Michel Pierre Talagrand (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 Mathématique of 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 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 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.[2]
In particular, the monograph offers an exposition of Talagrand's proof [3] of the validity of the
Parisi formula.
Personal life
He is married to Wansoo Rhee, a now retired professor of management science at
Ohio State University, whom he met on his first ever trip to the USA. They have two sons.[4]
Talagrand, Michel (1984). Pettis integral and measure theory. Providence, R.I., USA: American Mathematical Society.
ISBN978-0-8218-2307-1.
OCLC851088223.
Ledoux, Michel (1991). Probability in Banach Spaces : Isoperimetry and Processes. Berlin, Heidelberg: Springer Berlin Heidelberg.
ISBN978-3-642-20212-4.
OCLC851818740.
Talagrand, Michel (2003). Spin glasses : a challenge for mathematicians : cavity and mean field models. Berlin New York: Springer.
ISBN978-3-540-00356-4.
OCLC52509569.
Talagrand, Michel (2005). The generic chaining : upper and lower bounds of stochastic processes. Berlin: Springer.
ISBN978-3-540-27499-5.
OCLC262680717.
Talagrand, Michel (2014). Upper and lower bounds for stochastic processes : modern methods and classical problems. Heidelberg: Springer.
ISBN978-3-642-54075-2.
OCLC871255685.[15]
Talagrand, Michel (21 December 2021). Upper and Lower Bounds for Stochastic Processes: Decomposition Theorems. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. Vol. 60. Springer Cham.
doi:
10.1007/978-3-030-82595-9.
ISBN978-3-030-82594-2.
S2CID123995577.
^Talagrand, Michel (2010-11-12). Mean Field Models for Spin Glasses: Volume I: Basic Examples. Berlin Heidelberg: Springer. p. xii.
ISBN978-3-642-15201-6.
^Talagrand, Michel (1990). "Some isoperimetric inequalities and their applications". Proc. Int. Congress of Mathematicians, Kyoto. Vol. 2. pp. 1011–1024.
CiteSeerX10.1.1.465.1304.
^"The Loeve Prize". University of California, Berkeley. Retrieved 2024-03-22.
^"Lauréats du prix Fermat". Université Paul Sabatier. Institut de Mathématiques de Toulouse (in French). 2023-11-21. Retrieved 2024-03-22.