University of Paris-Est Créteil, Laboratory of Analysis and Applied Mathematics, France
Biography:
RESEARCH FIELDS
I am interested in fractal geometry, which leads me to work on various mathematical fields :
— Study of the local regularity of functions, measures, and distributions (for example, using
functional analysis and wavelet methods).
— Multifractal analysis of deterministic and random functions and measures.
— Regularity of trajectories of stochastic processes : Lévy processes, Markov processes, solutions of SDEs.
— Genericity and prevalence of regularity properties for functions and measures.
— Geometric measure theory, Dynamical systems, and Ergodic theory.
— Metric theory of Diophantine approximation. Ubiquity theorems, large intersections.
— Multiscale methods for the analysis of signals, images, and urban data. Multifractal analysis of multivariate signals.
All my articles are available on HAL, ArXiv, or
on my website.
CURRICULUM VITAE
025- : Director of LAMA (Laboratory of Analysis and Applied Mathematics).
Mathematics department, Universitté Paris-Est Créteil
2022 : Promoted to "Professeur de classe exceptionnelle" (Full Professor,
Exceptional Class).
2016 - 2018 : Visiting Professor, University of Luxembourg.
2016 - 2020 : President of the French Mathematical Society.
Sept. 2013 - : Full Professor
Université Paris-Est Créteil.
03 Nov. 2008 : Habilitation to Supervise Research.
”Multifractal analysis and Diophantine approximation”.
2005-2013 : Associate Professor, Université Paris-Est Créteil.
2003 - 2005 : Post-Doctoral Researcher at the SISYPHE team, INRIA, France.
2000 - 2003 : PhD, École Polytechnique (defended on November 5, 2003) :
“Local regularity analysis, some applications to multifractal analysis”.
Oct. 1999 - Jun. 2000 : Master’s degree in numerical analysis, Sorbonne Université
Apr. 1999 - Nov. 1999 : Consultant at ”AT&T Labs”, New Jersey, USA, in the TCP
traffic analysis team, under the supervision of W. Willinger.
1998 - 2000 : Télécom Paris.
Apr. 1998 - Jul. 1998 : Research internship under the supervision of Ingrid Daubechies,
Princeton University, USA.
Award from École Polytechnique for the report “Wavelet methods for the numerical resolution of elliptic equations”.
1995 - 1998 : École Polytechnique, Palaiseau.
PUBLICATIONS
I collaborated with around 30 colleagues, who themselves worked in many countries :
France, of course, M. Ben Abid (Tunisia), Z. Buczolich (Hungary), L. Daw (Saudi Arabia), A.
Gilbert (USA), E. Jarvenpaa, M. Myllyoja (Finland), I. Nourdin, G. Peccati (Luxembourg),
B. Solomyak, Y. Peres (Israel), J. Schmeling (Sweden), A. Ubis (Spain), L. Liao, B. Wang
(China).
• JOURNALS :
[J54] Sparse sampling and dilation operations on a Gibbs weighted tree, and multifractal
formalism, with J. Barral.
Asian J. Math. , 27(4) 493-52 2023.
[J53] Multifractal analysis of sums of random pulses, with G. Saes.
Math. Proc. Cambridge Phil. Soc., 175 (3) 569 - 593 2023.
[J52] Potential theory for the macroscopic Hausdorff dimension, and a projection theorem,
with L. Daw.
Adv. Maths, vol. 417 2023.
[J51] The Frisch-Parisi conjecture II : Besov spaces in multifractal environment, and a full
solution,, with J. Barral.
J. Maths Pures et Appliquées, 175, 281-329 2023.
[J50] The Frisch-Parisi conjecture I : Prescribed multifractal behavior, and a partial solution,
with J. Barral.
J. Maths Pures et Appliquées, 175, 76-108 2023.
[J49] Measures, annuli and dimensions, with Z. Buczolich.
Math. Zeitschrift, 303, 303 :79 2023.
[J48] Multifractal formalisms for multivariate analysis, with P. Abry, S. Jaffard, R. Leonarduzzi, H. Wendt.
