Titlebook: Visions in Mathematics; GAFA 2000 Special Vo N. Alon,J. Bourgain,V. Milman Book 2010 Birkh?user Basel 2010 Mathematica.algebra.combinatoric

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Perspectives on the Analytic Theory of ,-Functions,ribe the central problems connected with them. We give a sample (this is certainly not meant to be a survey) of results towards these conjectures as well as some problems that can be resolved by finessing these conjectures. We also mention briefly some of the successful present-day tools and the role they might play in the big picture.

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Addendum: Discussions at the Dead Sea,of the Mathematical Community with the World around us, the future attractiveness of Mathematics to the younger generation, new opportunities (and dangers) connected with the explosion of Computer Science, our traditional contacts with Mathematical Physics and many other subjects.

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forthy

Noncommutative Geometry Year 2000,ng coordinates on the phase space of atomic systems entails an equally drastic evolution. We describe a basic construction which extends the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. The basic tools of the theo

CARE

Introduction to Symplectic Field Theory,ir Lagrangian submanifolds in the spirit of topological field theory, and at the same time serves as a rich source of new invariants of contact manifolds and their Legendrian submanifolds. Moreover, we hope that the applications of SFT go far beyond this framework..

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