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

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Holomorphic Curves and Real Three-Dimensional Dynamics,In this paper we describe new tools for studying smooth dynamical systems on three-manifolds. We also mention some interesting open problems.

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Quantum Information Theory: Results and Open Problems,The discipline of information theory was founded by Claude Shannon in a truly remarkable paper [.] which laid down the foundations of the subject. We begin with a quote from this paper which is an excellent summary of the main concern of information theory:

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Reflections on the Development of Mathematics in the 20th Century,Let us compare mathematics as it was at the beginning of the century with contemporary mathematics. What has happened in the past hundred years?

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Universality, Phase Transitions and Statistical Mechanics, for interacting spins. The phase transition of the Ising model is believed to describe liquid-gas transitions, coupled chains of quantum anharmonic oscillators, certain quantum field theories and models of probabilistic cellular automata. The last section is devoted to a review of some problems in

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