Listing 1 - 10 of 46 | << page >> |
Sort by
|
Choose an application
Written and revised by D. B. A. Epstein.
Category theory. Homological algebra --- 515.14 --- Algebraic topology --- Homology theory. --- 515.14 Algebraic topology --- Cohomology theory --- Contrahomology theory --- Algebra homomorphism. --- Algebra over a field. --- Algebraic structure. --- Approximation. --- Axiom. --- Basis (linear algebra). --- CW complex. --- Cartesian product. --- Classical group. --- Coefficient. --- Cohomology operation. --- Cohomology ring. --- Cohomology. --- Commutative property. --- Complex number. --- Computation. --- Continuous function. --- Cup product. --- Cyclic group. --- Diagram (category theory). --- Dimension. --- Direct limit. --- Embedding. --- Existence theorem. --- Fibration. --- Homomorphism. --- Hopf algebra. --- Hopf invariant. --- Ideal (ring theory). --- Integer. --- Inverse limit. --- Manifold. --- Mathematics. --- Monomial. --- N-skeleton. --- Natural transformation. --- Permutation. --- Quaternion. --- Ring (mathematics). --- Scalar (physics). --- Special unitary group. --- Steenrod algebra. --- Stiefel manifold. --- Subgroup. --- Subset. --- Summation. --- Symmetric group. --- Symplectic group. --- Theorem. --- Uniqueness theorem. --- Upper and lower bounds. --- Vector field. --- Vector space. --- W0.
Choose an application
The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Cartes harmoniques --- Harmonic maps --- Harmonische kaarten --- Immersies (Wiskunde) --- Immersions (Mathematics) --- Immersions (Mathématiques) --- Harmonic maps. --- Differential equations, Elliptic --- Applications harmoniques --- Immersions (Mathematiques) --- Équations différentielles elliptiques --- Numerical solutions. --- Solutions numériques --- Équations différentielles elliptiques --- Solutions numériques --- Differential equations [Elliptic] --- Numerical solutions --- Embeddings (Mathematics) --- Manifolds (Mathematics) --- Mappings (Mathematics) --- Maps, Harmonic --- Arc length. --- Catenary. --- Clifford algebra. --- Codimension. --- Coefficient. --- Compact space. --- Complex projective space. --- Connected sum. --- Constant curvature. --- Corollary. --- Covariant derivative. --- Curvature. --- Cylinder (geometry). --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential equation. --- Differential geometry. --- Elliptic partial differential equation. --- Embedding. --- Energy functional. --- Equation. --- Existence theorem. --- Existential quantification. --- Fiber bundle. --- Gauss map. --- Geometry and topology. --- Geometry. --- Gravitational field. --- Harmonic map. --- Hyperbola. --- Hyperplane. --- Hypersphere. --- Hypersurface. --- Integer. --- Iterative method. --- Levi-Civita connection. --- Lie group. --- Mathematics. --- Maximum principle. --- Mean curvature. --- Normal (geometry). --- Numerical analysis. --- Open set. --- Ordinary differential equation. --- Parabola. --- Quadratic form. --- Sign (mathematics). --- Special case. --- Stiefel manifold. --- Submanifold. --- Suggestion. --- Surface of revolution. --- Symmetry. --- Tangent bundle. --- Theorem. --- Vector bundle. --- Vector space. --- Vertical tangent. --- Winding number. --- Differential equations, Elliptic - Numerical solutions
Choose an application
Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.
