Frank Merle (mathematician)
Frank Merle | |
---|---|
Born | |
Citizenship | French |
Alma mater | École normale supérieure University of Paris IV |
Awards | Bôcher Prize (2005) Prix Ampere (2018) |
Scientific career | |
Fields | Partial differential equations Mathematical physics |
Institutions | University of Cergy-Pontoise Courtant Institute of Mathematical Sciences Stanford University Rutgers University University of Chicago Leiden University University of Tokyo |
Thesis | Contributions a l'etude de certaines equations aux derivees partielles non lineaires de la physique mathematique (1987) |
Frank Merle (born 22 November 1962, in Marseille) is a French mathematician, specializing in partial differential equations and mathematical physics.
Education and career[edit]
After graduation from the École normale supérieure (ENS), Merle received in 1987 his Ph.D. from the University of Paris VI under Henri Berestycki with thesis Contributions a l'etude de certaines equations aux derivees partielles non lineaires de la physique mathematique.[1][2] He became a researcher for CNRS at ENS. In 1989/90 he was an assistant professor at the Courant Institute of Mathematical Sciences of the University of New York. Since 1991 Merle has been a professor at the University of Cergy-Pontoise. From 1998 to 2003 he was a member of the Institut Universitaire de France. In the fall of 1996, the fall of 2001, and the academic year 2003–2004 he was a visiting scholar at the Institute for Advanced Study.[3] He was a visiting professor at Stanford University, Rutgers University, the University of Chicago, the Mathematical Sciences Research Institute (MSRI) at Berkeley, Leiden University, and the University of Tokyo.
Mathematical research[edit]
Merle does research on partial differential equations (PDEs) and mathematical physics, notably dispersive nonlinear PDEs such as the nonlinear Schrödinger equation and the Korteweg-de Vries equation, and the study of such PDE solutions which over time break down or diverge (blow up). Such research earned him in 2005 the Bôcher Prize.
Selected publications[edit]
- with Yvan Martel: Martel, Yvan; Merle, Frank (2002). "Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation". Annals of Mathematics. 155 (1): 235–280. arXiv:math/0405229. doi:10.2307/3062156. JSTOR 3062156. S2CID 14960075.
- with Y. Martel: "Blow up in finite time and dynamics of blow up solutions for the L2-critical generalized KdV equation". J. Amer. Math. Soc. 15: 617–664. 2002. doi:10.1090/S0894-0347-02-00392-2. MR 1896235.
- with Pierre Raphäel: "On universality of blow-up profile for L2 critical nonlinear Schroedinger equation". Inventiones Mathematicae. 156: 565–672. 2004. Bibcode:2004InMat.156..565M. doi:10.1007/s00222-003-0346-z. S2CID 122944822.
Awards and honors[edit]
- 1997 : Prix de l'Institut Poincaré en Physique théorique
- 1998 : Invited speaker at the International Congress of Mathematicians in Berlin; lecture entitled Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations[4]
- 2000 : Prix Charles-Louis de Saulse de Freycinet de l'Académie des Sciences de Paris
- 2005 : Médaille d'argent du CNRS
- 2005 : Bôcher Prize[5]
- 2014 : Plenary speaker at the International Congress of Mathematicians in Seoul; lecture entitled Asymptotics for critical nonlinear dispersive equations
- 2018 : Prix Ampère awarded by French Academy of Sciences
References[edit]
- ^ Contributions a l'etude de certaines equations aux derivees partielles non lineaires de la physique mathematique par Frank Merle, theses.fr
- ^ Frank Merle at the Mathematics Genealogy Project
- ^ Merle, Frank | Institute for Advanced Study
- ^ Merle, Frank (1998). "Blow-up phenomena for critical nonlinear Schrödinger and Sakharov equations". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. III. pp. 57–66.
- ^ "2005 Bôcher Prize" (PDF). Notices of the AMS. 52 (4): 443–444. April 2005.
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- 1962 births
- Living people
- PDE theorists
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- École Normale Supérieure alumni
- University of Paris alumni
- Institute for Advanced Study visiting scholars
- Scientists from Marseille
- Courant Institute of Mathematical Sciences faculty