Besson, Gérard

Annales de l’institut Fourier (AIF)

ANNALESDEL’INSTITUTFOURIERANNALESDEL’INSTITUT FOURIERGérard BESSONPierre and Sylvestre: some recollectionsTome 60, no 7 (2010), p. 2303-2305.<http://aif.cedram.org/item?id=AIF_2010__60_7_2303_0>© Association des Annales de l’institut Fourier, 2010, tous droitsréservés.L’accès aux articles de la revue « Annales de l’institut Fourier »(http://aif.cedram.org/), implique l’accord avec les conditionsgénérales d’utilisation (http://aif.cedram.org/legal/). Toute re-production en tout ou partie cet article sous quelque forme que cesoit pour tout usage autre que l’utilisation à fin strictement per-sonnelle du copiste est constitutive d’une infraction pénale. Toutecopie ou impression de ce fichier doit contenir la présente mentionde copyright.cedramArticle mis en ligne dans le cadre duCentre de diffusion des revues académiques de mathématiqueshttp://www.cedram.org/Ann. Inst. Fourier, Grenoble60, 7 (2010) 2303-2305PIERRE AND SYLVESTRE: SOME RECOLLECTIONSby Gérard BESSONMy first encounters with Pierre Bérard and Sylvestre Gallot were atthe Geometry seminar in Paris VII. The seminar was called le SéminaireArthur Besse and Marcel Berger was in charge of things. At that timeI was looking for an advisor so I turned up, hoping to find one, for thelatest talk. I sat there in the lecture room and, needless to say, did notunderstand a single word. However, I do remember clearly that a theoremon harmonic manifolds due to Alamigeon was cited. Just then, a youngfellow at the back, who was taking notes enthusiastically, asked a question.Marcel Berger replied ”Well, this is a question for you !”. The young guywas Sylvestre who had not as yet defended his ” thèse d’état ” but wasvery close to doing so. Pierre, on the other hand, was not at the talk thatday. He was visiting IMPA as part of his military service and so I first methim a couple of years later, again at the seminar Besse, when he returnedto France. I had started to work on the spectrum of the Laplacian underthe supervision of Marcel Berger, and after a lecture that I gave he kindlycame up to me and we discussed my project. In those days Pierre had abeard, the one we see on the picture.In 1978, Sylvestre defended his thesis. It was a tradition to give a secondlecture after the defense, called ” deuxième thèse ”, which was more like amasters’ thesis. Sylvestre’s thesis was about inequalities for the eigenvaluesof the Laplacian and lower bound on the Ricci curvature; some strikingresults were described which put Sylvestre’s works in light. His ” second ”thesis was about Nash’s embedding theorem and all I can remember is aslide full of Sobolev spaces and maps between them.I really started to discuss mathematics with Pierre after his beautiful pa-per on the spectrum of certain domains in the Euclidean space related to2304 Gérard BESSONcrystallographic groups. To my knowledge it was the first systematic com-putation of the spectrum of the Laplacian for both Dirichlet and Neumannboundary conditions for a wide class of Euclidean domains. One strikingexample is one half of an equilateral triangle for which the spectrum wasnot know at all before!It was not so easy to get a position in France at that time; I rememberone year with no assistant position and just around ten professor positions.Nevertheless, Sylvestre got hired in Chambéry in 1980 and Pierre got ajob there too a year later. They started to work on a wonderful programon isoperimetric inequalities on Riemannian manifolds satisfying a lowerbound on the Ricci curvature. Yves Colin de Verdière was in Grenobleand naturally there was a lot of activity on spectral theory of Riemannianmanifold concentrated in the two towns which are only 60km apart. Andso I moved to Grenoble in 1981. We had a joint seminar which wouldmeet every week alternately in Chambéry or Grenoble. In 1983, we beganpublishing the proceedings of our seminar in which various works of Pierreand Sylvestre may be found. Their research culminated with the result onthe estimate on the heat kernel which is an analytical translation of someisoperimetric inequalities à la Gromov. In 1984, I had just finished somework and was wondering what I should do next. They kindly invited meto join them in their project and what followed was an amazingly excitingtime.In 1986, Pierre moved to Grenoble. Sylvestre got jobs at the École Poly-technique and at the École Normale Supérieure de Lyon before finally mov-ing to Grenoble in 1998. Roughly at the same time, in 1987, Sylvestre, GillesCourtois and myself started working together on the entropy of symmet-ric spaces of negative curvature. Pierre began studying isospectrality ofRiemannian manifolds, became one of the few renowned specialist in theworld before turning to spectral problems in the theory of minimal sur-faces theory. During this time, we all shared the same passion for Italy anddeveloped fruitful exchanges with our colleagues there.I omitted some fundamental aspects of Pierre and Sylvestre activities.Pierre has been involved in the development of mathematics at the highestlevels, International Mathematical Union, French ministry of research, the"IST infrastructure cellule Math-Doc", University Joseph Fourier as Vice-President in charge of the Research, etc.. Sylvestre has devoted himself toa large number of graduate students, who have almost invariably turnedout to be very successful.ANNALES DE L’INSTITUT FOURIERPIERRE AND SYLVESTRE: SOME RECOLLECTIONS 2305This short historical account describes an exceptional and passionatejourney through Mathematics and Riemannian Geometry in particular.The influence of both Pierre and Sylvestre’s works is testified by the qualityof the participant at the workshop. I wish to thank all of them as well asthose who were eager to come but could not for their contribution to thesuccess of the workshop. But above all it is the story of our friendship; noworkshop nor proceedings could ever show how precious this friendship hasbeen.Gérard BESSONInstitut Fourier UMR 5582CNRS-UJFBP 7438402 Saint Martin d’Hères Cedex (France)gbesson@ujf-grenoble.frTOME 60 (2010), FASCICULE 7

Pierre and Sylvestre: some recollections

Numérisation de Documents Anciens Mathématiques

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Pierre and Sylvestre: some recollections

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Annales de l’institut Fourier (AIF)

Numérisation de Documents Anciens Mathématiques