Proc. Royal Acad. Science A, 2229 (475) 25 September 2019, 2020.
[J47] Sojourn time dimensions of fractional Brownian motion, with I.Nourdin et G. Peccati.
Bernoulli, 26 no. 3, 1619–1634 2020.
[J46] Random sparse sampling in a Gibbs weighted tree, with J. Barral.
Journal de l’Institut Mathématique de Jussieu, 19(1) 65-116 2020.
[J45] On sojourn of Brownian motion inside moving boundaries, with X. Yang.
Stochastic Processes and its Applications, 129 no. 3, 978–994 2019.
[J44] Multivariate multifractal analysis, with P.Abry, S. Jaffard, R. Leonarduzzi, H. Wendt.
Applied and Computational Harmonic Analysis, 46 no. 3, 653–663 2019.
[J43] Multifractal properties of typical convex functions, with Z. Buczolich.
Monatsh. Math., 187 no. 1, 59–78 2018.
[J42] Ultrasonic characterization and multiscale analysis for the evaluation of dental implant
stability :A sensitivity study, with I. Scala, VH Nguyen, R. Vayron, G. Haiat, S. Jaffard, S.
Naili.
Biomedical Signal Processing and Control, Volume 42, 37-44 April 2018.
[J41] Inhomogeneous Dvoretzky coverings of tological Markov shifts.
Math. Proc. Cambridge Math. Soc., 165(2) 341-357 2018.
[J40] Multifractal analysis for the occupation measure of stable-like processes, with X. Yang.
Elec. J. of Probability, vol 22, paper no 47, 36 pages 2017.
[J39] Local L2-regularity of Riemann’s Fourier series, with A. Ubis.
Ann. Inst. Fourier, 67(5) 2237-2264 2017.
[J38] Multifractal analysis in Heisenberg and Carnot groups, with F. Vigneron.
Journal de l’Institut Mathématique de Jussieu, 16(1) 1-38 2017.
[J37] Fixed points for the multifractal spectrum application, with D. Maman.
Constructive approximation, 43(3) 337-356 2016.
[J36] Quantitative recurrence properties in conformal iterated function system, with B. Wang.
Advances in Mathematics, 280 (6) 472–505 2015.
[J35] Hardy-Littlewood series and even continued fractions, with T. Rivoal.
Journal d’Analyse Mathématique, 125(1) 175–225 2015.
[J34] Homogeneously multifractal measures with disjoint spectra and mono-Hölder monotone
functions, with Z. Buczolich.
Real Analysis Exchange, 40(2) 277–290 2015.
[J33] Measures and functions with prescribed multifractal spectrum, with Z.Buczolich.
Journal of Fractal Geometry, 1 (3) 2014.
[J32] Hausdorff dimensions of sets generated by multiplication by 2 and 3, with Y. Peres, B.
Solomyak, J. Schmeling.
Israel Journal of Mathematics, 199 687-710 2014.
[J31] Quelques résultats d’analyse multifractale en analyse.
Séminaire Laurent Schwarz - EDP et applications, exposé XVI, 21p. 2014.
[J30] Local behavior of traces of Besov functions : Prevalent results, with J.-M. Aubry, D.
Maman.
Journal of Functional Analysis, 264(3) 631-660 2013.
[J29] Diophantine approximation by obits of expanding Markov maps, with L. Liao.
Erg. Th. Dyn. Syst., 33(2) 585-608 2013.
[J28] Multiscale Heart Rate Variability via Large Deviations Estimates, with P. Loiseau, C.
Médigue, P. Gonçalves, N. Attia, F. Cottin, J. Barral, D. Chemla, M. Sorine.
Physica A, 391, 5658–5671 2012.
[J27] Hölder spectrum of functions monotone in several variables, with Z. Buczolich.
J. Math. Analysis and Appl., 382(1), 110-126 2011.
[J26] Singularity spectrum of generic α-Holder regular functions after time subordination, with
Z. Buczolich.
J. Fourier Analysis and Appl., 17(3), 457-485 2011.
[J25] A localized Jarnik-Besicovich theorem, with J. Barral.
