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Mathematical theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold
Singularity_theory
Condition in which spacetime itself breaks down
A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that
Gravitational_singularity
Point where a mathematical object behaves irregularly
an algebraic variety. For singularities in differential geometry, see singularity theory. In real analysis, singularities are either discontinuities
Singularity_(mathematics)
Topic in systems theory
In systems theory, a singularity refers to a critical condition in which relatively small changes, perturbations, or events may produce disproportionately
Singularity_(systems_theory)
Hypothetical event
The technological singularity, often simply called the singularity, is a hypothetical event in which technological growth accelerates beyond human control
Technological_singularity
Concept in algebraic topology
fairly concrete constructions (see also the related theory simplicial homology). In brief, singular homology is constructed by taking maps of the standard
Singular_homology
Time period of seeming infinite density just after the Big Bang
The initial singularity or the Big Bang singularity is a simplified model for the origin of the universe, obtained by extrapolating the Big Bang model
Initial_singularity
Topics referred to by the same term
Look up Singularity or singularity in Wiktionary, the free dictionary. Singularity or singular point may refer to: Mathematical singularity, a point at
Singularity
Russian mathematician (1937–2010)
differential-geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem. In his later years
Vladimir_Arnold
Key results in general relativity on gravitational singularities
general theory of relativity". A singularity in solutions of the Einstein field equations is one of three things: Spacelike singularities: The singularity lies
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Concept in algebraic geometry
does not is given by the isolated singularity of x2 + y3z + z3 = 0 at the origin. Blowing it up gives the singularity x2 + y2z + yz3 = 0. It is not immediately
Resolution_of_singularities
Point on a curve where motion must move backwards
type A2-singularity. Let f (x, y) be a smooth function of x and y and assume, for simplicity, that f (0, 0) = 0. Then a type A2-singularity of f at (0
Cusp_(singularity)
Description of the degeneracy of a function
In mathematics, and in particular singularity theory, an Ak singularity, where k ≥ 0 is an integer, describes a level of degeneracy of a function. The
Ak_singularity
Philosophical movement
only the will of mankind as a whole. The concept of the technological singularity, or the ultra-rapid advent of superhuman intelligence, was first proposed
Transhumanism
Solution to the Einstein field equations
Schwarzschild metric has a singularity for r = 0, which is an intrinsic curvature singularity. It also seems to have a singularity on the event horizon r
Schwarzschild_metric
Singularities of algebraic varieties
(1985) and Reid. In particular, a terminal 3-fold singularity is the quotient of a hypersurface singularity with multiplicity 2 by a finite cyclic group.
Canonical_singularity
Algebraic structure used in topology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a way of attaching algebraic invariants to a topological space or
Cohomology
Area of mathematics
theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in
Catastrophe_theory
Point without a tangent space
two and the tangent cone is not singular outside its vertex. Milnor map Resolution of singularities Singularity theory Zariski tangent space Hartshorne
Singular point of an algebraic variety
Singular_point_of_an_algebraic_variety
American mathematician (1907–1989)
founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes and, geometric integration theory. Hassler
Hassler_Whitney
2012 film
The Singularity is a 2012 documentary film about the technological singularity, produced and directed by Doug Wolens. The film has been called "a large-scale
The_Singularity_(film)
Russian mathematician
singularity theory, whose contributions to the subject are fundamental. He has published several books and a variety of papers in singularity theory,
Victor_Goryunov
Mathematical concept describing isolated singularity of an algebraic surface
a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex
Du_Val_singularity
{x} \}\times M\to \mathbb {R} } has degenerate singularity at some p. A function has degenerate singularity if both the Jacobian matrix of first order partial
Affine_focal_set
Quantum description of black holes
the gravitational singularity that exists within the event horizon of a black hole. General relativity predicts that at the singularity, the curvature of
Fuzzball_(string_theory)
French mathematician (1923–2002)
reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the
René_Thom
Gravitational singularity of a rotating black hole
A ring singularity or ringularity is the gravitational singularity of a rotating black hole, or a Kerr black hole, that is shaped like a ring. When a
