Michel Talagrand

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French mathematician (born 1952)

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 *ysis Team of the Ins*ut de Mathématique of Paris. 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.

Talagrand studies mainly functional *ysis and probability theory and their applications.

1 Scientific activity
2 Awards
3 Selected publications
4 Reference Books
5 See also
6 References
7 External links

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 methodsto 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 quan*y 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 cl*ical 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 quan*ies, like for instance in statistical mechanics (disordered systems), theoretical computer science, random matrices, and statistics (empirical processes).The recent works of Talagrand concern spin gl*es 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-*ytiques". The Annals of Mathematics. JSTOR. 110 (3): 407–438. doi:10.2307/1971232. ISSN:0003-486X. JSTOR:1971232.
Talagrand, Michel (1987). "Regularity of gaussian processes". Acta Mathematica. International Press of Boston. 159: 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. *ociation for Computing Machinery (ACM). 35 (3): 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. JSTOR. 3 (1): 9–29. doi:10.2307/1990983. ISSN:0894-0347. JSTOR:1990983.
Talagrand, Michel (1992). "Type, infratype and the Elton-Pajor theorem". Inventiones Mathematicae. Springer Science and Business Media LLC. 107 (1): 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. Ins*ute of Mathematical Statistics. 22 (1). 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. American Mathematical Society (AMS). 7 (2): 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. Springer Science and Business Media LLC. 81 (1): 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. International Press of Boston. 175 (2): 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. Elsevier BV. 342 (7): 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 gl*es:: 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 gl*es. Berlin Heidelberg: Springer. ISBN:978-3-642-15202-3. OCLC:695389115.
Talagrand, Michel (2011). Mean field models for spin gl*es. Berlin: Springer. ISBN:978-3-642-22253-5. OCLC:755538109.
Talagrand, Michel (2014). Upper and lower bounds for stochastic processes:: modern methods and cl*ical problems. Heidelberg: Springer. ISBN:978-3-642-54075-2. OCLC:871255685.

References

External links

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