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Beskrivning
The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk “Mathematics as Metaphor” summarises the author's view on mathematics as an outgrowth of natural language.
Part 1 Algebraic geometry: the Hasse-Witt matrix of an algebraic curve; rational points of algebraic curves over functional fields; correspondences, motive and monoidal transforms; new directions in geometry; arrangements of hyperplanes, higher braid groups and higher Bruhat orders. Part 2 Modular forms and diophantine equations: the p-torsion of elliptic curves is uniformly bounded; parabolic points and zeta-functions of modular curves; periods of p-adic Schottky groups; rational points of bounded height of Fano varieties; points of bounded height on del Pezzo surfaces. Part 3 Differential equations and mathematical physics: long wave equation with free boundary - 1; conservation laws and solutions; long wave equations with a free surface - 2; Hamiltonian structure and higher equations; a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy; the Momford form and the Polyakov measure in string theory; Gromov-Witten classes, quantum cohomology and enumerative geometry; and other papers.
