Publications
 Dynamique des perturbations holomorphes des rotations
 ER.
Ph D thesis, École Polytechnique (1996). Dis  Linéarisation des perturbations holomorphes des rotations et applications
 ER.
Mém. Soc. Math. Fr., 77 (1999), pp. 1–102. Mon
Download PDF full text Permalink  Compacts connexes invariants par une application univalente
 ER.
Fund. Math., 161 (1999), pp. 241–277. Art
Download PDF full text Permalink  Spatial unfoldings of elementary bifurcations
 Pierre Coullet, ER, Nicolas Vandenberghe.
J. Stat. Phys., 101.1 (2000), pp. 521–541. Art
Download PDF full text DOI  Criteria for the stability of spatial extensions of fixed points and periodic orbits of differential equations in dimension 2
 ER.
Phys. D, 146 (2000), pp. 121–136. Art
Download PDF full text DOI  Spatially extended differential equations in a potential: On the borders of the basins of attraction related to local minima
 ER.
J. Differential Equations, 166.2 (2000), pp. 347–384. Art
Download PDF full text DOI  Selfparametric instability in spatially extended systems
 Médéric Argentina, Pierre Coullet, ER.
Phys. Rev. Lett., 86.5 (2001), pp. 807–809. Art
Download PDF full text DOI  A direct computation of the phase stability criterion for spatially homogeneous time periodic solutions close to a Hopf bifurcation
 ER.
Int. J. Bifur. Chaos, 11.8 (2001), pp. 2097–2105. Art
Download PDF full text DOI  Generic instability of spatial unfoldings of almost homoclinic periodic orbits
 ER.
Comm. Math. Phys., 216 (2001), pp. 325–356. Art
Download PDF full text DOI  Axisymmetric capillary surfaces as a dynamical system
 Christophe Riera, ER.
Nonlinearity, 15.6 (2002), pp. 1843–1879. Art
Download PDF full text DOI  Travelling waves and dispersion relation in the spatial unfolding of a periodic orbit
 ER.
C. R. Acad. Sci. Paris, Ser. I, 334.9 (2002), pp. 833–838. Art
Download PDF full text DOI  Spatial unfolding of homoclinic bifurcations
 Pierre Coullet, ER, Nicolas Vandenberghe.
Nonlinear PDE's in Condensed Matter and Reactive Flows (2002), pp. 399–412. Proc
Download PDF full text DOI  Sur quelques phénomènes d'évolution non linéaires
 ER.
Habilitation to conduct researches ("Habilitation à diriger des recherches") dissertation (2002). Dis
Download PDF full text  A variational proof of global stability for bistable travelling waves
 Thierry Gallay, ER.
Differential Integral Equations, 20.8 (2007), pp. 901–926. Art
Download PDF full text Permalink  Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure
 ER.
Ann. Inst. H. Poincaré Anal. Non Linéaire, 25.2 (2008), pp. 381–424. Art
Download PDF full text DOI  A semantic approach to life cycle assessment applied on energy environmental impact data management
 Benjamin Bertin, VasileMarian Scuturici, JeanMarie Pinon, ER.
Proceedings of the 2012 Joint EDBT/ICDT Workshops, March 26–30, 2012  Berlin, Germany, pp. 87–94. Proc
Download PDF full text DOI  Modélisation sémantique des relations de dépendance entre les processus de l'analyse en cycle de vie
 Benjamin Bertin, VasileMarian Scuturici, JeanMarie Pinon, ER.
Actes du XXXème Congrès INFORSID, Montpellier, France, 29–31 mai 2012, pp. 507–522. Proc
Download PDF full text Permalink  Semantic Modelling of Dependency Relations between Life Cycle Analysis Processes
 Benjamin Bertin, VasileMarian Scuturici, JeanMarie Pinon, ER.
ICTGLOW 2012, Vienna, Austria, September 6, 2012, pp. 109–124. Proc
Download PDF full text DOI  CarbonDB: a Semantic Life Cycle Inventory Database
 Benjamin Bertin, VasileMarian Scuturici, JeanMarie Pinon, ER.
Proceedings CIKM'12, Maui, HI, USA, October 29–November 02, 2012, pp. 2683–2685. Proc
Download PDF full text DOI  Base de données sémantique d'inventaires en cycle de vie
 Benjamin Bertin, VasileMarian Scuturici, JeanMarie Pinon, ER.
Ingénierie des Systèmes d'Information, 18.2 (2013), pp. 103–128. Art
Download PDF full text DOI  Uniqueness of the pendent drop of infinite length
 ER.
2015, 12 pp. Pre
Download PDF full text arXiv  Global relaxation of bistable solutions for gradient systems in one unbounded spatial dimension
 ER.
2016, 69 pp. Pre
Download PDF full text arXiv  Global behaviour of bistable solutions for gradient systems in one unbounded spatial dimension
 ER.
2016, 91 pp. Pre
Download PDF full text arXiv  Global behaviour of bistable solutions for hyperbolic gradient systems in one unbounded spatial dimension
 ER.
2017, 75 pp. Pre
Download PDF full text arXiv  Global behaviour of radially symmetric solutions stable at infinity for gradient systems
 ER.
2017, 52 pp. Pre
Download PDF full text arXiv  Retracting fronts for the nonlinear complex heat equation
 Guillaume Réocreux, ER.
2017, 21 pp. Pre
Download PDF full text arXiv  Competition between stable equilibria in reactiondiffusion systems: the influence of mobility on dominance
 ER.
2017, 43 pp. Pre
Download PDF full text arXiv
Teaching
Links
There are nowadays so many awesome contents about teaching mathematics available online that dozens of pages would not be
sufficient to list them. The following links are a personal selection of a few contents I like, among
those I showed at the beginning of my lessons during academic year 20132014. Many other can be found
following this link.

