of sciences, Lycée Louis Barthou (Pau, France). Mention bien.

Research (key words)• Shape optimization, shape sensitivity analysis, shape derivative, topological derivative,

numerical shape optimization.• Inverse problems, inverse obstacle problem, data completion problem.• Control, Carleman inequalities, stability inequalities.• Asymptotic analysis.• Generalized impedance boundary conditions.

Distinctions2014– PEDR, Beneficiary of the Prime d’Encadrement Doctoral et de Recherche.

Collaborations2015– Member of the research project “Nouvelles Niches d’Excellence”, “Shape opti-

mization under unilateral constraints”.2014– Member of the research project ECOS-CONICYT C13E05 (Shape and Topol-

ogy Optimization in Coupled Models), funded by CONICYT (Comisión Nacional deInvestigación Científica y Tecnológica).

2012–2016 Member of the research project Optiform, funded by l’Agence Nationale de laRecherche.

2012–2014 Collaboration with the "DéFI" research team between l’INRIA and l’École Poly-technique, on an imaging problem by magnetic resonance.

2009–2012 Member of the research project GAOS (Geometric Analysis of Optimal Shapes),funded by l’Agence Nationale de la Recherche.

Publications and preprintsPublished or accepted papers

2016 Flip procedure in geometric approximation of multiple-components shapes –Application to multiple-inclusions detection, SMAI Journal of Computational Mathe-matics, accepted, P. Bonnelie, L. Bourdin, F. Caubet and O. Ruatta (22 pages).

2016 New transmission condition accounting for diffusion anisotropy in thin layersapplied to diffusion MRI, ESAIM: Mathematical Modelling and Numerical Analysis,accepted, F. Caubet, H. Haddar, J.-R. Li and D.V. Nguyen (25 pages).

2016 Stability estimates for Navier-Stokes equations and application to inverse prob-lems, Discrete and Continuous Dynamical Systems - Series B, accepted, M. Badra, F. Caubetand J. Dardé (29 pages).

2015 On the detection of several obstacles in 2D Stokes flow: topological sensitivityand combination with shape derivatives, Inverse Problems and Imaging, 10(2):327–367,F. Caubet, C. Conca and M. Godoy (41 pages).

2013 Shape optimization methods for the Inverse Obstacle Problem with general-ized impedance boundary conditions, Inverse Problems, 29(11):115011, F. Caubet,M. Dambrine and D. Kateb (26 pages).

2013 Stability of critical shapes for the drag minimization problem in Stokes flow,Journal de Mathématiques Pures et Appliquées, 100(3):327–346, F. Caubet and M. Dambrine(20 pages).

2013 Instability of an inverse problem for the stationary Navier-Stokes equations,SIAM Journal on Control and Optimization, 51(4):2949–2975, F. Caubet (28 pages).

2013 A Kohn-Vogelius formulation to detect an obstacle immersed in a fluid, InverseProblems and Imaging, 7(1):123–157, F. Caubet, M. Dambrine, D. Kateb and C.Z. Timimoun(35 pages).

2012 Localisation of small obstacles in Stokes flow, Inverse Problems, 28(10):105007, 31,F. Caubet and M. Dambrine (31 pages).

2011 Detecting an obstacle immersed in a fluid by shape optimization methods, Math-ematical Models and Methods in Applied Sciences, 21(10):2069–2101, M. Badra, F. Caubetand M. Dambrine (33 pages).

Preprints2016 On the data completion problem and the inverse obstacle problem with partial

Cauchy data for Laplace’s equation, F. Caubet, J. Dardé and M. Godoy (33 pages).

SupervisionPhD thesis supervision

2014–2016 PhD thesis of Matías Godoy Campbell, co-supervision with C. Conca, University ofChile, El problema inverso de detección de obstáculos por métodos de optimización (Theinverse problem of obstacle detection via optimization methods).

Master 2 projects supervision2014-2017 Mini-projects of students in M2 ACSYON, Université de Limoges, Shape optimization

problem on the minimization of the compliance.

Oral contributionsOral communications with proceedings

Sept. 16, 2010 Detecting an obstacle immersed in a fluid (the Stokes case), Eleventh InternationalConference Zaragoza-Pau on Applied Mathematics and Statistics, Jaca (Spain).

Interventions in national and international conferencesMay 29, 2015 AIP 2015, Helsinki (Finland).Mar. 26, 2014 SMAI–MODE 2014, Rennes (France).Nov. 07, 2013 ANR CISIFS, IHP (Paris, France).May 27, 2013 SMAI 2013, Seignosse (France).Apr. 03, 2012 PICOF 2012, École Polytechnique (Palaiseau, France).Oct. 12, 2011 ANR GAOS, IECN (Nancy, France).Mar. 08, 2011 ANR GAOS, IHP (Paris, France).June 02, 2010 CANUM 2010, Carcans-Maubuisson (France).