Advances in Mathematics, 226(4) 3191-3215 2011.
[J24] Typical measures on [0; 1]d satisfy a multifractal formalism, with Z. Buczolich.
Nonlinearity, Vol. 23(11) 2010.
[J23] A pure jump Markov process with a random singularity spectrum, with J. Barral, N.
Fournier, S. Jaffard.
Ann. Prob., 38 (5) 1924–1946 2010.
[J22] Hölder regularity of µ-similar functions, with M. Ben Abid.
Constr. Approx., 31(1) 69—93 2010.
[J21] The singularity spectrum of the inverse of the cookie-cutter, with J. Barral.
Ergod. Th. Dyn. Syst., 29 (4) 1075–1095 2009.
[J20] On multifractality and time subordination for continuous functions.
Adv. Math., 220(3) 936-963 2009.
[J19] Ubiquity and large intersection property under digit frequency constraints, with J. Barral.
Math. Proc. Cambridge Phil. Soc., 145(3) 527-548 2008.
[J18] The singularity spectrum of the Fish’s boundary, with J. Brémont.
Ergod. Th. Dyn. Syst., 28(1) 49–66 2008.
[J17] The multifractal nature of heterogeneous sums of Dirac masses, with J. Barral.
Math. Proc. Cambridge Phil. Soc., 144(3) 707-727 2008.
[J16] On multifractal time subordination (Sur le changement de temps multifractal).
Notes aux CRAS Série I, 346(1-2), 11-16 2008.
[J15] Information parameters and large deviations spectrum of discontinuous measures, with
J. Barral.
Real Anal. Ex., 32(2), 429-454 2007.
[J14] Threshold and Hausdorff spectrum of discontinuous measures, with J. Barral.
Real Anal. Ex., 32(2), 455-472 2007.
[J13] The singularity spectrum of Lévy processes in multifractal time, with J. Barral.
Adv. Math., 14 (1), 437-468 2007.
[J12] Heterogeneous ubiquitous systems in Rd and Hausdorff dimensions, with J. Barral.
Bull. Brazilian Math. Soc., 38(3), 467-515 2007.
[J11] Renewal of singularity sets of independent random cascades, with J. Barral.
Adv. Appl. Prob., 39(1), 162-188 2007.
[J10] Detecting and creating oscillations using multifractal methods.
Math. Nach., 279(11), 1195-1211 2006.
[J9] A class of multifractal semi-stable processes including Lévy subordinators and Mandelbrot
multiplicative cascades, with J. Barral.
Notes aux CRAS Série I, 341(9), 579-582 2005.
[J8] Inside singularity sets of random Gibbs measures, with J. Barral.
J. Stat. Phys., 120(5-6), 1101-1124 2005.
[J7] Combining multifractal additive and multiplicative chaos, with J. Barral.
Comm. Math. Phys., 257 (2), 473–497 2005.
[J6] Sums of Dirac masses and conditioned ubiquity, with J. Barral.
Notes aux CRAS Série I, 339 (11), 787–792 2005.
[J5] Multifractal wavelet series built using multifractal measures, with J. Barral.
Notes aux CRAS Série I, 341, 353-356 2005.
[J4] From multifractal measures to multifractal wavelet series, with J. Barral.
J. Fourier Anal. Appl., 11(5), 589–614 2005.
[J3] Function series with multifractal variations, with J. Barral.
Math. Nach., 274–275, 3–18 2004.
[J2] A time domain characterization of 2-microlocal spaces, with J. Lévy Vehel..
J. Fourier Anal. Appl., 9 (5) 473–495 2003.
[J1] The local Hölder function of a continuous function, with J. Lévy Vehel.
Appl. Comput. Harm. Anal., 13 (3), 263–276 2002.
CHAPERS IN BOOK, CONFERENCE PROCEEDINGS :
[C1] The local oscillations of Yves Meyer.
