Michel Talagrand

Michel Talagrand
Born	(1952-02-15) 15 February 1952
Nationality	French
Alma mater	Paris VI University
Known for	Talagrand's concentration inequality
Awards	Loève Prize (1995) Fermat Prize (1997) Shaw Prize (2019)
Scientific career
Fields	Mathematics
Institutions	CNRS
Doctoral advisor	Gustave Choquet

Michel Pierre Talagrand (born 15 February 1952) is a French mathematician. Docteur ès sciences since 1977, he has been, since 1985, Directeur de Recherches at CNRS and a member of the Functional Analysis Team of the Institut de Mathématique of Paris. Talagrand was elected as correspondent of the Académie des sciences of Paris on March 1997, and then as a full member on November 2004, in the Mathematics section.

Talagrand studies mainly functional analysis and probability theory and their applications.

Scientific activity

Talagrand has been interested in probability with minimal structure. He has obtained a complete characterization of bounded Gaussian processes in very general settings, and also new methods to bound stochastic processes. He discovered new aspects of the isoperimetric and concentration of measure phenomena for product spaces, by obtaining inequalities which make use of new kind of distances between a point and a subset of a product space. These inequalities show in great generality that a random quantity which depends on many independent variables, without depending too much on one of them, does have only small fluctuations. These inequalities helped to solve most classical problems in probability theory on Banach spaces, and have also transformed the abstract theory of stochastic processes. These inequalities have been successfully used in many applications involving stochastic quantities, like for instance in statistical mechanics (disordered systems), theoretical computer science, random matrices, and statistics (empirical processes). The recent works of Talagrand concern spin glasses mean fields models. His objective is to give a mathematical foundation to numerous remarkable works of physicists in this domain. Talagrand showed for instance recently the validity of the Parisi formula.

Awards

• Peccot-Vimont Prize of the French Collège de France (1980)
• Servant Prize of the French Académie des sciences (1985)
• Invited Speaker to the International Congress of Mathematicians (Kyoto 1990)
• Loève Prize in Probability (1995)
• Fermat Prize for mathematical research (1997)
• Corresponding member of the French Academy of Sciences (1997)
• Plenary Speaker to the International Congress of Mathematicians (Berlin 1998)
• Member of the French Academy of Sciences (2004)
• Chevalier of the Order of the Legion of Honor (2011)
• Shaw Prize in mathematics (2019)

Selected publications

• Talagrand, Michel (1979). "Espaces de Banach Faiblement κ-Analytiques". The Annals of Mathematics. 110 (3). JSTOR: 407–438. doi:10.2307/1971232. ISSN 0003-486X. JSTOR 1971232.
• Talagrand, Michel (1987). "Regularity of gaussian processes". Acta Mathematica. 159. International Press of Boston: 99–149. doi:10.1007/bf02392556. ISSN 0001-5962. S2CID 121218656.
• Rhee, Wansoo T.; Talagrand, Michel (1988). "Some distributions that allow perfect packing". Journal of the ACM. 35 (3). Association for Computing Machinery (ACM): 564–578. doi:10.1145/44483.44487. ISSN 0004-5411. S2CID 14177183.
• Talagrand, Michel (1990). "The Three-Space Problem for L 1". Journal of the American Mathematical Society. 3 (1). JSTOR: 9–29. doi:10.2307/1990983. ISSN 0894-0347. JSTOR 1990983.
• Talagrand, Michel (1992). "Type, infratype and the Elton-Pajor theorem". Inventiones Mathematicae. 107 (1). Springer Science and Business Media LLC: 41–59. Bibcode:1992InMat.107...41T. doi:10.1007/bf01231880. ISSN 0020-9910. S2CID 121425985.
• Talagrand, M. (1 January 1994). "Sharper Bounds for Gaussian and Empirical Processes". The Annals of Probability. 22 (1). Institute of Mathematical Statistics. doi:10.1214/aop/1176988847. ISSN 0091-1798.
• Talagrand, M. (1994). "Matching theorems and empirical discrepancy computations using majorizing measures". Journal of the American Mathematical Society. 7 (2). American Mathematical Society (AMS): 455–537. doi:10.1090/s0894-0347-1994-1227476-x. ISSN 0894-0347.
• Talagrand, Michel (1995). "Concentration of measure and isoperimetric inequalities in product spaces". Publications mathématiques de l'IHÉS. 81 (1). Springer Science and Business Media LLC: 73–205. arXiv:math/9406212. doi:10.1007/bf02699376. ISSN 0073-8301. S2CID 119668709.
• Talagrand, Michel (1995). "Sections of smooth convex bodies via majorizing measures". Acta Mathematica. 175 (2). International Press of Boston: 273–300. doi:10.1007/bf02393307. ISSN 0001-5962. S2CID 120408547.
• Talagrand, Michel (1 January 2006). "The Parisi formula". Annals of Mathematics. 163 (1): 221–263. doi:10.4007/annals.2006.163.221. ISSN 0003-486X.
• Talagrand, Michel (2006). "Maharam's problem". Comptes Rendus Mathematique. 342 (7). Elsevier BV: 501–503. arXiv:math/0601689. Bibcode:2006math......1689T. doi:10.1016/j.crma.2006.01.026. ISSN 1631-073X.

Reference Books

• M. Talagrand, Pettis Integral and Measure Theory, Memoirs of the AMS no. 307 (1984)
• M. Ledoux & M. Talagrand, Probability in Banach Spaces, Springer-Verlag (1991)
• M. Talagrand, Spin glasses, a Challenge for Mathematicians, Springer-Verlag (2003)
• M. Talagrand, The Generic Chaining, Springer-Verlag (2005)
• M. Talagrand, Mean Field Models for Spin Glasses. Volume I: Basic Examples, Springer-Verlag (2011)
• M. Talagrand, Mean Field Models for Spin Glasses. Volume II: Advanced Replica-Symmetry and Low Temperature, Springer-Verlag (2011)
• M. Talagrand, Upper and Lower Bounds for Stochastic Processes, Springer-Verlag (2014)

See also

• Talagrand's concentration inequality

External links

• The personal web page of Michel Talagrand
• Michel Talagrand at the Mathematics Genealogy Project