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Dedicated to the memory of Chih-Han Sah, this volume continues a
long tradition of one of the most influential mathematical seminars
of this century. A number of topics are covered, including
combinatorial geometry, connections between logic and geometry, Lie
groups, algebras and their representations. An additional area of
importance is noncommutative algebra and geometry, and its
relations to modern physics. Distinguished mathematicians
contributing to this work: T.V. Alekseevskaya V. Kac A.V. Borovik
A. Kazarnovsky-Krol C.-H. Sah* M. Kontsevich G. Cherlin A. Radul
J.L. Dupont A.L. Rosenberg I.M. Gelfand N. White The Gelfand
Mathematical Seminar volumes stimulate the birth of significant
ideas in contemporary mathematics and remain invaluable reference
material. * indicates deceased contributor (Production: please
ensure that appropriate symbol be incorporated onto the final back
cover design)
It is very tempting but a little bit dangerous to compare the style
of two great mathematicians or of their schools. I think that it
would be better to compare papers from both schools dedicated to
one area, geometry and to leave conclusions to a reader of this
volume. The collaboration of these two schools is not new. One of
the best mathematics journals Functional Analysis and its
Applications had I.M. Gelfand as its chief editor and V.I. Arnold
as vice-chief editor. Appearances in one issue of the journal
presenting remarkable papers from seminars of Arnold and Gelfand
always left a strong impact on all of mathematics. We hope that
this volume will have a similar impact. Papers from Arnold's
seminar are devoted to three important directions developed by his
school: Symplectic Geometry (F. Lalonde and D. McDuff), Theory of
Singularities and its applications (F. Aicardi, I. Bogaevski, M.
Kazarian), Geometry of Curves and Manifolds (S. Anisov, V.
Chekanov, L. Guieu, E. Mourre and V. Ovsienko, S. Gusein-Zade and
S. Natanzon). A little bit outside of these areas is a very
interesting paper by M. Karoubi Produit cyclique d'espaces et
operations de Steenrod.
(Very preliminary)A tribute to the vision and legacy of Israel
Gelfand, the invited papers in this volume reflect the unity of
mathematics as a whole, with particular emphasis on the many
connections among the fields of geometry, physics, and
representation theory. Written by leading mathematicians, the text
is broadly divided into two sections: the first is devoted to
developments at the intersection of geometry and physics, and the
second to representation theory and algebraic geometry. Topics
include conformal field theory, K-theory, noncommutative geometry,
gauge theory, representations of infinite-dimensional Lie algebras,
and various aspects of the Langlands program. Graduate students and
researchers will benefit from and find inspiration in this broad
and unique work, which brings together fundamental results in a
number of disciplines and highlights the rewards of an
interdisciplinary approach to mathematics and physics.Contributors:
M. Atiyah, A. Beilinson, J. Bernstein, A. Connes, P. Deligne, R.
Dijkgraaf, D. Gaitsgory, M. Gromov, F. Hirzebruch, M. Hopkins, D.
Kazhdan, F. Kirwan, M. Kontsevich, B. Kostant, G. Lusztig, D.
McDuff, H. Nakajima, S. Novikov, P. Sarnak, A.
It is very tempting but a little bit dangerous to compare the style
of two great mathematicians or of their schools. I think that it
would be better to compare papers from both schools dedicated to
one area, geometry and to leave conclusions to a reader of this
volume. The collaboration of these two schools is not new. One of
the best mathematics journals Functional Analysis and its
Applications had I.M. Gelfand as its chief editor and V.I. Arnold
as vice-chief editor. Appearances in one issue of the journal
presenting remarkable papers from seminars of Arnold and Gelfand
always left a strong impact on all of mathematics. We hope that
this volume will have a similar impact. Papers from Arnold's
seminar are devoted to three important directions developed by his
school: Symplectic Geometry (F. Lalonde and D. McDuff), Theory of
Singularities and its applications (F. Aicardi, I. Bogaevski, M.
Kazarian), Geometry of Curves and Manifolds (S. Anisov, V.
Chekanov, L. Guieu, E. Mourre and V. Ovsienko, S. Gusein-Zade and
S. Natanzon). A little bit outside of these areas is a very
interesting paper by M. Karoubi Produit cyclique d'espaces et
operations de Steenrod.
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