Biography:Michel Talagrand
Michel Talagrand | |
|---|---|
 | |
| Born | 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 in March 1997, and then as a full member in 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).
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.[1]
In particular, the monograph offers an exposition of Talagrand's proof [2] of 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)[3]
- 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)[4]
- Member of the French Academy of Sciences (2004)
- Chevalier of the Order of the Legion of Honor (2011)
- Shaw Prize in mathematics (2019)
- Stefan Banach Medal of the Polish Academy of Sciences (2022)[5]
Selected publications
- Talagrand, Michel (1979). "Espaces de Banach Faiblement κ-Analytiques". The Annals of Mathematics (JSTOR) 110 (3): 407–438. doi:10.2307/1971232. ISSN 0003-486X. http://www.numdam.org/item/SAF_1977-1978____A10_0/.
- Talagrand, Michel (1987). "Regularity of gaussian processes". Acta Mathematica (International Press of Boston) 159: 99–149. doi:10.1007/bf02392556. ISSN 0001-5962.
- Rhee, Wansoo T.; Talagrand, Michel (1988). "Some distributions that allow perfect packing". Journal of the ACM (Association for Computing Machinery (ACM)) 35 (3): 564–578. doi:10.1145/44483.44487. ISSN 0004-5411.
- 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.
- Talagrand, Michel (1992). "Type, infratype and the Elton-Pajor theorem". Inventiones Mathematicae (Springer Science and Business Media LLC) 107 (1): 41–59. doi:10.1007/bf01231880. ISSN 0020-9910. Bibcode: 1992InMat.107...41T.
- Talagrand, M. (1 January 1994). "Sharper Bounds for Gaussian and Empirical Processes". The Annals of Probability (Institute 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. doi:10.1007/bf02699376. ISSN 0073-8301.
- 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.
- 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. doi:10.1016/j.crma.2006.01.026. ISSN 1631-073X. Bibcode: 2006math......1689T.
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.[6]
- Talagrand, Michel (21 December 2021). Upper and Lower Bounds for Stochastic Processes: Decomposition Theorems. Springer Cham. doi:10.1007/978-3-030-82595-9. ISBN 978-3-030-82594-2.
- Talagrand, Michel (22 February 2022). What Is a Quantum Field Theory?. Cambridge University Press. doi:10.1017/9781108225144. ISBN 978-1-108-22514-4.
See also
References
- ↑ Talagrand, Michel (2010-11-12). Mean Field Models for Spin Glasses: Volume I: Basic Examples. Berlin Heidelberg: Springer. p. xii. ISBN 978-3-642-15201-6.
- ↑ Talagrand, Michel (2006-01-01). "The Parisi formula". Annals of Mathematics 163 (1): 221–263. doi:10.4007/annals.2006.163.221. ISSN 0003-486X.
- ↑ Talagrand, Michel (1990). "Some isoperimetric inequalities and their applications". Proc. Int. Congress of Mathematicians, Kyoto. 2. pp. 1011–1024.
- ↑ Talagrand, Michel (1998). "Huge random structures and mean field models for spin glasses". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I. pp. 507–536. https://www.elibm.org/ft/10011735000.
- ↑ "News". https://www.impan.pl/en/events/news/2022/wreczenie-medalu-banacha.
- ↑ Auffinger, Antonio (2015). "Book Review: Upper and lower bounds for stochastic processes". Bulletin of the American Mathematical Society 53 (1): 173–177. doi:10.1090/bull/1511. ISSN 0273-0979.
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