Michel Talagrand
Born (1952-02-15) 15 February 1952
NationalityFrench
Alma materParis VI University
Known forTalagrand's concentration inequality
AwardsLoève Prize (1995)
Fermat Prize (1997)
Shaw Prize (2019)
Scientific career
FieldsMathematics
InstitutionsCNRS
Doctoral advisorGustave 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

Selected publications

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. S2CID 123995577.
  • Talagrand, Michel (22 February 2022). What Is a Quantum Field Theory?. Cambridge University Press. doi:10.1017/9781108225144. ISBN 978-1-108-22514-4. S2CID 247078928.

See also

References

  1. ↑ 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.
  2. ↑ 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.
  3. ↑ Talagrand, Michel (1990). "Some isoperimetric inequalities and their applications". Proc. Int. Congress of Mathematicians, Kyoto. Vol. 2. pp. 1011–1024. CiteSeerX 10.1.1.465.1304.
  4. ↑ 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.
  5. ↑ "News". www.impan.pl. Retrieved 2022-09-22.
  6. ↑ 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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