Ring_singularity
matrix theory Representation theory Ring theory Scheme theory Semigroup theory Set theory Shape theory Sheaf theory Sieve theory Singularity theory Soliton
List_of_mathematical_theories
Branch of mathematics
theory, such as the field of rational numbers, number fields, finite fields, function fields, and p-adic fields. A large part of singularity theory is
Algebraic_geometry
Hypothetical phenomenon
In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon. When there exists at least one causal
Naked_singularity
Matrix of second derivatives
saddle point). However, more can be said from the point of view of Morse theory. The second-derivative test for functions of one and two variables is simpler
Hessian_matrix
Hypothetical object of spacetime
general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy, matter, light
White_hole
Type of spacetime singularity in fiction
term quantum singularity is used to refer to many different phenomena in fiction. They often only approximate a gravitational singularity in the scientific
Quantum_singularity
Computer algebra system
commutative and non-commutative algebra, algebraic geometry, and singularity theory. Singular has been released under the terms of GNU General Public License
Singular_(software)
In algebraic geometry, a crepant resolution of a singularity is a resolution that does not affect the canonical class of the manifold. The term "crepant"
Crepant_resolution
British mathematician (1925–2016)
geometric topology and singularity theory. Zeeman's main contributions to mathematics were in topology, particularly in knot theory, the piecewise linear
Christopher_Zeeman
Envelope of rays either reflected or refracted by a manifold
More generally, especially as applied to symplectic geometry and singularity theory, a caustic is the critical value set of a Lagrangian mapping (π ○
Caustic_(mathematics)
Invariant that plays a role in algebraic geometry and singularity theory
hypersurface singularity. Assume it is an isolated singularity: in the case of holomorphic mappings it is said that a hypersurface singularity f {\displaystyle
Milnor_number
Point on a curve not given by a smooth embedding of a parameter
y 2 = 0. {\displaystyle x^{5}-y^{2}=0.} Singular point of an algebraic variety Singularity theory Morse theory Hilton Chapter II §1 Hilton Chapter II §2
Singular_point_of_a_curve
Val singularities. Elliptic singularity (Kollár & Mori 1998, Theorem 5.22.) (Artin 1966) Artin, Michael (1966), "On isolated rational singularities of
Rational_singularity
Point where the derivative of a function is zero or undefined (in certain cases)
polynomials that define the variety. Singular point of a curve Singularity theory Nullcline Milnor, John (1963). Morse Theory. Princeton University Press. ISBN 0-691-08008-9
Critical_point_(mathematics)
Singularities of algebraic varieties
In algebraic geometry, a normal crossing singularity looks locally like a union of coordinate hyperplanes. There are two variants of the concept, a divisor
Normal_crossing_singularity
Catastrophe theory a branch of bifurcation theory from dynamical systems theory, and also a special case of the more general singularity theory from geometry
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Theorem in mathematical analysis
There are many variants of this lemma, which plays a basic role in singularity theory among other fields. The case m = 1 {\displaystyle m=1} was proven
Sard's_theorem
Right conoid ruled surface
important in the field of singularity theory, as a simple local model of a pinch point singularity. The pinch point and the fold singularity are the only stable
Whitney_umbrella
In mathematics, especially in singularity theory, the splitting lemma is a useful result due to René Thom which provides a way of simplifying the local
Splitting_lemma_(functions)
Location around which a function displays irregular behavior
essential singularity of a function is a "severe" singularity near which the function exhibits striking behavior. The category essential singularity is a "left-over"
Essential_singularity
Russian American mathematician
have been in symplectic topology and singularity theory, as well as their relation to topological string theories. Givental graduated from the famed Moscow
Alexander_Givental
(also spelled Arnol'd) is a spectral sequence used in singularity theory and normal form theory as an efficient computational tool for reducing a function
Arnold's_spectral_sequence
Superconductivity theory
(1 July 2013). "The Witten equation, mirror symmetry, and quantum singularity theory". Annals of Mathematics. 178 (1): 1–106. arXiv:0712.4021. doi:10.4007/annals
Ginzburg–Landau_theory
Geometric arrangements of points, foundational to Lie theory
connection to Lie theory (such as singularity theory). Finally, root systems are important for their own sake, as in spectral graph theory. As a first example
Root_system
Study of smooth real-valued functions on manifold and their singularities
In mathematics, at the junction of singularity theory and differential topology, Cerf theory is the study of families of smooth real-valued functions
