Mathematics: Frontiers and PerspectivesVladimir Igorevich Arnolʹd This volume is a celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians. Authors of 14 contributions were recognized in various years by the IMU as recipients of the Fields Medal, from K.F. Roth (Fields Medalist, 1958) to W.T. Gowers (Fields Medalist, 1998). |
Contents
Number theory transcendence and Diophantine geometry in the next | 1 |
How much may they contribute | 13 |
Back to Riemann | 33 |
Copyright | |
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abelian algebraic algebro-geometric arithmetic automorphism bound bundle Calabi-Yau Calabi-Yau manifolds classical coefficients cohomology combinatorics compact complex conjecture connected construction defined denote differential equations dimension dimensional discrete dynamics eigenvalues example existence f-vectors finite formula Fourier fundamental Galois geometry given global graph Hilbert holomorphic ideas integer International Mathematical Union invariant isomorphism Kähler Kähler manifolds Kähler-Einstein metrics L-functions Lagrangian lattice linear manifolds Math mathematicians mathematics methods metric minimal submanifolds modular moduli space nonnegative nontrivial number theory p-adic p-motives Phys physicists physics Poincaré points polynomial polytopes poset problem proof proved quadratic quantum cohomology quantum field theory question random rational curves real number representation Ricci curvature Riemann scalar curvature simplicial singular smooth solutions solved sphere stochastic string theory structure subgroup subset surfaces symplectic symplectic manifold theorem topology turbulent variables vector zero zeta function