Everything I believe about maths, what they are, how they should and should not be teached (and much more)
lies in this monument video (two hours, in french).

The maths teacher I admire most is about half my age, is neither teacher nor mathematician, and
is a child of youtube rather than of traditional
maths education. Try not to watch the second episode after you have watched the first!

My preferred proof of Pythagora's theorem (by the same author).
Many other awesome contents on her youtube channel or website.

The next gift you should offer to your child
(or maybe one of those ?).

To reach a master's degree level in dynamical systems, you may either work hard during five years at university, or
just relax
one evening in front of this sequence of videos (many languages available).

Stereographic projection is conformal, explained by Étienne Ghys… what else ?

The video that makes me feel sad to be so ignorant about fluid mechanics.

Universal covering of SO(3) is degree two: how to feel it in your own body (a standard),
the explanation, and
how to spoil half an hour lesson on the subject.

A certain idea of 2^{1012}
(far from being original, but I don't get tired of).

A nice way to humiliate a topologist if you would like to.

Why there is nothing really simpler than a cusp, and
why Whitney's singularity theory should be part of elementary school programs.

Why you will never be able to hair you (a standard).

The picture where saddles and nodes will never look the same again.

My favorite way to teach the
frequency decomposition of a function or
GramSchmidt orthonormalization process or
eigenmodes of Laplace operator or
vibration and wave phenomena
(and so many other things) is to do nothing but press the play button…
 … and my favorite way to teach undergraduate mathematics is to give the following link
to my students and let them go.

Not only maths education is in trouble. To improve things,
should you vote for this guy ?
or vote for this guy ?
or vote for this guy ?
Academic year 20132014
Only during academic year 20132014 did I have the opportunity and found the time to teach
maths the way I think they should be taught: as an experimental science, leaning upon pictures, drawings, videos,
simulation and calculation tools, real experiments, tight connexions to mechanics, physics, chemistry,
biology, social sciences, and to the real world, video captures of lessons, students kept active and regularly
(weekly) controlled by an extensive use of clickers, focus on phenomena and vision rather than
formalism or theorems or proofs, prohibition to "learn" anything, but encouragement to observe and try to understand
the world around.
During this academic year, with undergraduate students in their second academic year (post french "baccalauréat"),
equipped with a basic knowledge of one variable real analysis and linear algebra, the following subjects were treated
(in about 70h of lessons and 85h of seminars):
 bifurcations and singularities of mappings in dimensions one, two, three (folds, cusps, caustics);
 nonlinear dynamics, bifurcations and singularities of differential equations in dimensions one, two, three;
 centrallimit theorem, brownian motion, Fick laws, heat kernel, heat equation;
 Fourier series, Dirichlet and Fejér kernels, wave equation, Fourier transform, Frauenhofer diffraction;
 symmetry groups;
 scalar products, rotation group, exponential map, polar decomposition, principal component analysis;
 mean curvature, Laplace equation, harmonic functions, capillarity;
 Gauss curvature, shell rigidity;
 Euler characteristics, GaussBonnet formula, index theorem;
 ruled surfaces, developable surfaces.
Unfortunately, lack of time prevented us from treating exterior differential, Stokes formula, Poincaré duality,
and connections to physics.
All the contents (lesson slides, tutorials, exams and corrections, video captures of lessons, links to videos and other
online contents displayed during lessons, weekly minitests using clikers, and debrifing pdfs and videos, are available
online (in french) at this address.
By the way, the video captures of my lessons might be useful as a comprehensive gallery of what should NOT be done to keep
a student's assembly quiet, especially on a friday afternoon…
I warmly thank all my students from this year, their enthusiasm pushed me forward during this awesome experience.
And I apologize to the others (those I had the other years for undergraduate courses at INSA de Lyon) for
the oldfashioned usual boring staff they endured.
Other academic years
I gave courses on the following subjects, at various graduate and undergraduate levels:
 nonlinear dynamics of differential and/or partial diffential equations or systems, bifurcations;
 probability theory, random walks, mathematical finance;
 Markov chains, game theory, elementary statistics, modelling in general;
 differential geometry;
 general undergraduate mathematics.