Cerf_theory
Intellectual frameworks for interpreting archaeological data
occasionally referred to as philosophy of archaeology. There is no one singular theory of archaeology, but many, with different archaeologists believing that
Archaeological_theory
Three-dimensional shape
deltoid. The umbilic torus occurs in the mathematical subject of singularity theory, in particular in the classification of umbilical points which are
Umbilic_torus
Belizean-American mathematical physicist
geometry, singularities, and probability theory. His monograph "Singularity Theory and Gravitational Lensing" developed a mathematical theory of gravitational
Arlie_Petters
American mathematician (born 1983)
geometry course under Hironaka in his sixth year which focused on singularity theory and was based on Hironaka's current research rather than established
June_Huh
American mathematician (1942–2017)
was a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He was descended from Atherton Mather (1663–1734)
John_N._Mather
such as the Jones polynomial. He also works on singularity theory, topology, computational complexity theory, integral geometry, symplectic geometry, partial
Victor_Vasiliev
British mathematician and educator
at University of Bristol. Her research focuses on applications of singularity theory to the physical sciences. She has a strong interest in science policy
Catherine_Hobbs
Light bending by mass between source and observer
. Petters, Arlie O.; Levine, Harold; Wambsganss, Joachim (2001). Singularity Theory and Gravitational Lensing. Progress in Mathematical Physics. Vol. 21
Gravitational_lens
Academic journal
The Journal of Singularities is a peer-reviewed open-access scientific journal which publishes research in the area of singularity theory. It was established
Journal_of_Singularities
Square matrix without an inverse
quantum mechanics, signal processing, and more) for dealing with singularity. Today, singular matrices are a canonical subject in linear algebra: they delineate
Singular_matrix
hypersurface singularity. This has a similar setup, where a polynomial f {\displaystyle f} with f = 0 {\displaystyle f=0} having a singularity at the origin
Milnor_map
American mathematician (born 1931)
spheres where μ is known as the Milnor number. Milnor's 1968 book on his theory, Singular Points of Complex Hypersurfaces, inspired the growth of a huge and
John_Milnor
Way of decomposing a topological space
Spec ( − ) {\displaystyle {\text{Spec}}(-)} is the prime spectrum. Singularity theory Whitney conditions Stratifold Intersection homology Thom's first isotopy
Thom–Mather_stratified_space
Operation in differential geometry
each point of its domain. Although this is the definition of a jet, the theory of jets regards these polynomials as being abstract polynomials rather than
Jet_(mathematics)
American cosmologist (born 1950)
University of Oregon for work with Richard Barrar on singularity theory, with a dissertation titled Singularities in the N-Body Problem. Swimme's published work
Brian_Swimme
English mathematician, mathematical physicist (born 1931)
singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of
Roger_Penrose
\ldots ,{\frac {\partial f}{\partial x_{n}}}\right\rangle .} In deformation theory, the deformations of a hypersurface given by a polynomial f {\displaystyle
Jacobian_ideal
American mathematician
fundamental contributions to singularity theory – in particular, to the fields of singularities of maps and equisingularity theory. He is a Professor of Mathematics
Terence_Gaffney
Theory of gravitation as curved spacetime
the classical models predict the big bang singularity. An authoritative answer would require a complete theory of quantum gravity, which has not yet been
General_relativity
Topologies defined on the set of smooth mappings between manifolds
mathematics, and especially differential topology, functional analysis and singularity theory, the Whitney topologies are a countably infinite family of topologies
Whitney_topologies
In mathematics, stratified Morse theory is an analogue to Morse theory for general stratified spaces, originally developed by Mark Goresky and Robert
Stratified_Morse_theory
Stratifiability condition in mathematical topology
to Heisuke Hironaka). This has led to their use in engineering, control theory and robotics. In a thesis under the direction of Wieslaw Pawlucki at the
Whitney_conditions
Russian and Canadian mathematician (born 1947)
commutative algebra, singularity theory, differential geometry and differential equations. His research is in the development of the theory of toric varieties
Askold_Khovanskii
Polynomial related to differential operators
polynomials used in approximation theory. It has applications to singularity theory, monodromy theory, and quantum field theory. Severino Coutinho (1995) gives
Bernstein–Sato_polynomial
Swiss mathematician (born 1941)
A'Campo (born 27 April 1941) is a Swiss mathematician working on singularity theory. He earned a doctorate in 1972 from the University of Paris-Sud. In
Norbert_A'Campo
