Every idea

Ideas 7801–7950 of 14183.

Name	Kind	Subject
Lazard's theorem on p-adic analytic groups	Theorem	Topological groups, Lie groups
Margulis superrigidity theorem	Theorem	Topological groups, Lie groups
Automorphism	Concept	General algebraic systems
Admissible decision rule	Concept	Statistics
Stationary process	Concept	Probability theory and stochastic processes
Direct collocation	Definition	Calculus of variations and optimal control; optimization
Essentially self-adjoint operator	Concept	Operator theory
Compactness via ultrafilters	Theorem	General topology
Pfaffian system	Definition	Global analysis, analysis on manifolds
Spherical harmonics	Definition	Special functions
Topos	Definition	Category theory; homological algebra
Moser's worm problem	Problem	Convex and discrete geometry
Left ideal	Definition	Associative rings and algebras
O-minimal theory	Concept	Mathematical logic and foundations
Initial value problem for a recurrence	Definition	Difference and functional equations
Presheaf	Definition	Category theory; homological algebra
Countably compact space	Definition	General topology
Quasilinear PDE	Definition	Partial differential equations
Atomistic lattice	Definition	Order, lattices, ordered algebraic structures
Optimal control of partial differential equations	Definition	Calculus of variations and optimal control; optimization
Dirichlet-to-Neumann operator	Definition	Partial differential equations
Raviart–Thomas elements	Object	Numerical analysis
Curve-shortening flow	Concept	Differential geometry
Stone's theorem on one-parameter unitary groups	Theorem	Operator theory
Morrey quasiconvexity	Concept	Calculus of variations and optimal control; optimization
Bessel potential space	Concept	Functional analysis
Coequalizer	Concept	Category theory; homological algebra
Plateau's problem	Problem	Calculus of variations and optimal control; optimization
Dirichlet form	Definition	Potential theory
Loeb measure	Concept	Measure and integration
Validated numerics	Concept	Numerical analysis
Riesz–Markov–Kakutani representation theorem	Theorem	Measure and integration
Lebesgue integral	Concept	Measure and integration
Poisson's equation	Concept	Partial differential equations
Universal covering group	Definition	Topological groups, Lie groups
Harmonic space	Concept	Potential theory
Perfectly normal space	Definition	General topology
Many-valued logic	Concept	Mathematical logic and foundations
Affine connection	Definition	Differential geometry
C-infinity ring	Definition	Global analysis, analysis on manifolds
Laplace transform of the error function	Example	Integral transforms, operational calculus
Minimum description length	Definition	Statistics
Surface of general type	Definition	Algebraic geometry
Degree of a continuous map	Definition	Algebraic topology
The Klein four-group is abelian but not cyclic	Example	Group theory and generalizations
Darcy's law	Fact	Fluid mechanics
CAT(0) group	Definition	Group theory and generalizations
Section and retraction	Concept	Category theory; homological algebra
Expander graph	Concept	Combinatorics
Pixley term	Definition	General algebraic systems
von Neumann regular ring	Concept	Associative rings and algebras
Hypergeometric function of a matrix argument	Concept	Special functions
Kobayashi metric	Concept	Several complex variables and analytic spaces
James space	Example	Functional analysis
Hyperbolic knot	Definition	Manifolds and cell complexes
Kendall rank correlation coefficient	Concept	Statistics
Priestley space	Definition	Order, lattices, ordered algebraic structures
Borel measure	Concept	Measure and integration
Levi–Malcev decomposition	Theorem	Topological groups, Lie groups
Minimal variety	Definition	General algebraic systems
Locally finite family	Concept	General topology
Integral equation of the third kind	Concept	Integral equations
Inverse limit	Concept	Category theory; homological algebra
Newton series	Definition	Difference and functional equations
Schubert variety	Definition	Algebraic geometry
Unitary representation	Definition	Topological groups, Lie groups
Birkhoff–Frink theorem	Theorem	Order, lattices, ordered algebraic structures
Merton's portfolio problem	Problem	Game theory, economics, finance, and other social and behavioral sciences
Hermite interpolation	Definition	Approximations and expansions
Elementary abelian group	Concept	Group theory and generalizations
Picard group of a ring	Concept	Commutative algebra
Coordinate ring	Definition	Algebraic geometry
Fenichel's theorem	Theorem	Ordinary differential equations
