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Michel Talagrand
Born	(1952-02-15) 15 February 1952 (age 72) Béziers
Nationality	French
Alma mater	Paris VI University
Known for	Talagrand's concentration inequality
Awards	Loève Prize (1995) Fermat Prize (1997) Shaw Prize (2019) Abel Prize (2024)
Scientific career
Fields	Mathematics
Institutions	CNRS
Doctoral advisor	Gustave Choquet

Michel Pierre Talagrand (born 15 February 1952) is a French mathematician. Doctor of Science 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 also a faculty member at The Ohio State University for more than fifteen years. Talagrand was elected as correspondent of the Académie des sciences of Paris in March 1997, and then as a full member in November 2004, in the Mathematics section. In 2024, Talagrand received the Abel Prize. ^[1]

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

Career

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 kinds 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).

Talagrand commented in the introduction to his two volume monograph on mean field models of spin glasses:

More generally theoretical physicists have discovered wonderful new areas of mathematics, which they have explored by their methods. This book is an attempt to correct this anomaly by exploring these areas using mathematical methods, and an attempt to bring these marvelous questions to the attention of the mathematical community. ^[2]

In particular, the monograph offers an exposition of Talagrand's proof ^[3] of the validity of the Parisi formula.

Personal life

He is married to Wansoo Rhee, a now retired professor of management science at Ohio State University, whom he met on his first ever trip to the USA. They have two sons. ^[4]

Awards

• Peccot Lectures of the French Collège de France (1980) ^[5]
• 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) ^[6]
• Loève Prize in Probability (1995) ^[7]
• Fermat Prize for mathematical research (1997) ^[8]
• Corresponding member of the French Academy of Sciences (1997)
• Plenary Speaker to the International Congress of Mathematicians (Berlin 1998) ^[9]
• Member of the French Academy of Sciences ^{[10] [11]} (2004)
• Chevalier of the Order of the Legion of Honor (2011) ^[12]
• Shaw Prize in mathematics (2019) ^[13]
• Stefan Banach Medal of the Polish Academy of Sciences (2022) ^[14]
• The Abel Prize (2024) ^[1]

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

• Talagrand, Michel (1984). Pettis integral and measure theory. Providence, R.I., USA: American Mathematical Society. ISBN  978-0-8218-2307-1. OCLC  851088223.
• Ledoux, Michel (1991). Probability in Banach Spaces : Isoperimetry and Processes. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN  978-3-642-20212-4. OCLC  851818740.
• Talagrand, Michel (2003). Spin glasses : a challenge for mathematicians : cavity and mean field models. Berlin New York: Springer. ISBN  978-3-540-00356-4. OCLC  52509569.
• Talagrand, Michel (2005). The generic chaining : upper and lower bounds of stochastic processes. Berlin: Springer. ISBN  978-3-540-27499-5. OCLC  262680717.
• Talagrand, Michel (2011). Mean field models for spin glasses. Berlin Heidelberg: Springer. ISBN  978-3-642-15202-3. OCLC  695389115.
• Talagrand, Michel (2011). Mean field models for spin glasses. Berlin: Springer. ISBN  978-3-642-22253-5. OCLC  755538109.
• Talagrand, Michel (2014). Upper and lower bounds for stochastic processes : modern methods and classical problems. Heidelberg: Springer. ISBN  978-3-642-54075-2. OCLC  871255685. ^[15]
• Talagrand, Michel (21 December 2021). Upper and Lower Bounds for Stochastic Processes: Decomposition Theorems. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. Vol. 60. Springer Cham. doi: 10.1007/978-3-030-82595-9. ISBN  978-3-030-82594-2. S2CID  123995577.
• Talagrand, Michel (22 February 2022). What Is a Quantum Field Theory?. Cambridge University Press. Bibcode: 2022wiqf.book.....T. doi: 10.1017/9781108225144. ISBN  978-1-108-22514-4. S2CID  247078928.

See also

• Talagrand's concentration inequality

References

External links

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