English mathematician (1945–2017)
interaction, medical imaging, patent writing and singularity theory. His books on catastrophe theory and on differential geometry and relativity are still
Tim_Poston
Physical theory of the cosmos
gravitational singularity with infinite density and temperature at a finite time in the past. However this classical gravitational theory is expected to
Big_Bang
Notion in algebraic geometry
branches of algebraic geometry, most notably birational geometry and singularity theory. Roughly speaking, motivic integration assigns to subsets of the arc
Motivic_integration
Two functions having equal values and derivatives at a given point
Legendre transformation. Contact between manifolds is often studied in singularity theory, where the type of contact are classified, these include the A series
Contact_(mathematics)
the Columbia University and Harvard University. He specializes in singularity theory in algebraic geometry. In 1958, while studying at the University of
Joseph_Lipman
Test of a machine's ability to imitate human intelligence
zombie Problem of other minds Sentience Social bot Technological singularity Theory of mind Voight-Kampff machine (fictitious Turing test from Blade Runner)
Turing_test
Brazilian mathematician
Brazilian mathematician specializing in differential geometry and singularity theory. She was a professor at the University of São Paulo. Ruas was born
Maria_Aparecida_Soares_Ruas
Type of surface singularity used in algebraic geometry
algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic genus
Elliptic_singularity
Bois singularities are singularities of complex varieties studied by Du Bois. Schwede gave the following characterisation of Du Bois singularities. Suppose
Du_Bois_singularity
singularity theory and other parts of algebraic geometry. They are those homology cycles of a smooth fiber in a family which vanish in the singular fiber
Vanishing_cycle
Mathematical equivalence relation
map germs. It was introduced by John Mather in his seminal work in Singularity theory in the 1960s as a technical tool for studying stable maps. Since then
K-equivalence
Conjecture in physics
Penrose–Hawking singularity theorems, singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe
Cosmic_censorship_hypothesis
Concept in differential equation mathematics
coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction
Regular_singular_point
Methods of mathematical approximation
shell-crossing (sc) occurs in perturbation theory when matter trajectories intersect, forming a singularity. This limits the predictive power of physical
Perturbation_theory
"Geometric methods in the representation theory of Hecke algebras and quantum groups", Representation theories and algebraic geometry (Montreal, PQ, 1997)
Springer_resolution
British mathematician
singularity theory, "The Geometry of Topological Stability" (1995) (containing a great deal of original work) with Andrew du Plessis, and "Singular Points
C._T._C._Wall
1966b), is the intersection of a small sphere around the origin with the singular, complex hypersurface x 1 k 1 + ⋯ + x n k n = 0 {\displaystyle x_{1}^{k_{1}}+\cdots
Brieskorn_manifold
Conjecture in algebraic geometry
free module over R, then V is smooth. Nakai, Yoshikazu (1961), "On the theory of differentials in commutative rings", Journal of the Mathematical Society
Nakai_conjecture
French mathematician (born 1943)
following the pioneering efforts of Stephen Smale, and also worked on singularity theory. Later in his career he worked on mathematical problems of celestial
Alain_Chenciner
2022 novel by John Banville
theory, a mathematical concept of space and time which predicted multiple universes. He published his theories in a paper entitled "On singularities and
The_Singularities
Class of discontinuous functions
Singularity functions are a class of discontinuous functions that contain singularities, i.e., they are discontinuous at their singular points. Singularity
Singularity_function
Theorem about smooth complex functions
Golubitsky, Martin; Guillemin, Victor (1973), Stable Mappings and Their Singularities, Graduate Texts in mathematics 14, Springer-Verlag, ISBN 0-387-90073-X
Malgrange_preparation_theorem
Theoretical future event
arguing that a big crunch/ final singularity is still required under many current universal models. The technological singularity is the hypothetical advent
Omega_Point
SINGULARITY THEORY
SINGULARITY THEORY
Boy/Male
Muslim
Singularity
Surname or Lastname
English
English : according to Reaney this is a nickname from an unattested Old English word cybbe meaning ‘clumsy’ or ‘thickset’. Reaney’s speculation is apparently based on taking the Middle English word kibble ‘cudgel’ as a diminutive of an unattested Old English word. Corresponding personal names have been postulated for the place names Kibworth (‘enclosure of a man called Cybba’) and Kibblesworth (‘enclosure of a man called Cybbel’); so, in theory, the surname could be a reflex of these Old English personal names.North German : nickname for a cantankerous person, from Middle Low German, Middle High German kiven ‘to quarrel’.