To be published in Yves Meyer - Selecta, SMF 16 pages. 2025
[C2] A survey on prescription of multifractal behaviors.
Published in the book Fractal geometry and stochastics 6, 20 pages, Birkhauser 2020.
[C3] A multivariate multifractal analysis of lacunary wavelet series, with P. Abry, S.Jaffard,
R. Leonarduzzi et H. Wendt.
In the conference CAMSAP, 2019.
[C4] Multifractals and Wavelets.
Paru dans New trends in harmonic analysis, 48 pages, Springer 2016.
[C5] Local multifractal analysis, with J. Barral, A. Durand, S. Jaffard.
Paru dans Applications of Fractals and Dynamical Systems in Science and Economics, Contempory Mathematics, D. Carfi, M. Lapidus, E. Pearse, M. v. Frankenhuijsen eds,
2014.
[C6] On measures resisting multifractal analysis, with J. Schmeling.
Paru dans Nonlinear Dynamics : New Directions, Theoretical Aspects, (in honor of
V. Afraimovich), Mathematical Methods and Modeling, Springer 2014.
[C7] The 2-microlocal formalism, with J. Lévy Vehel.
Proceedings of Symposia in Pure Mathematics, “Fractal Geometry and Applications :
A Jubilee of Benoît Mandelbrot”, Providence, RI, 67 pages 2004.
[C8] Pointwise Hölder Exponent Estimation, with A. Gilbert.
IP Traffic Measurement, Modeling and Management, Monterey, USA, Sept.18-20
2000.
POSTERS IN CONFERENCES :
[Po1] Assessing cross-dependencies using bivariate multifractal analysis, with P.Abry, S. Jaffard, R. Leonarduzzi, S. Roux, H. Wendt.
IEEE Intern. Conf. on Acoustics, Speech and Signal Processing, 2018.
[Po2] Evaluation of dental implant stability using ultrasonic characterization and multifractal
analysis, with I. Scala, G. Rosi, V.-H. Nguyen, S. Naili, R. Vayron, G. Haiat, S. Jaffard.
Congrès français de mécanique, 2017.
[Po3] Numerical simulation and multifractal signal processing used in ultrasonic characterization of bone-implant interface in case of dental implants, with G. Rosi, I. Scala, V.-H. Nguyen,
S. Naili, R. Vayron, G. Haiat, S. Jaffard.
Computer Methods in Biomechanics and Bio-Engineering, Tel Aviv 2016.
BOOKS :
[B1] A. Bonami, S. Jaffard, S. Seuret, Editors of Yves Meyer - Selecta - volume 1.
Collection "Documents mathématiques" SMF, 2025.
[B2] A. Bonami, S. Jaffard, S. Seuret, Editors of Yves Meyer - Selecta - volume 2.
Collection "Documents mathématiques" SMF, 2026.
[B3] A. Bonami, S. Jaffard, S. Seuret, Editors of Yves Meyer - Selecta - volume 3.
Collection "Documents mathématiques" SMF, 2026.
[B4] J. Barral, A.Batakis, S. Seuret, Editors of Recent Developments in Fractals and Related
Fields III.
Collection "New trends in Mathematics" Birkhauser, 2025.
[B5] Comité éditorial SMF, Editors of Gazette des 150 ans de la SMF.
Gazette spéciale de la SMF, 2022.
[B6] J. Barral, S. Seuret, Editors of Recent Developments in Fractals and Related Fields II.
Collection "New trends in Mathematics" Birkhauser, 2017.
[B7] J. Barral, S. Seuret, Editors of Recent Developments in Fractals and Related Fields.
Collection "Applied and Numerical Harmonic Analysis" Birkhauser, 2010.
[B8] J. Barral, S. Seuret, Editors of Further Developments in Fractals and Related Fields.
Collection "New trends in Mathematics" Birkhauser, 2013.
[B9] S. Jaffard, S. Seuret, Editors of la Gazette dédiée à Benoit Mandelbrot.