Mathematical logic --- Mathematics --- Logic, Symbolic and mathematical --- Mathématiques --- Logique symbolique et mathématique --- Philosophy --- Philosophie --- Logic, Symbolic and mathematical. --- Philosophy. --- Set theory --- Théorie des ensembles --- Continuity --- Continu (philosophie) --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Logic of mathematics --- Mathematics, Logic of --- Absoluteness. --- Addition. --- Axiom of choice. --- Axiom of extensionality. --- Axiom of infinity. --- Axiom. --- Axiomatic system. --- Boolean algebra (structure). --- Constructible set (topology). --- Continuum hypothesis. --- Existence theorem. --- Existential quantification. --- Integer. --- Mathematical induction. --- Mathematical logic. --- Mathematics. --- Metatheorem. --- Order by. --- Ordinal number. --- Propositional function. --- Quantifier (logic). --- Reductio ad absurdum. --- Requirement. --- Set theory. --- Theorem. --- Transfinite induction. --- Transfinite. --- Variable (mathematics). --- Well-order. --- Théorie des ensembles --- Logique mathématique --- Axiome du choix
Choose an application
Mathematical No/ex, 27Originally published in 1981.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Riemannian manifolds. --- Minimal surfaces. --- Surfaces, Minimal --- Maxima and minima --- Manifolds, Riemannian --- Riemannian space --- Space, Riemannian --- Geometry, Differential --- Manifolds (Mathematics) --- Differential geometry. Global analysis --- Addition. --- Analytic function. --- Branch point. --- Calculation. --- Cartesian coordinate system. --- Closed geodesic. --- Codimension. --- Coefficient. --- Compactness theorem. --- Compass-and-straightedge construction. --- Continuous function. --- Corollary. --- Counterexample. --- Covering space. --- Curvature. --- Curve. --- Decomposition theorem. --- Derivative. --- Differentiable manifold. --- Differential geometry. --- Disjoint union. --- Equation. --- Essential singularity. --- Estimation. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- First variation. --- Flat topology. --- Fundamental group. --- Geometric measure theory. --- Great circle. --- Homology (mathematics). --- Homotopy group. --- Homotopy. --- Hyperbolic function. --- Hypersurface. --- Integer. --- Line–line intersection. --- Manifold. --- Measure (mathematics). --- Minimal surface. --- Monograph. --- Natural number. --- Open set. --- Parameter. --- Partition of unity. --- Pointwise. --- Quantity. --- Regularity theorem. --- Riemann surface. --- Riemannian manifold. --- Scalar curvature. --- Scientific notation. --- Second fundamental form. --- Sectional curvature. --- Sequence. --- Sign (mathematics). --- Simply connected space. --- Smoothness. --- Sobolev inequality. --- Solid torus. --- Subgroup. --- Submanifold. --- Summation. --- Theorem. --- Topology. --- Two-dimensional space. --- Unit sphere. --- Upper and lower bounds. --- Varifold. --- Weak topology.
Choose an application
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.
Mathematics --- Shimura varieties. --- MATHEMATICS / Number Theory. --- Varieties, Shimura --- Arithmetical algebraic geometry --- Math --- Science --- Abelian variety. --- Absolute value. --- Algebraic group. --- Algebraically closed field. --- Artinian. --- Automorphic form. --- Base change. --- Bijection. --- Canonical map. --- Codimension. --- Coefficient. --- Cohomology. --- Compactification (mathematics). --- Conjecture. --- Corollary. --- Dimension (vector space). --- Dimension. --- Direct limit. --- Division algebra. --- Eigenvalues and eigenvectors. --- Elliptic curve. --- Embedding. --- Equivalence class. --- Equivalence of categories. --- Existence theorem. --- Field of fractions. --- Finite field. --- Function field. --- Functor. --- Galois cohomology. --- Galois group. --- Generic point. --- Geometry. --- Hasse invariant. --- Infinitesimal character. --- Integer. --- Inverse system. --- Isomorphism class. --- Lie algebra. --- Local class field theory. --- Maximal torus. --- Modular curve. --- Moduli space. --- Monic polynomial. --- P-adic number. --- Prime number. --- Profinite group. --- Residue field. --- Ring of integers. --- Separable extension. --- Sheaf (mathematics). --- Shimura variety. --- Simple group. --- Special case. --- Spectral sequence. --- Square root. --- Subset. --- Tate module. --- Theorem. --- Transcendence degree. --- Unitary group. --- Valuative criterion. --- Variable (mathematics). --- Vector space. --- Weil group. --- Weil pairing. --- Zariski topology.
Choose an application
The description for this book, Surface Area. (AM-35), Volume 35, will be forthcoming.
Surfaces. --- Absolute continuity. --- Addition. --- Admissible set. --- Arc length. --- Axiom. --- Axiomatic system. --- Bearing (navigation). --- Bounded variation. --- Calculus of variations. --- Circumference. --- Compact space. --- Complex analysis. --- Concentric. --- Connected space. --- Continuous function (set theory). --- Continuous function. --- Corollary. --- Countable set. --- Covering set. --- Curve. --- Derivative. --- Diameter. --- Differentiable function. --- Differential geometry. --- Direct proof. --- Dirichlet integral. --- Disjoint sets. --- Empty set. --- Equation. --- Equicontinuity. --- Existence theorem. --- Existential quantification. --- Function (mathematics). --- Functional analysis. --- Geometry. --- Hausdorff measure. --- Homeomorphism. --- Homotopy. --- Infimum and supremum. --- Integral geometry. --- Intersection number (graph theory). --- Interval (mathematics). --- Iterative method. --- Jacobian. --- Lebesgue integration. --- Lebesgue measure. --- Limit (mathematics). --- Limit point. --- Limit superior and limit inferior. --- Linearity. --- Line–line intersection. --- Locally compact space. --- Mathematician. --- Mathematics. --- Measure (mathematics). --- Metric space. --- Morphism. --- Natural number. --- Nonparametric statistics. --- Orientability. --- Parameter. --- Parametric equation. --- Parametric surface. --- Partial derivative. --- Potential theory. --- Radon–Nikodym theorem. --- Representation theorem. --- Representation theory. --- Right angle. --- Semi-continuity. --- Set function. --- Set theory. --- Sign (mathematics). --- Smoothness. --- Space-filling curve. --- Subset. --- Summation. --- Surface area. --- Tangent space. --- Theorem. --- Topological space. --- Topology. --- Total order. --- Total variation. --- Uniform convergence. --- Unit square.
