Vitali Davidovich Milman ( he, ויטלי מילמן; russian: Виталий Давидович Мильман) (born 23 August 1939) is a

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 ...

specializing in

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

. He is a professor at the

Tel Aviv University Tel Aviv University (TAU) ( he, אוּנִיבֶרְסִיטַת תֵּל אָבִיב, ''Universitat Tel Aviv'') is a public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Locate ...

. In the past he was a President of the

Israel Mathematical Union The Israel Mathematical Union (IMU) ( he, הַאִיגּוּד הַיִשְׂרְאֵלִי לְמָתֶמָטִיקָה) is an association of professional mathematicians in Israel. It is a member of the European Mathematical Society and the Int ...

and a member of the “ Aliyah” committee of Tel Aviv University.

Work

Milman received his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

at Kharkiv State University in 1965 under the direction of Boris Levin. In a 1971 paper, Milman gave a new proof of

Dvoretzky's theorem In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander Grothendieck. In essence, it says that every sufficiently high-dimens ...

, 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 arbitrarily close to being isometric 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 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 ...

phenomenon which has since found numerous applications. Milman made important contributions to the study of Banach spaces 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 In mathematics, particularly, in asymptotic convex geometry, Milman's reverse Brunn–Minkowski inequality is a result due to Vitali Milman that provides a reverse inequality to the famous Brunn–Minkowski inequality for convex bodies in '' ...

and the quotient of subspace theorem.

Positions

He holds several positions including being the advisor to the Israel Ministry of Science on the immigration of scientists, and being a member of the European Mathematical Union. He is on the editorial boards of several journals, including

Geometric and Functional Analysis ''Geometric and Functional Analysis'' (''GAFA'') is a mathematical journal published by Birkhäuser, an independent division of Springer-Verlag. The journal is published approximately bi-monthly. The journal publishes papers on broad range of top ...

. He has published over 150 scientific publications, a monograph and eleven edited books. He has delivered lectures at Universities such as MIT, IAS Princeton, Berkeley, IHES Paris, Cambridge.

Awards and honors

Milman was an Invited Speaker of the International Congress of Mathematicians in 1986 in Berkeley and in 1998 in Berlin. He received the Landau Prize in Mathematics in 2002 and the

EMET Prize The EMET Prize for Art, Science and Culture is an Israeli prize awarded annually for excellence in academic and professional achievements that have far-reaching influence and make a significant contribution to society. Prizes are awarded in the fol ...

in mathematics in 2007. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Family

Mathematics runs in the Milman family. His father is the mathematician David Milman, who devised the

Krein–Milman theorem In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). This theorem generalizes to infinite-dimensional spaces and to arbitrar ...

. His brother is the mathematician

Pierre Milman Pierre D. Milman (russian: Пьер Д. Мильман), born 1945 in Odessa, 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 Uni ...

and his son is the young mathematician Emanuel Milman.

Selected works

Notes

External links

Vitali Milman's website
* {{DEFAULTSORT:Milman, Vitali Ukrainian Jews Soviet mathematicians 20th-century Israeli mathematicians 1939 births Living people Tel Aviv University faculty Fellows of the American Mathematical Society National University of Kharkiv alumni 20th-century Ukrainian mathematicians