Volume spécial de la Gazette des mathématiciens Soc. Math. de France, 2013.
PREPRINTS SUBMITTED :
[P1] On the multivariate multifractal formalism : examples and counter-examples.
Preprint, 2024.
[P2] Multifractal analysis of the parametrized von Koch functions, with Z. Buczolich, Y. Demichel.
Preprint, 2025.
[P3] On the multifractal properties of the von Koch functions with small parameters, with Z.
Buczolich, Y. Demichel.
Preprint, 2025.
[P4] Hitting probabilites, and the Ekström-Persson conjecture, with E. Jarvenpaa, M. Myllyojal.
Preprint, 2025.
Conferences and invitations (last 10 years):
I have been invited to around fifty conferences and sixty seminars. Here is the list for the
last 10 years.
2025 : - Séminaire analyse, Bordeaux
- Conf. on Analysis, Probability, and Math. Physics on Fractals , Cornell Univ.
- One-world fractals, on-line seminar
- Fractional calculus seminar, on-line seminar
- 2èmes Journées de l’axe Multifractal du RT Anais, Vannes
- Diophantine approximation and related fields, York University
- Int. Conf. of Image Proc., Wavelet and Appl. on Real World Problems, Istanbul
2024 : - Diophantine Approximation, Fractal Geometry and Related Topics, Marne-lavallée
- Séminaire Bézout, Université Gustave Eiffel
- Time-scale and time-frequency analysis, Bruxelles
- Workshop on the Geometry of Deterministic and Random Fractals, Budapest
- Séminaire de la FRUMAM, Marseille
- Séminaire d’analyse, Univ. Aut. Madrid
- Fractal Geometry and Stochastics 7, Chemnitz, Allemagne
2023 : - Workshop Analyse harmonique, Bordeaux
- Dynamics and Fractals, Bedlewo
- Continued fractions : multifractal and dynamical aspects, CIRM
- Harmonic and multifractal analyses : From Mathematics to Quantitative Neurosciences, Montréal - mini-cours de 4h
- Fractal geometry and Related topics, Hong-Kong
- Journées annuelles du GDR AHFP
- Journée d’équipe, UPEC.
2022 : - Fractional kinetics, hydrodynamic limits and fractals, Cambridge Univ.
- Geometry of Deterministic and Random Fractals, Budapest
- Probability seminar, Université du Luxembourg
- Laboratory seminar, Université Gustave Eiffel
- Séminaire, Brunel University
2021 : - New frontiers in dimension theory of dynamical systems, Ins. Mittag-Leffler.
- Séminaire de systèmes dynamiques, IMPAN (Pologne).
2020 : - Séminaire cristollien d’analyse multifractale, Créteil.
- Journée du GDR d’analyse harmonique et probabilités.
- Finnish Mathematical days (rencontre bi-annuelle des mathématiciens finlandais
exposé d’ouverture), 2 janvier 2020.
2019 : - Séminaire cristollien d’analyse multifractale, Créteil.
- Conférence du GDR analyse multifractale, Belgique.
- "Dynamical systems, statistical properties, fractal geometry thermodynamical formalism, and applications", conférence finale de la chaire Jean Morlet CIRM.
- "Les probabilités de demain", juin 2019.
2018 : - Séminaire de théorie des nombres, York University.
- Séminaire, Chinese University of Hong-Kong.
- "Fractal geometry and Stochastics 6" (keynote speaker) Allemagne.
- Séminaire de probabilités (2 exposés), Université du Luxembourg.
2017 : - Séminaire au semestre "Fractal Geometry and Dynamics", Mittag-Leffler Institute.
- "Workshop on Ergodic Theory & Symbolic Dynamics", Queen Mary Univ., London.
- Colloque GDR Multifractales.
- Séminaire de probabilités, Université du Luxembourg.
2016 : - "Workshop on Probabilistic Aspects of Multiple Ergodic Averages", CIRM, Marseille, Décembre 2016.
- "Analysis and probability". Conférence to honor J.-P. Kahane, IHP.