Choose an application
The description for this book, Degrees of Unsolvability. (AM-55), Volume 55, will be forthcoming.
Recursive functions. --- Unsolvability (Mathematical logic) --- Addition. --- Aleph number. --- Algebraic topology. --- Approximation. --- Arithmetic function. --- Arithmetical set. --- Axiom of choice. --- Baire category theorem. --- Cardinality of the continuum. --- Cardinality. --- Cartesian product. --- Category theory. --- Commutative property. --- Conjecture. --- Continuum hypothesis. --- Contradiction. --- Corollary. --- Countable set. --- Disjoint union. --- Effective method. --- Empty set. --- Enumeration. --- Equation. --- Existence theorem. --- Existential quantification. --- Finite set. --- Fixed-point theorem. --- Fourier analysis. --- Fubini's theorem. --- Gödel numbering. --- Identity function. --- Inequality (mathematics). --- Infimum and supremum. --- Integer. --- Lebesgue measure. --- Limit of a sequence. --- Limit point. --- Mathematical induction. --- Mathematics. --- Mean of a function. --- Measure (mathematics). --- Metric space. --- Monotonic function. --- Mostowski. --- Mutual exclusivity. --- Natural number. --- Null set. --- Open set. --- Partial function. --- Partially ordered set. --- Predicate (mathematical logic). --- Product measure. --- Product topology. --- Real number. --- Recursion. --- Recursive set. --- Recursively enumerable set. --- Reductio ad absurdum. --- Regular space. --- Requirement. --- Scientific notation. --- Sequence. --- Set (mathematics). --- Simultaneous equations. --- Subset. --- Theorem. --- Topology. --- Transfinite induction. --- Tychonoff's theorem. --- Uncountable set. --- Union (set theory). --- Upper and lower bounds. --- Variable (mathematics). --- W0. --- Well-order. --- Without loss of generality. --- Zorn's lemma.
Choose an application
Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph.
Functional analysis --- Neumann problem --- Differential operators --- Complex manifolds --- Complex manifolds. --- Differential operators. --- Neumann problem. --- Differential equations, Partial --- Équations aux dérivées partielles --- Analytic spaces --- Manifolds (Mathematics) --- Operators, Differential --- Differential equations --- Operator theory --- Boundary value problems --- A priori estimate. --- Almost complex manifold. --- Analytic function. --- Apply. --- Approximation. --- Bernhard Riemann. --- Boundary value problem. --- Calculation. --- Cauchy–Riemann equations. --- Cohomology. --- Compact space. --- Complex analysis. --- Complex manifold. --- Coordinate system. --- Corollary. --- Derivative. --- Differentiable manifold. --- Differential equation. --- Differential form. --- Differential operator. --- Dimension (vector space). --- Dirichlet boundary condition. --- Eigenvalues and eigenvectors. --- Elliptic operator. --- Equation. --- Estimation. --- Euclidean space. --- Existence theorem. --- Exterior (topology). --- Finite difference. --- Fourier analysis. --- Fourier transform. --- Frobenius theorem (differential topology). --- Functional analysis. --- Hilbert space. --- Hodge theory. --- Holomorphic function. --- Holomorphic vector bundle. --- Irreducible representation. --- Line segment. --- Linear programming. --- Local coordinates. --- Lp space. --- Manifold. --- Monograph. --- Multi-index notation. --- Nonlinear system. --- Operator (physics). --- Overdetermined system. --- Partial differential equation. --- Partition of unity. --- Potential theory. --- Power series. --- Pseudo-differential operator. --- Pseudoconvexity. --- Pseudogroup. --- Pullback. --- Regularity theorem. --- Remainder. --- Scientific notation. --- Several complex variables. --- Sheaf (mathematics). --- Smoothness. --- Sobolev space. --- Special case. --- Statistical significance. --- Sturm–Liouville theory. --- Submanifold. --- Tangent bundle. --- Theorem. --- Uniform norm. --- Vector field. --- Weight function. --- Operators in hilbert space
Choose an application
Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.
