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What's Next?

The Mathematical Legacy of William P. Thurston (AMS-205)

Dylan Thurston (Hrsg.)

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ca. 72,99
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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

William Thurston (1946–2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of areas of mathematics, from foliations, contact structures, and Teichmüller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. In What's Next?, many of today's leading mathematicians describe recent advances and future directions inspired by Thurston's transformative ideas.

This book brings together papers delivered by his colleagues and former students at "What's Next? The Mathematical Legacy of Bill Thurston," a conference held in June 2014 at Cornell University. It discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. Incisive and wide-ranging, the book explores how he introduced new ways of thinking about and doing mathematics—innovations that have had a profound and lasting impact on the mathematical community as a whole—and also features two papers based on Thurston's unfinished work in dynamics.

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Schlagwörter

Faithful representation, Preorder, Hyperbolic manifold, Commutative property, Pullback (category theory), HNN extension, Moduli space, Saddle point, Hypercube, Pair of pants (mathematics), Probability measure, Mapping cylinder, Convex hull, Special case, Unit sphere, Unit disk, Kleinian group, Topology, Hyperbolic geometry, Non-positive curvature, Leech lattice, Limit point, Dehn's lemma, Incompressible surface, Lebesgue measure, Central series, Open set, Upper and lower bounds, Quasi-isometry, Geometry, Conjugacy class, Jordan curve theorem, Asymptotic expansion, Maxima and minima, Polynomial, Symplectic geometry, Sectional curvature, Mahler measure, JSJ decomposition, Braid group, Branch point, Endomorphism, Orientability, Euclidean space, Riemannian manifold, Homotopy, Hyperbolic space, Normal subgroup, Vector bundle, Coxeter group, Julia set, Arbitrarily large, Möbius strip, Theorem, Cohomology operation, Character variety, Epimorphism, Pullback (differential geometry), Eigenfunction, Conjecture, Diagram (category theory), Equivalence class, Free product, Klein bottle, Extreme point, Quasiconvex function, Cohomology, Rectangle, Pleated surface, Inclusion map, Subgroup, Lyapunov exponent, Simple algebra, Free group, Covering space, Sign (mathematics), Simply connected space, Total order, Non-Euclidean geometry, Characterization (mathematics), Disjoint union, Geometrization conjecture, Big O notation, Quadric, Fundamental group, Haar measure, Marriage theorem, Natural topology, Automorphism, Equivalence relation, Manifold decomposition, Subset, Curvature, Riemann surface, Fiber bundle, Hyperbolic 3-manifold, I0, Möbius transformation, Homeomorphism, Perfect group