Frank Merle (mathematician)

For the American filmmaker, see Frank Merle.

Frank Merle
Born	(1962-11-22) 22 November 1962 Marseilles, France
Citizenship	French
Alma mater	École normale supérieure University of Paris IV
Awards	Bôcher Prize (2005) Prix Ampère (2018) Bôcher Memorial Prize (2023) Clay Research Award (2023)
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

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. 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. 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

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 which he earned again in 2023.

Selected publications

• 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: Merle, Frank; Raphael, Pierre (2004). "On universality of blow-up profile for L² critical nonlinear Schroedinger equation". Inventiones Mathematicae. 156 (3): 565–672. Bibcode:2004InMat.156..565M. doi:10.1007/s00222-003-0346-z. S2CID 122944822.

Awards and honors

• 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
• 2000 : Prix Charles-Louis de Saulse de Freycinet de l'Académie des Sciences de Paris
• 2005 : Médaille d'argent du CNRS
• 2005 : Bôcher Memorial Prize
• 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
• 2023 : Bôcher Memorial Prize, jointly to Merle, Raphaël, Rodnianski, and Szeftel
• 2023 : Clay Research Award