Michel Talagrand Explained

Michel Talagrand
Birth Date:	15 February 1952
Birth Place:	Béziers
Nationality:	French
Fields:	Mathematics
Workplaces:	CNRS
Alma Mater:	Paris VI University
Doctoral Advisor:	Gustave Choquet
Known For:	Talagrand's concentration inequality
Awards:	Loève Prize (1995) Fermat Prize (1997) Shaw Prize (2019) Abel Prize (2024)

Michel Pierre Talagrand (pronounced as /fr/; 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 mathématiques de Jussieu in 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 any one of them, has only small fluctuations. These inequalities helped to solve several 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:

In particular, the monograph offers an exposition of Talagrand's proof ^[2] of the validity of the Parisi formula.

Michel Talagrand was awarded the Abel Prize from The Norwegian Academy of Science and Letters for 2024 for his work in ‘Suprema of stochastic processes’, ‘Concentration of measures’ and ‘Spin glass’.^[3]

Personal life

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

Reference Books

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

See also

• Talagrand's concentration inequality

References

1. Web site: Michel Talagrand awarded the 2024 Abel Prize . The Abel Prize . 2024-03-20 . 2024-03-20 . https://web.archive.org/web/20240320121519/https://abelprize.no/article/2024/michel-talagrand-awarded-2024-abel-prize . live .
2. Talagrand . Michel . The Parisi formula . . 163 . 1 . 2006-01-01 . 0003-486X . 10.4007/annals.2006.163.221 . 221–263. free .
3. Web site: Michel Talagrand awarded the 2024 Abel Prize | the Abel Prize .
4. Web site: Michel Talagrand: A brief biography The Abel Prize . 2024-03-28 . abelprize.no.
5. Book: Assemblées des Professeurs. Comptes-rendus XX-XXIèmes siècles . Service archives du Collège de France . Paris.
6. Book: Talagrand, Michel. Some isoperimetric inequalities and their applications. Proc. Int. Congress of Mathematicians, Kyoto. 2. 1011–1024. 1990. 10.1.1.465.1304.
7. Web site: The Loeve Prize . 2024-03-22 . University of California, Berkeley.
8. Web site: 2023-11-21 . Lauréats du prix Fermat . 2024-03-22 . Université Paul Sabatier. Institut de Mathématiques de Toulouse . fr.
9. Book: Talagrand, Michel. Huge random structures and mean field models for spin glasses. Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I. 1998. 507–536. https://www.elibm.org/ft/10011735000. 2019-11-04. 2019-08-07. https://web.archive.org/web/20190807083037/https://elibm.org/ft/10011735000. live.
10. News: 2024-03-20 . Le Français Michel Talagrand reçoit le prix Abel, prestigieuse récompense en mathématiques . 2024-03-22 . Le Monde.fr . fr.
11. Web site: Michel Talagrand, lauréat du prix Abel 2024 . 2024-03-22 . Academie Sciences.
12. Web site: Ordre de la Légion d'honneur - Nominations, promotions et élévations du 31-12-2010 . 2024-03-22 . France Phaleristique.
13. Web site: 2019 Mathematical Sciences . 2024-03-22 . The Shaw Prize . en-US.
14. Web site: News . 2022-09-22 . www.impan.pl . 2022-09-22 . https://web.archive.org/web/20220922155626/https://www.impan.pl/en/events/news/2022/wreczenie-medalu-banacha . live .
15. Auffinger. Antonio. Antonio Auffinger. Book Review: Upper and lower bounds for stochastic processes. Bulletin of the American Mathematical Society. 53. 1. 2015. 173–177. 0273-0979. 10.1090/bull/1511. free.

External links

• The personal web page of Michel Talagrand