Hall subgroup	Definition	Group theory and generalizations
Dowker space	Definition	General topology
Chern–Simons theory	Definition	Manifolds and cell complexes
Ternary operation	Definition	General algebraic systems
Del Pezzo surface	Definition	Algebraic geometry
Long exact sequence of homotopy groups	Theorem	Algebraic topology
Arithmetic–geometric mean and elliptic integrals	Theorem	Special functions
Discriminant of a number field	Concept	Number theory
Canonical correlation	Concept	Statistics
Monstrous moonshine	Theorem	Number theory
Euler–Lotka equation	Example	Integral equations
Complexification of a Lie group	Definition	Topological groups, Lie groups
Residue calculus for Laplace inversion	Concept	Integral transforms, operational calculus
Admissible representation	Definition	Topological groups, Lie groups
Heat potential	Definition	Partial differential equations
Invertible ideal	Concept	Commutative algebra
Fold catastrophe	Example	Global analysis, analysis on manifolds
Recurrent point	Definition	Dynamical systems and ergodic theory
Graded manifold	Concept	Global analysis, analysis on manifolds
ℓ-adic cohomology	Concept	Algebraic geometry
s-cobordism theorem	Theorem	Manifolds and cell complexes
Kaplansky's zero divisor conjecture	Conjecture	Associative rings and algebras
Involute	Concept	Differential geometry
Kloosterman sum	Concept	Number theory
Semianalytic set	Concept	Several complex variables and analytic spaces
Subdivision surface	Definition	Numerical analysis
Closing lemma	Theorem	Dynamical systems and ergodic theory
Toric variety	Definition	Algebraic geometry
Proximal operator	Concept	Operations research, mathematical programming
Weak equivalence	Concept	Category theory; homological algebra
Self-avoiding walk	Concept	Statistical mechanics, structure of matter
Craig interpolation theorem	Theorem	Mathematical logic and foundations
Regular function	Definition	Algebraic geometry
Line with two origins	Counterexample	General topology
Indecomposable module	Concept	Associative rings and algebras
Rosenbrock methods	Proposition	Numerical analysis
Singular integral equation	Concept	Integral equations
Residuated lattice	Concept	Order, lattices, ordered algebraic structures
Special adjoint functor theorem	Theorem	Category theory; homological algebra
Higher-order differences	Definition	Difference and functional equations
Berezin integral	Definition	Global analysis, analysis on manifolds
L-estimator	Concept	Statistics
Completeness of the real numbers	Theorem	Real functions
Hyperbolic group	Definition	Group theory and generalizations
Lie pseudogroup	Concept	Global analysis, analysis on manifolds
Fréchet mean	Concept	Statistics
Wigner's classification	Theorem	Topological groups, Lie groups
Ramanujan summation	Concept	Sequences, series, summability
Noncentral chi-squared distribution	Definition	Statistics
Furstenberg's multiple recurrence theorem	Theorem	Dynamical systems and ergodic theory
Transcendence basis	Concept	Field theory and polynomials
Blowing up	Definition	Algebraic geometry
Muller's method	Theorem	Numerical analysis
Kirby–Siebenmann class	Concept	Manifolds and cell complexes
Differential equations in Banach spaces	Definition	Ordinary differential equations
Order topology	Definition	General topology
Characterizations of semisimple modules	Theorem	Associative rings and algebras
Maximal order	Concept	Associative rings and algebras
Schouten–Nijenhuis bracket	Definition	Global analysis, analysis on manifolds
Hájek–Le Cam convolution theorem	Theorem	Statistics
Wente torus	Counterexample	Differential geometry
SU(2)	Example	Topological groups, Lie groups
Planar ternary ring	Definition	Geometry
Menger's theorem	Theorem	Combinatorics
Lawvere–Tierney topology	Concept	Category theory; homological algebra
Energy of a map between Riemannian manifolds	Concept	Global analysis, analysis on manifolds
Realizability	Definition	Mathematical logic and foundations
Infinite product measure	Definition	Measure and integration
Green's function of a Markov process	Definition	Probability theory and stochastic processes
Kernel pair	Concept	Category theory; homological algebra
Bessel function of the second kind	Definition	Special functions
Total variation of a measure	Definition	Measure and integration
Littlewood's three principles	Definition	Measure and integration
Functional square root	Concept	Difference and functional equations
Zariski tangent space	Concept	Algebraic geometry
Glivenko–Cantelli theorem	Theorem	Statistics
Complexification of a real analytic manifold	Theorem	Several complex variables and analytic spaces