Vitali Milman
Encyclopedia
Vitali Davidovich Milman (born 23 August 1939) is a mathematician
specializing in analysis
. He is currently a professor at the Tel-Aviv University. In the past he was a President of the Israel Mathematical Union and a member of the “Aliyah” committee of Tel-Aviv University.
at Kharkov State University
in 1965 under the direction of Boris Levin.
In a famous 1971 paper, Milman gave a new proof of Dvoretzky's theorem
, stating that every convex body in dimension N has a section of dimension d(N), with d(N) tending to infinity with N, that is isomorphic to an ellipsoid. Milman's proof gives the optimal bound d(N) ≥ const log N. In this proof, Milman put forth the concentration of measure
phenomenon which has since found numerous applications.
Milman made important contributions to the study of Banach space
s of large (finite) dimension, which led to the development of asymptotic geometric analysis. His results in this field include Milman's reverse Brunn–Minkowski inequality and the Quotient of subspace theorem
.
in mathematics in 2007.
He is on the editorial boards of several reputed journals, including Geometric and Functional Analysis. He has published over 150 scientific publications, a monograph and eleven edited books. He has delivered lectures at many Universities such as MIT, IAS Princeton, Berkeley, IHES Paris, Cambridge.
who devised the Krein–Milman theorem. His brother is the mathematician Pierre Milman
and his son is the young mathematician Emanuel Milman.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
specializing in analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
. He is currently a professor at the Tel-Aviv University. In the past he was a President of the Israel Mathematical Union and a member of the “Aliyah” committee of Tel-Aviv University.
Work
Milman received in Ph.D.Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
at Kharkov State University
Kharkiv University
The University of Kharkiv or officially the Vasyl Karazin Kharkiv National University is one of the major universities in Ukraine, and earlier in the Russian Empire and Soviet Union...
in 1965 under the direction of Boris Levin.
In a famous 1971 paper, Milman gave a new proof of Dvoretzky's theorem
Dvoretzky's theorem
In mathematics, in the theory of Banach spaces, Dvoretzky's theorem is an important structural theorem proved by Aryeh Dvoretzky in the early 1960s. It answered a question of Alexander Grothendieck...
, stating that every convex body in dimension N has a section of dimension d(N), with d(N) tending to infinity with N, that is isomorphic to an ellipsoid. Milman's proof gives the optimal bound d(N) ≥ const log N. In this proof, Milman put forth the concentration of measure
Concentration of measure
In mathematics, concentration of measure 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 variable that depends in a Lipschitz way on many independent variables ...
phenomenon which has since found numerous applications.
Milman made important contributions to the study of Banach space
Banach space
In mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...
s of large (finite) dimension, which led to the development of asymptotic geometric analysis. His results in this field include Milman's reverse Brunn–Minkowski inequality and the Quotient of subspace theorem
Quotient of subspace theorem
The quotient of subspace theorem is an important property of finite dimensional normed spaces, discovered by Vitali Milman.Let be an N-dimensional normed space...
.
Positions
He holds several important positions including being the advisor to the Israel Ministry of Science on the immigration of scientists, and a member of the European Mathematical Union. Milman received the Landau Prize in Mathematics in 2002 and the EMET PrizeEMET Prize
The Emet Prize for Art, Science and Culture is an annual Israeli prize given for excellence in academic and professional achievements that have far reaching influence and significant contribution to society....
in mathematics in 2007.
He is on the editorial boards of several reputed journals, including Geometric and Functional Analysis. He has published over 150 scientific publications, a monograph and eleven edited books. He has delivered lectures at many Universities such as MIT, IAS Princeton, Berkeley, IHES Paris, Cambridge.
Family
Math runs in the Milman family. His father is the mathematician David MilmanDavid Milman
David Pinhusovich Milman was a Soviet and later Israeli mathematician specializing in functional analysis. He was one of the major figures of the Soviet school of functional analysis...
who devised the Krein–Milman theorem. His brother is the mathematician Pierre Milman
Pierre Milman
Pierre D. Milman is a mathematician and a professor at the University of Toronto.Milman graduated with a B.A. from the University of Moscow in 1967. He obtained his Ph.D. from the University of Tel Aviv in 1975 after an interlude of several years as researcher at the Institute of Chemical Physics...
and his son is the young mathematician Emanuel Milman.