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Nicolas Juillet
IRMA
7 rue René-Descartes
67 084 Strasbourg Cedex
Tel : (00 33) 3 68 85 01 43
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Bienvenue sur ma page web! Welcome
to my web page !
Since September 2009, I am a "Maître de conférence" of the "Université de Strasbourg" at the "Institut de Recherche
Mathématique Avancée" (IRMA).
In December 2008, I've been defending my doctoral thesis in
mathematics at the Institut Fourier (Université Grenoble 1) and
the Institut
für angewandte Mathematik (Universität Bonn). My advisors
were Hervé
Pajot and Karl-Theodor Sturm. My thesis is called "Optimal
transport and geometric analysis in Heisenberg groups" (other link). Composition of the jury: H.
Pajot, K.-T. Sturm, L. Ambrosio (referee), D. Bakry (referee), G.
Besson (president Grenoble), R. Flume, H. Koch (president
Bonn)).
Work
- Here is my paper about hypoelliptic diffusion seen from the
point of view of optimal transport (still for Heisenberg
groups). The last version is of December 2011(.pdf)
- My small paper on the structure of the Euclidean Wasserstein
space, entitled "On displacement interpolation of measures
involved in Brenier's Theorem" has appeared in Proc.
of AMS, 139(10) (2011). (.pdf)
- "A counterexample to the geometric traveling salesman problem
in the Heisenberg group" has appeared in the
Revista Matematica Ibroamericana, 26(3) (2010). It
presents a rectifiable curve that does not satisfy a criterion
that was supposed to be true for all rectifiable curves of the
Heisenberg group. (see .pdf)
- In a paper with Alessio
Figalli we answer an open question of L. Ambrosio and S.
Rigot (JFA 2004) about the optimal transport in the Heisenberg
group : during an optimal transport starting from an absolutely
continuous measure, the interpolated intermediate measures are
absolutely continuous too. This paper is published in Journal
of Functional Analysis, 255 (2008), no 1. see (.pdf)
- There are certain new synthetic Ricci curvature bounds whose
definition is adapted to the metric measure spaces. If you want
to know what happens when you consider them for the Heisenberg
group, you can have a look at Int.
Math. Res. Not. IMRN 2009, no. 13, 2347-2373. or (.pdf)
NB: this paper is called
"Geometric inequalities and generalized Ricci bounds in the
Heisenberg group". It is sometimes still referred under its
preliminary name: "Ricci curvature bounds and geometric inequalities
in the Heisenberg group".
Pictures and
animations
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I have written some animations with Geogebra: In this animation,
you can examinate the shape of the triangles of the
Heisenberg group. The second animation
shows how the third coordinate of an horizontal
curve evolves with respect to the swept algebraic area.
During my thesis defense I have used this animation.
On the left, the .gif file shows the
construction of a so-called "cochleoid". I found it on Mathcurve (in french).
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Talks, surveys and slides
A list of talks with sometimes a survey in proceedings. I've added some slides presentations: this is sometimes the companion of some chalk and blackboard talks and thus not "self-contained".
- München, "Perspectives in Optimal transport", December 2011 (.pdf)
- Bonn, Intern. Conf. on Stoch. Anal. and App. (invited
session), September 2011
- Wien, Seminar Finanzmathematik, May 2011
- Dijon, séminaire "Statistiques, probabilités et applications",
May 2011
- Dijon, Conference in Memory of Paul Malliavin, October 2010
- Nice, "New trends in subRiemannian geometry", April 2010
- Maynooth (Ireland), colloquium, March 2010 (.pdf)
- IHES, "Analysis and geometry on groups", September 2009
- Grenoble, conférence interdisciplinaire "Repère et espace",
April 2009. Text for the proceedings, in french (.pdf).
- Marseille, séminaire d'analyse appliquée, March 2009
- Strasbourg, séminaire "GT3", January 2009. I've never used these slides! In french (.pdf)
- Nice, séminaire "Géométrie et analyse", January 2009
- Orsay, séminaire d'analyse harmonique, March 2009
- Kyoto, contributed talk in the conference "Probabilistic
approach to Geometry", August 2008. This survey is published in
the conference proceedings of the ASPM
57 . (.pdf)
- Luxembourg, mathematics seminar, June 2008
- CIRM (French mathematical center in Marseille), workshop
"Espaces métriques mesurés, courbure de Ricci minorée et
transport optimal", March 2008
- Nantes, séminaire de géométrie, January 2008
- Bologna, seminario di analisi matematica, November 2007
- Lausanne, séminaire de géométrie et théorie ergodique,
September 2007
- Levico Terme (close to Trento), conference "Analysis and
Geometry in metric measure spaces", June 2007
- Orsay (Paris sud), séminaire d'analyse harmonique, Mai 2007
- Toulouse, groupe de travail "optimal transport", January 2007
- Grenoble, séminaire de théorie spectrale et géométrie, October
2006. The related survey was published in the"Actes du Séminaire de Théorie Spectrale et
Géometrie"of the Institut Fourier. (.ps)
Last updated December 9th 2011.