Michel Talagrand

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 on March 1997, and then as a full member on November 2004, in the Mathematics section.

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

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). The recent works of Talagrand concern spin glasses 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

Selected publications
  • Espaces de Banach faiblement K-analytiques, Annals of Mathematics 110 (1979) 407-438
  • Regularity of Gaussian processes, Acta Math. 159 (1987) 99-149
  • Some distributions that allow perfect packing, (avec W. Rhee), J. A.C.M. 35 (1988) 564-578
  • The Three Space Problem for L1, J. Amer. Math. Soc. 3 (1989) 9-30
  • Type, infratype and the Elton-Pajor theorem Invent. Math. 107 (1992 )41-59
  • Sharper bounds for Gaussian and empirical processes, Ann. Probab. 22 (1994) 28-76
  • Matching theorems and discrepancy computations using majorizing measures, J. Amer. Math. Soc. 7 (1994) 455-537
  • Concentration of measure and isoperimetric inequalities in product spaces, Publications I.H.E.S. 81 (1995) 73-205
  • Sections of smooth convex bodies via majorizing measures, Acta. Math 175 (1995) 273-306
  • The Parisi Formula, Annals of Mathematics 163 (2006) 221-263
  • Maharam's Problem, Annals of Mathematics 168 (2008) 981-1009

Reference Books
  • M. Talagrand, Pettis Integral and Measure Theory, Memoirs of the AMS no. 307 (1984)
  • M. Ledoux & M. Talagrand, Probability in Banach Spaces, Springer-Verlag (1991)
  • M. Talagrand, Spin glasses, a Challenge for Mathematicians, Springer-Verlag (2003)
  • M. Talagrand, The Generic Chaining, Springer-Verlag (2005)
  • M. Talagrand, Mean Field Models for Spin Glasses. Volume I: Basic Examples, Springer-Verlag (2011)
  • M. Talagrand, Mean Field Models for Spin Glasses. Volume II: Advanced Replica-Symmetry and Low Temperature, Springer-Verlag (2011)
  • M. Talagrand, Upper and Lower Bounds for Stochastic Processes, Springer-Verlag (2014)[3]
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gollark: I only noticed because I'm running the thing manually before installing my shiny new backup disk.

See also

References
  1. 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.
  2. 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.
  3. 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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