Mathematics --- Mathématiques --- Congresses --- Congrès --- 51 --- -Math --- Science --- Congresses. --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Math --- Mathématiques --- Congrès --- A priori estimate. --- Addition. --- Additive group. --- Affine space. --- Algebraic geometry. --- Algebraic group. --- Atiyah–Singer index theorem. --- Bernoulli number. --- Boundary value problem. --- Bounded operator. --- C*-algebra. --- Canonical transformation. --- Cauchy problem. --- Characteristic class. --- Clifford algebra. --- Coefficient. --- Cohomology. --- Commutative property. --- Commutative ring. --- Complex manifold. --- Complex number. --- Complex vector bundle. --- Dedekind sum. --- Degenerate bilinear form. --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential operator. --- Dimension (vector space). --- Ellipse. --- Elliptic operator. --- Equation. --- Euler characteristic. --- Euler number. --- Existence theorem. --- Exotic sphere. --- Finite difference. --- Finite group. --- Fourier integral operator. --- Fourier transform. --- Fourier. --- Fredholm operator. --- Hardy space. --- Hilbert space. --- Holomorphic vector bundle. --- Homogeneous coordinates. --- Homomorphism. --- Homotopy. --- Hyperbolic partial differential equation. --- Identity component. --- Integer. --- Integral transform. --- Isomorphism class. --- John Milnor. --- K-theory. --- Lebesgue measure. --- Line bundle. --- Local ring. --- Mathematics. --- Maximal ideal. --- Modular form. --- Module (mathematics). --- Monoid. --- Normal bundle. --- Number theory. --- Open set. --- Parametrix. --- Parity (mathematics). --- Partial differential equation. --- Piecewise linear manifold. --- Poisson bracket. --- Polynomial ring. --- Polynomial. --- Prime number. --- Principal part. --- Projective space. --- Pseudo-differential operator. --- Quadratic form. --- Rational variety. --- Real number. --- Reciprocity law. --- Resolution of singularities. --- Riemann–Roch theorem. --- Shift operator. --- Simply connected space. --- Special case. --- Square-integrable function. --- Subalgebra. --- Submanifold. --- Support (mathematics). --- Surjective function. --- Symmetric bilinear form. --- Symplectic vector space. --- Tangent space. --- Theorem. --- Topology. --- Variable (mathematics). --- Vector bundle. --- Vector space. --- Winding number. --- Mathematics - Congresses
Choose an application
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
Algebraic geometry --- Topology --- Toposes --- Categories (Mathematics) --- Categories (Mathematics). --- Toposes. --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Category theory (Mathematics) --- Topoi (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Functor theory --- Adjoint functors. --- Associative property. --- Base change map. --- Base change. --- CW complex. --- Canonical map. --- Cartesian product. --- Category of sets. --- Category theory. --- Coequalizer. --- Cofinality. --- Coherence theorem. --- Cohomology. --- Cokernel. --- Commutative property. --- Continuous function (set theory). --- Contractible space. --- Coproduct. --- Corollary. --- Derived category. --- Diagonal functor. --- Diagram (category theory). --- Dimension theory (algebra). --- Dimension theory. --- Dimension. --- Enriched category. --- Epimorphism. --- Equivalence class. --- Equivalence relation. --- Existence theorem. --- Existential quantification. --- Factorization system. --- Functor category. --- Functor. --- Fundamental group. --- Grothendieck topology. --- Grothendieck universe. --- Group homomorphism. --- Groupoid. --- Heyting algebra. --- Higher Topos Theory. --- Higher category theory. --- Homotopy category. --- Homotopy colimit. --- Homotopy group. --- Homotopy. --- I0. --- Inclusion map. --- Inductive dimension. --- Initial and terminal objects. --- Inverse limit. --- Isomorphism class. --- Kan extension. --- Limit (category theory). --- Localization of a category. --- Maximal element. --- Metric space. --- Model category. --- Monoidal category. --- Monoidal functor. --- Monomorphism. --- Monotonic function. --- Morphism. --- Natural transformation. --- Nisnevich topology. --- Noetherian topological space. --- Noetherian. --- O-minimal theory. --- Open set. --- Power series. --- Presheaf (category theory). --- Prime number. --- Pullback (category theory). --- Pushout (category theory). --- Quillen adjunction. --- Quotient by an equivalence relation. --- Regular cardinal. --- Retract. --- Right inverse. --- Sheaf (mathematics). --- Sheaf cohomology. --- Simplicial category. --- Simplicial set. --- Special case. --- Subcategory. --- Subset. --- Surjective function. --- Tensor product. --- Theorem. --- Topological space. --- Topology. --- Topos. --- Total order. --- Transitive relation. --- Universal property. --- Upper and lower bounds. --- Weak equivalence (homotopy theory). --- Yoneda lemma. --- Zariski topology. --- Zorn's lemma.
Listing 1 - 10 of 46 | << page >> |
Sort by
|