- Analysis seminar, Oulu University (Finlande).
- Probability seminar, Michigan State University (USA)
Editorial activities:
- Member of the editorial board of the Gazette des Mathématiciens 2014-2016.
- Between 2016 and 2020, I was director of the publishing house of the Société Mathématique de France. The SMF is an independent publishing house (without recurring support
from any institution) publishing approximately 5,000 original pages of mathematics (a total
of around 20,000 volumes/year), and manages their distribution entirely via its electronic and
paper subscriptions (distributed to several hundred subscribers worldwide).
I developed an ambitious policy focused on digital technology and sought ways to make
our journals and collections more easily accessible. For example, all volumes of Astérisque
have been digitized and made available online : such a project, requested by the community,
is delicate and requires significant preparation : recovering paper volumes in good condition,
sending them for digitization, checking the quality of the digitization, creating PDF files, and
coordinating their online publication. The CNRS Mathdoc service managed most of these
steps, but the SMF was very involved, initiating and driving the process throughout. Similarly,
since November 2018, all members have had access to all Bourbaki presentations (which did
not even exist on our old site—we did a huge amount of work digitizing and recovering files
for this). The SMF must be very careful in managing this activity, particularly in the current
very delicate context of scientific publishing (open access, "free access," APC (no APC for
the SMF, of course), etc.).
I have also taken steps to diversify the themes covered by SMF journals, which could
sometimes be perceived as too specialized.
PhD jurys:
In addition to supervising my doctoral students, I have been :
Referre for 10 PhD theses :
- S. Ghobber (2011, Univ. Orléans, dir : F. Jaming)
- H. Ben Braiek (2012, Université Paris-Diderot, dir : G. Bourdaud)
- M. Wu (2013, Univ. Amiens, dir : A.-H. Fan)
- I. Petryckiewicz (2015, Univ. Grenoble, dir. T. Rivoal)
- C. Pastor (2018, Univ. Autonoma de Madrid, dir. F. Chamizo)
- M. Rosenblatt (2019, Univ. Buenos Aeres, dir. U. Molter)
- A. Molla (2022, Univ. Liège, dir. S. Nicolay)
- J. Llorente (2024, Univ. Aut. Madrid, dir. G. Fernandez)
- Megala M (2024, Indian Institute of Technology Tirupati, dir. S. Prasad)
- T. Lamby (2025, Univ. Liège, dir. S. Nicolay)
Jury member for 11 PhD theses :
- J. Xiong (2011, Univ. Paris-Sud, dir. J. Barral)
- N. Attia (2012, Univ. Paris 13, dir. M. Mensi)
- L. Phun (2014, Univ. Orléans, dir. M. Zinsmeister)
- J Z.-H. Yuan (2015, Paris 13, dir. J. Barral)
- W. He (2017, Univ. Paris-Sud , dir. E. Breuillard)
- L. Zheng (2019, South China University of Technology, dir. : B. Li)
- K. Song (2020, Wuhan University, dir : M. Wu)
- G. Brunet (2022, Sorbonne Paris Nord, dir. J. Barral)
- J. Feng (2024, Wuhan Univ., dir. L. Liao)
- W. Nasr Ben Amor (2024, UPEC, dir. S. Jaffard)
- Q. Zhang (2025, UPEC, dir. S. Jaffard, L. Liao)
Member of 1 habilitation jury :
- L. Liao (Univ. Paris-Est, 2017).
Organization of symposiums and conferences
I will focus on the last 10 years :
• June 2024 and 2025 : Co-organizer of the "Multifractal Analysis and Self-Similarity"
conference of the CNRS ANAIS Thematic Network.
• June 2023 : Co-organizer of the CIRM meeting "Multifractal analysis and self-similarity."
• September 2022 : Co-organizer of the conference Fractals and Related Fields IV,
which has been postponed from 2020 to 2022. As in previous editions, we expect the entire
international mathematical community involved in fractal geometry to attend.
• September 2021 : Member of the scientific committee and co-organizer of the GDR
Multifractales colloquium.