Invitations to seminarsDec. 16, 2015 CPT seminar, Université Aix-Marseille (Marseille, France).Dec. 04, 2014 LMA seminar, Université d’Avignon (Avignon, France).Oct. 17, 2014 DMI seminar, Université de Limoges (Limoges, France).June 19, 2014 Workshop Mathematics Programmation (GDR RO), INPT – ENSEEIHT (Toulouse,

France).Nov. 29, 2013 IMT seminar, Université Toulouse III – Paul-Sabatier (Toulouse, France).Nov. 25, 2013 Workshop Optimization, LAAS-CNRS (Toulouse, France).Oct. 16, 2013 Workshop ONI, Université Toulouse III – Paul Sabatier (Toulouse, France).Apr. 24, 2013 IRIT seminar, INPT – ENSEEIHT (Toulouse, France).Apr. 04, 2013 IMB seminar, Université de Bourgogne (Dijon, France).Mar. 26, 2013 LM seminar, Université Blaise Pascal (Clermont-Ferrand, France).Mar. 22, 2013 GREMAQ seminar, Université Toulouse 1 – Capitole (Toulouse, France).Mar. 21, 2013 IMATH seminar, Université du Sud Toulon–Var (Toulon, France).Mar. 14, 2013 LJK seminar, Université Joseph Fourier (Grenoble, France).Mar. 12, 2013 LATP seminar, Université Aix–Marseille (Marseille, France).Jan. 07, 2013 LAMFA seminar, Université de Picardie (Amiens, France).Dec. 18, 2012 IECN seminar, Université Henri Poincaré (Nancy, France).Dec. 14, 2012 LAMA seminar, Université de Savoie (Chambéry, France).Dec. 13, 2012 IRMAR seminar, Université Rennes 1 (Rennes, France).Oct. 09, 2012 LMAC seminar, Université de Technologie de Compiègne (Compiègne, France).Apr. 28, 2011 LMAP seminar, Université de Pau, UPPA (Pau, France).

PostersJuly 06, 2011 Detecting an obstacle immersed in a fluid, OPTPDE, BCAM (Bilbao, Spain).

TeachingAt Université de Limoges

2014–2016 Practical programming for students in M2 ACSYON, shape optimization, use ofFreefem++.

At the Université Paul Sabatier – Toulouse III (UPS – IUT A)2015–2016 Lecture and exercises for the second year students, DUT GMP, functions of several

variables, differentiability, double and triple integrals.2014–2016 Lecture, exercises and practical programming for the third year students, TIAS,

differential equations, matrix calculus, numerical integration, Newton’s method, programma-tion with Excel.

2013–2016 Lecture and exercises for the first year students, DUT GMP, vectorial calculus,continuity, differentiability, bijection, polynomials, Taylor’s formula, probability, statistics.

2013–2014 Lecture and exercises for the second year students, DUT GMP, parametric equa-tions, polar curves, line integrals, diagonalization, application to solving system of equationsand to reduction of quadratic forms, series.

2013–2014 Exercises for the first year students, DUT GMP, matrix calculus, diagonalization,applications to solving systems of equations.

2013–2014 Exercises for the second year students, DUT GMP, matrix calculus, diagonalization,linear application.

At the Université de Technologie de Compiègne (UTC)2012–2013 Exercises for the first year students, "tronc commun", MT 22: functions of several

variables, vector analysis, double and triple integrals, line integrals, surface integrals, integraltheorems.

2012–2013 Exercises for the first year students, "tronc commun", MT 90/91: sets, applications,real numbers, sequences, limits, continuity, differentiability, Taylor’s formula, integrals,complex numbers, polynomials, differential equations.

At the Université de Pau (UPPA)2011–2012 Practical programming with Scilab for the 3rd year students in mathematics, nu-

merical analysis, matrix, matrix norms, conditioning, linear systems, interpolation, numericalintegration.

2011–2012 Exercises for the 2nd year students in physics, generalized integrals, series, sequencesof functions, series of functions, entire series, Fourier series.

2010–2011 Exercises for the 2nd year students in mathematics, generalized integrals, series,sequences of functions, series of functions, entire series, Fourier series.

2010–2011 Exercises for the 2nd year students in chemistry (SDM), generalized integrals, series,sequences of functions, series of functions, entire series, Fourier series.

2009–2010 Exercises for the 2nd year students in economic and social sciences (MASS),functions of several variables, entire series.

2009–2010 Lecture in general mathematics for the 3rd year students in spanish, preparation forthe entrance examination to the I.U.F.M. (Institut Universitaire de Formation des Maîtres).

2007 Preparing for the second examination session for the 1st year students in eco-nomic and social sciences (MASS), functions, real sequences.

Collective and vulgarization activitiesCollective activities

2014–2017 Co-organizer of the seminar of the MIP team of the IMT, UPS (Toulouse, France).2011–2012 Member of educational committee, trainings of the doctoral school of the exact sciences

and their applications of the UPPA (Pau, France).2011–2012 Representative of the PhD students, council of the doctoral school of the exact sciences

and their applications of the UPPA (Pau, France).2010–2011 Co-organizer and co-founder of the PhD students seminar of LMAP, UPPA (Pau,

France).

Vulgarization activitiesFeb. 22, 2012 Vulgarization talk on optimal shapes, UPPA (Pau, France), PhD students seminar of

LMAP.Nov. 18, 2010 Vulgarization talk on shape optimization, UPPA (Pau, France), PhD students seminar

of LMAP.

Scientific expertiseReferee, for the journals Acta Applicandae Mathematicae; Boundary value problems; ESAIM:Control, Optimisation and Calculus of Variations; Inverse Problems; Inverse Problems inScience & Engineering and SIAM Journal on Control and Optimization.Referee, for Mathematical Reviews.

Computing and languageComputing

Languages Python, C++, Fortran 77 Web HTML

numericalcalculussoftware

Scilab, Matlab, Maple Operatingsystems

Unix, GNU/Linux, Windows

Finiteelementssoftware

Freefem++, Mélina Officeautomation

Latex, Microsoft Office

Certificates C2I (level 1)

LanguagesFrench read, written, spoken native

English read, written, spoken professional

Spanish read, written, spoken novice