Michel Pierre Talagrand (born 15 February 1952) is a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. 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 Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

. Talagrand was elected as correspondent of the

Académie des sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...

of Paris in March 1997, and then as a full member in November 2004, in the Mathematics section. Talagrand studies mainly

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...

and

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

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 In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname(S) of a set S\subset\R^n ...

and

concentration of measure In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that "A random v ...

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 In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...

, 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 computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the ...

random matrices In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...

, and statistics (empirical processes). The recent works of Talagrand concern

spin glass In condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called 'freezing temperature' ''Tf''. In ferromagnetic solids, component atoms' magne ...

es mean fields models. His objective is to give a mathematical foundation to numerous remarkable works of

physicists A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...

in this domain. Talagrand showed for instance recently the validity of the Parisi formula.

Awards

* Peccot-Vimont Prize of the French

Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment ('' grand établissement'') in France. It is located in Paris n ...

(1980) * Servant Prize of the French

(1985) *Invited Speaker to the International Congress of Mathematicians (Kyoto 1990) * Loève Prize in Probability (1995) *

Fermat Prize The Fermat prize of mathematical research biennially rewards research works in fields where the contributions of Pierre de Fermat have been decisive: * Statements of variational principles * Foundations of probability and analytic geometry * Numbe ...

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) *Stefan Banach Medal of the Polish Academy of Sciences (2022)

Selected publications

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Reference Books

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References

External links