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(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.
The text is based on an established graduate course given at MIT
that provides an introduction to the theory of the dynamical
Yang-Baxter equation and its applications, which is an important
area in representation theory and quantum groups. The book, which
contains many detailed proofs and explicit calculations, will be
accessible to graduate students of mathematics, who are familiar
with the basics of representation theory of semi-simple Lie
algebras.
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