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CRM - University of Ottawa Distinguished Lecture Series

TITLE:Asymptotic Geometric Analysis; Geometrization of Probability
SPEAKER:Vitali Milman (Tel-Aviv University)
DATE:Vendredi, 21 Septembre 2007
TIME:3:30 pm
ROOM:KED B005
ABSTRACT:

We study the asymptotic behavior of finite- (but very high-)dimensional normed spaces and convex bodies when dimension tends to infinity. Contrary to common intuition, which anticipates enormous diversity and chaotic behavior, we observe a uniform behavior for the whole family of finite- (but high-)dimensional spaces. In the first part of our talk we will discuss different and unexpected phenomena accompanying high dimension. In the second, the main part of the talk we will explain how the geometric theory of convexity is extended to a larger category of log-concave measures which bring inside this class of (probability) measures geometric vision and approach. This brings inside the theory functional versions for many geometric inequalities, and also leads to solutions of some central problems of the theory.

The talk will be understandable to any graduate student in Mathematics.

<p> About the speaker Professor Vitali Milman obtained his Ph.D. from Kharkov University (Ukraine, then USSR) in 1965 and a higher doctorate (habilitation) in 1970, from the famous Kharkov Physical Institute of Low Temperatures which at the time had a constellation of mathematics stars. In 1973 Vitali Milman emigrated to Israel to become Associate, then (1980) Full Professor at the Tel-Aviv University.

Professor Milman is credited with the creation of the subject of Asymptotic Geometric Analysis, in particular, with the current widespread interest in, and applications of, the phenomenon of concentration of measure on high-dimensional structures.

Professor Milman's list of publications includes over 160 scientific publications, a monograph (joint with Schechtman), and 16 edited books.

Vitali Milman have invited sessional lectures at ICM86, Berkeley (Analysis section) and ICM98, Berlin (Analysis section), as well as at 1996 European Congress of Mathematicians, Budapest (plenary address). He delivered Pichorides Lecture, Crete, 1997, Carl Stromberg Memorial Lecture, KSU, 2006, and Ordway Lecture, Minneapolis, 2007. Professor Milman is a recepient of 2002 Landau Prize in Mathematics.

Professor Milman is the Managing Editor of Geometric and Functional Analysis (GAFA), one of the top mathematical journals of today in terms of citation impact. He is an Editor of Israel Journal of Mathematics and Communications in Contemporary Mathematics.

He served as President of the Israel Mathematical Union, member of the Council of the European Mathematical Union.

Vitali Milman organized a number of large-scale programs at prestigeous mathematical centres, including MSRI, PIMS, Schrödinger Institute, and Centre Emil Borel. He held numerous visiting positions in many universities and mathematics institutes around the world, including the Institutes of Advanced Study in: Princeton (IAS), Paris (IHES), Bonn (Max-Plank Inst.), Zurich (ETH), Camberra (ANU), and Institutes of Mathematics at Berkeley (MSRI), Cambridge (England) and others.

The present CRM Distinguished Lecture will be followed by a 3-day Fields Institute workshop on Geometrization of Probability, organized by Vitali Milman jointly with Vladimir Pestov. See the web page of the workshop where everyone is cordially invited:

http://www.fields.utoronto.ca/programs/scientific/07-08/geometrization/