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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 mathematical fields, 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. What's Next? brings together many of today's leading mathematicians to describe recent advances and future directions inspired by Thurston's transformative ideas.Including valuable insights from his colleagues and former students, What's Next? discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. This incisive and wide-ranging book also 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.

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