• June 2020 : Organizer, with J. Barral, of the "One World Fractal Seminar Fractals," a virtual conference with about twenty presentations, which replaced the "Fractals and
Related Fields VI" conference that did not take place for reasons we can imagine.
• Sept. 2018 : Member of the organizing committee of the GDR Multifractales conference.
• Sept. 2017 : Member of the scientific committee of the GDR Multifractales conference.
• June 2016 : Chair of the scientific committee of the 1st SMF Congress.
• Sept. 2015 and Sept. 2011 : Organizer, with J. Barral, of Fractals and Related Fields
II and III.
This conference brings together the international mathematical community around fractal
geometry (with more than 130 researchers and more than 60 presentations).
• Since 2005 : Co-organizer of the Cristolien Seminar on Multifractal Analysis
(SCAM) at the University of Paris-Est Créteil, with Stéphane Jaffard.
The aim of this seminar is to bring together the French multifractal scientific community
every six weeks for three presentations. This seminar is intended to be multidisciplinary and
generally consists of two presentations on mathematics and one more applied presentation.
Invitations to foreign universities:
Over the past 10 years, I have collaborated with many foreign researchers, inviting them
or visiting them on several occasions, including :
• 2024 : invitation to Eötvös University (Zoltan BUCZOLICH).
• I regularly visit Luxembourg as part of a collaboration with I. Nourdin, professor at the
University of Luxembourg.
• 2019 : one-week invitation to Hong Kong (De-Jun FENG).
• One-week invitation to York University, 2018 (Sanju VELANI).
• 2016-2018 : visiting professor, University of Luxembourg (Giovanni PECCATI, Jean-Marc
SCHLENKER).
• One-month invitation to the "Fractal geometry and dynamics" semester at the Mittag
Leffler Institute, Fall 2017.
• One-week invitation to Oulu University, 2016 (Esa JARVENPAA).
• One-week guest at Michigan State University, 2016 (Yimin XIAO)
• Mini-course at the CIMPA school "New Trends in Applied Harmonic Analysis," Mar del
Plata, Argentina, 2013.
• 2013 : one-week invitation to Wuhan University (Jun WU).
Dissemination, outreach:
As head of the SMF, I have often been asked to speak to the media about mathematics
education, its place, its importance, and also its obvious problems. Two topics in particular
are regularly raised by journalists : on the one hand, the apparent contradiction between the
mediocre results of middle and high school students in international tests and the excellence
of research, and on the other hand, the limited place reserved for our discipline in the new
high school organization. These questions are understandable.
I have therefore campaigned extensively in interviews, conferences, and seminars to emphasize the importance of mathematics in education, science in general, economics, and society.
This has resulted in several articles, for example :
- Le Monde (2018) : "Access to knowledge must be free and without borders" - opinion
piece against the increase in university tuition fees for foreign students.
- Interview ("grand format") on Europe 1 in March 2019 on the tenuous place of
mathematics in the new structure of high schools.
- Le Monde (2018) : Opinion piece on the renovation project for the Palais de la découverte.
- Special page in "Le Point" Special edition on the "Singapore method."
- Le Monde (2017) : "Science education is in serious crisis," 03/22/2017, co-written with
the presidents of SMAI, SIF, and SFP.
- In 2017, participation in a program on RFI "Why are people afraid of math ?"
Thesis supervision:
I have supervised/am currently supervising a total of 10 doctoral students :
• 2024 - : Danny MALLITASIG (joint supervision with A. Batakis, University of Orleans -
50%).
As part of a thesis funded by COFUND MathPhDinFrance, D. Mallitasig will construct
functions with prescribed bivariate multifractal spectra and study the prescribed multifractal
behavior of harmonic measures. Such questions involve harmonic analysis, wavelet techniques,
and measure theory (calculation of box and Hausdorff dimensions, etc.).
• 2024 - : Carmel ABOUA (co-supervised with F. Adiceam, UPEC - 50%).
