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Marmotte et Castor !
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Short Biography


I am an Austrian mathematician and mathematical physicist whose main interest lies in the applications of harmonic analysis (in the broad sense) to quantum mechanics. I work at the University of Vienna

 I was born in Berlin but I grew up mainly in France. I am married with Charlyne since 1970 (we met in Nice in 1969) and we have four children; Serge, Corinne, Samantha, and Sven. My mother was from Helsinki in Finland and my father from Vienna. My parents met in France while studying French at the University; they got married after the war in the lovely city of Saint Tropez on the French Riviera. I grew up in Berlin, and at the age of 6 I moved to France, first to Nice and then to Paris. I got my "Baccalauréat" at the Lycée de Saint-Cloud near Paris. I thereafter moved back to Nice to study mathematics at the newly founded University. I got my Ph.D. at the University of Nice in 1978 under the supervision of Jacques Chazarain. In 1992 I obtained a "Habilitation à Diriger des Recherches en Mathématiques Pures" at the University of Paris 6 under the mentorship of Jean Leray, at that time Professor at the Collège de France. Leray was to become a close friend. See the genealogy project

Broadly speaking my research interests lie in Analysis, Geometry, and their applications to mathematical physics. A more precise and technical definition of me as a mathematician would be "works in symplectic harmonic analysis". Currently, my main interest lies in the applications of these topics to quantum mechanics.

Some of my hobbies: epistemological and ontological questions in quantum mechanics. Dining out and enjoying good company.

You can  contact me using my private email address:

Wikipedia biographical article

Bourbaki and me

The University of Nice was in the 1970s a stronghold of the Bourbaki group. My teachers were J. Dieudonné, L. Boutet de Monvel, A. Douady during my undergraduate studies; they succeeded in convincing me of the superiority of Poincaré on Hilbert... For opinions (which I share) about the Bourbaki "school"  here are a few interesting texts:

And, talking about Arnol'd: here is a text by  Leonid Polterovich " Remembering Vladimir Arnold"  arnold4.pdf

Scientific Profile

I strongly believe in the absence of barriers between "pure" and "applied" mathematics and in the encouragement of links between them. Interdisciplinarity has led to the greatest achievements in Science: Isaac Newton and Henri Poincaré are only two examples, among the brightest. We are fortunately witnessing a return of these ideals which had been somewhat forgotten during part of the past century. Here is one of my favorite quotations (it is due to Bertrand Russell in "The Study of Mathematics"):

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."

My main areas of interest and research are:

  • Harmonic analysis in symplectic spaces: Feichtinger's theory of modulation spaces, partial differential equations (including pseudo-differential calculus and microlocal analysis), applications to time-frequency analysis;
  • Symplectic geometry and topology (symplectic and Lagrangian path intersection indices: Maslov index, Conley-Zehnder index, etc...) and their relations with the theory of the metaplectic group;
  • Mathematical physics, especially quantum mechanics and its semi-classical formulations; "dequantization".
  • The interplay between time-freequency analysis (also called Gabor analysis) and phase-space quantum mechanics;
  • Foundational questions in quantum physics.


About symplectic geometry:

 Symplectic geometry has deep roots in mathematics and physics going back to Huygens' study of optics and the Hamilton-Jacobi formulation of mechanics. It has grown to touch virtually all branches of mathematics, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.

About mathematical physics:

"Mathematical physics spans every subfield of physics. Its aim is to apply the most powerful mathematical techniques available to the formulation and solution of physical problems. Mathematics is the language of theoretical physics and, like other languages, it provides a means of organizing thought and expressing ideas in a precise consistent manner. Physicists who are articulate in the language of mathematics have made the greatest contributions to the modern formulations of physics. The list is long and includes such names as Newton, Maxwell, Einstein, Schrödinger, Heisenberg, Weyl, Wigner and Dirac." (David Rowe, author of Chapter 18 in the IUPAP Year 2000 book: Here is a good description of mathematical physics (from Stack Exchange):

"Mathematical physics is a branch of mathematics. It explores relations between abstract concepts, proves certain results contingent upon certain hypotheses, and establishes an interlinked set of tools that can be used to study anything that happens to match the relations and hypotheses on hand. This branch is motivated by the theories used in physics. It may seek to prove certain truths that were simply assumed by physicists, or carefully delineate the conditions under which certain theories hold, or even provide generally applicable tools to physicists, who can, in turn, apply them to nature. Mathematical physicists are mathematicians who are intrigued/inspired by physics."

I enjoy writing and assembling mathematical material into a coherent package, so a lot of my effort has gone into writing books concurrently with research papers; it is fun to write books and you learn lots from doing it! See my Research page for details.

During the summer session 2003 I gave a special "FIRST FACULTY IN RESIDENCE" course on some of these topics at the University of Colorado at Boulder.


Academic Degrees

Doctorat de 3. Cycle (PhD):  Université de Nice, June 1978. Title of thesis: "Hypoellipticité partielle à la frontière des opérateurs pseudo-différentiels de transmission".

My supervisor was Jacques Chazarain, at that time a leading specialist in partial differential equations (he now works in artificial intelligence). The subject of my thesis was a microlocal study of the transmission property for pseudo-differential opeartors, with applications to partial hypoellipticity. I later extended this work in a series of articles; in particular I succeded in defining a notion of "boundary wavefront set", which behaved well under the action of pseudo-differential operators with the transmission property

Habilitation à Diriger des Recherches: Université Pierre et Marie Curie (Paris 6), 1992.
My mentor was Jean Leray (Collège de France), one of the great mathematicians of last century. Did you know that Leray invented sheaf theory and spectral sequences while being a prisoner of war in Austria during WWII? See Haynes Miller's text in Gaz. Math. No. 84 (2000), 17-34 "Leray in Oflag XVIIA

The "Habilitation" is the highest French academic degree. It is necessary for applying for a professorship in France; it replaces the former Doctorat d'État. I was Leray's last student; his mentorship was actually unofficial since he was at that time over 85 years old: the French motto was (and still is!) place aux jeunes! My Habilitation thesis consisted of a series of papers, on partial differential equations and on a topological and combinatorial study of the Maslov index, with applications to the theory of the metaplectic group.


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