LNiM 1807 Geometric Aspects of Functional Analysis - V.D.Milman, G.Schechtman, Springer Verlag, 2003.pdf - MAT Lecture Notes in Mathematics - kf.mtsw

Lecture Notes in Mathematics

1807

Editors:

J.--M. Morel, Cachan

F. Takens, Groningen

B. Teissier, Paris

Berlin

Heidelberg

New York

Hong Kong

London

Milan

Paris

Tokyo

V. D. Milman G. Schechtman (Eds.)

Geometric Aspects

of Functional Analysis

Israel Seminar

2001--2002

Editors

Vitali D. Milman

Department of Mathematics

TelAvivUniversity

Ramat Aviv

69978

Te l Av i v

Israel

e-mail: milman@post.tau.ac.il

Gideon Schechtman

Department of Mathematics

The Weizmann Institute of Science

P. O. B o x

76100

Rehovot

Israel

e-mail: gideon@wisdom.weizmann.ac.il

http://www.wisdom.weizmann.ac.il/˜gideon

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Mathematics Subject Classification (2000):

46-06, 46B07, 52-06 60-06

ISBN

0075-8434

3-540-00485-8

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Springer-Verlag Berlin Heidelberg

2003

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Preface

During the last two decades the following volumes containing the proceedings

of the Israel Seminar in Geometric Aspects of Functional Analysis appeared

1983-1984 Published privately by Tel Aviv University

1985-1986 Springer Lecture Notes, Vol. 1267

1986-1987 Springer Lecture Notes, Vol. 1317

1987-1988 Springer Lecture Notes, Vol. 1376

1989-1990 Springer Lecture Notes, Vol. 1469

1992-1994 Operator Theory: Advances and Applications, Vol. 77, Birkhauser

1994-1996 MSRI Publications, Vol. 34, Cambridge University Press

1996-2000 Springer Lecture Notes, Vol. 1745.

Of these, the ﬁrst six were edited by Lindenstrauss and Milman, the sev-

enth by Ball and Milman and the last by the two of us.

As in the previous volumes, the current one reﬂects general trends of

the Theory. The connection between Probability and Convexity continues to

broaden and deepen and a number of papers of this collection reﬂect this fact.

There is a renewed interest (and hope for solution) in the old and fascinating

slicing problem (also known as the hyperplane conjecture). Several papers in

this volume revolve around this conjecture as well as around some related

topics as the distribution of functionals, regarded as random variables on

a convex set equipped with its normalized Lebesgue measure. Some other

papers deal with more traditional aspects of the Theory like the concentration

phenomenon. Finally, the volume contains a long paper on approximating

convex sets by randomly chosen polytopes which also contains a deep study

of ﬂoating bodies, an important subject in Classical Convexity Theory.

All the papers here are original research papers and were subject to the

usual standards of refereeing.

As in previous proceedings of the GAFA Seminar, we also list here all

the talks given in the seminar as well as talks in related workshops and

conferences. We believe this gives a sense of the main directions of research

in our area.

We are grateful to Ms. Diana Yellin for taking excellent care of the type-

setting aspects of this volume.

Vitali Milman

Gideon Schechtman

LNiM 1807 Geometric Aspects of Functional Analysis - V.D.Milman, G.Schechtman, Springer Verlag, 2003.pdf

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