Carmel ABOUA will focus on various versions of Riemann’s non-differentiable function,
which is currently very popular (see, for example, the excellent work of Banica-Vega). These
questions involve harmonic analysis combined with Diophantine approximation.
• 2022 - : Quentin RIBLE (co-supervised with S. Jaffard, UPEC - 50%).
Quentin RIBLE is interested in inhomogeneous Besov spaces and the prevalent properties
of the traces of functions belonging to these sets.
• 2019 - 2022 : Lara DAW (joint supervision with I. Nourdin, Univ. of Luxembourg - 50%).
Following my two-year stay in Luxembourg (made possible by my year of delegation to the
CNRS), I developed a research project with Ivan Nourdin on the study of the dimensional
properties of stochastic process trajectories. This thesis follows on from the article [J47] coauthored with I. Nourdin and G. Peccati, which deals with the dimensional description of
the residence time of fractional Brownian motion. The aim of the thesis is to extend these
results to broader classes of processes and to study the notion of macroscopic dimension. This
requires advances in the understanding of local times of stochastic processes and new methods
for calculating dimension, and in the medium term opens the door to the dimensional study
of the same properties for trajectories of EDPS solutions. Lara has published four articles
and has chosen to work in a private company (insurance) in Luxembourg.
• 2018 - 2023 : Edouard DAVIAUD (co-supervised with J. Barral, Paris 13 - 50%).
The thesis focused on the study of torus or fractal coverings by non-homogeneously distributed sets, and on the study of the multifractal properties of discontinuous self-affine measures.
In both cases, Hausdorff dimension calculations will need to be performed, and to complete
them, it will be necessary to develop Beresnevich-Velani-style "mass transfer principles" in
inhomogeneous settings. Edouard already has six research articles accepted in highly prestigious journals, with remarkable results. After a postdoc in Hong Kong, he is now a postdoc
at the University of Liège.
• 2016 - 2021 : Guillaume SAES (co-supervised with S. Jaffard, UPEC - 50%).
The objective was to study the convergence and local regularity properties of certain models
of random pulse sums introduced by Benoit Mandelbrot in a fairly general framework, as well
as simulations of such random processes, with the aim of modeling properties observed in
real signals. Guillaume has published three articles and several posters at renowned signal
processing conferences. Guillaume is currently an AI and data specialist at an IT consulting
firm, where he continues to apply the wavelet techniques he learned in his thesis.
• 2013 - 2017 : Liping XU (co-supervised with N. Fournier, UPMC - 50%).
The goal was to study the regularity properties of typical particle trajectories in a Boltzmann gas. L. Xu obtained a remarkable result, proving the multifractality of the typical
trajectory of a particle in a Boltzmann gas. She also worked on the existence and uniqueness
of solutions to the Boltzmann equation. Since 2018, Liping has been a lecturer at Beihang
University (China).
• 2013 - 2016 : Xiaochuan YANG (co-supervised with S. Jaffard, UPEC - 50%).
The objective was to study the dimensional properties of stochastic jump diffusion processes : multifractal analysis, image dimensions, graph dimension. His work has resulted in
several publications that are in the process of being accepted for publication. After several
successful post-docs and around fifteen high-level publications, Xiaochuan obtained a position
as Lecturer at Brunel University (London).
• 2008 - 2013 : Delphine MAMAN, 100%.
The theme was the study of the generic properties of traces of functions belonging to Besov
sets. The main result is that typical functions have better Besov regularity than that given by
classical trace theorems. This led to two research articles. Delphine is a high school teacher
in Toulouse (she did her thesis while working as a high school teacher and chose to remain in
that position).
• 2007 - 2009 : Moez BEN ABID (co-supervised with Fathi BEN NASR (Faculty of Sciences
of Monastir - 50%) defended in 2009.
The aim of the thesis, which I took on along the way, was to study a model of lacunar
series of functions combining wavelets and Gibbs measures. This thesis led to two publications
in international peer-reviewed journals. Moez is an assistant professor at the University of
Sousse, Tunisia.