Surname or Lastname
English, Scottish, and Irish (of Norman origin)
English, Scottish, and Irish (of Norman origin) : of disputed origin. It may be from a Celtic personal name derived from the element cam ‘bent’, ‘crooked’ (compare Cameron and Campbell). This was relatively frequent in Norfolk, Lincolnshire, and Yorkshire in the 12th and 13th centuries, perhaps as a result of Breton immigration. According to another theory it is a habitational name from Comines near Lille, but there is no evidence for this (no early forms with de have been found). In southern Ireland this Anglo-Norman name has been confused with 2.Irish : Anglicized form of Gaelic Mac CuimÃn (or Ó CuimÃn) ‘son (or ‘descendant’) of CuimÃn’, a personal name formed from a diminutive of cam ‘crooked’.Americanized form of French Canadian Vien, Viens, based on the misconception that these derive from French venire ‘to come’.
Surname or Lastname
English (mainly Gloucestershire), Dutch, and German (also Türk)
English (mainly Gloucestershire), Dutch, and German (also Türk) : from Middle English, Old French turc, Middle High and Low German Turc ‘Turk’, from Turkish türk. In theory this could be an ethnic name but, both in England and northwest Europe, it is generally a nickname for a person with black hair and a swarthy complexion or a cruel, rowdy, or unruly person. The Dutch and German surname also represents a house name, derived from the use of a picture of a Turk as a house sign. It is also found as a nickname for someone who had taken part in the wars against the Turks.English : from a medieval personal name, a back-formation from Turkel, misanalyzed as containing the Old French diminutive suffix -el.Scottish : reduced Anglicized form of Gaelic Mac Tuirc, a patronymic from the byname Torc ‘boar’.Jewish (Ashkenazic) : ethnic name denoting someone from Turkey or anywhere in the Ottoman Empire, or a nickname for someone thought to resemble a Turk.Americanized form of the Greek ethnic name Tourkos ‘Turk’. See also Turco.
Girl/Female
Muslim/Islamic
Singularity
Surname or Lastname
English and Scottish
English and Scottish : topographic name for someone who lived by a patch of wet ground overgrown with brushwood, northern Middle English kerr (Old Norse kjarr). A legend grew up that the Kerrs were left-handed, on theory that the name is derived from Gaelic cearr ‘wrong-handed’, ‘left-handed’.Irish : see Carr.This surname has also absorbed examples of German Kehr.
Girl/Female
Arabic, Muslim, Sindhi
Singularity
Surname or Lastname
English
English : unexplained. It may be a variant of a medieval name, Preville, a habitational name from a Norman place named with the elements pré ‘meadow’ + ville ‘settlement’. However, this theory is not supported by evidence of early forms.
Surname or Lastname
English
English : from a short form of the personal names Giles, Julian, or William. In theory the name would have a soft initial when derived from the first two of these, and a hard one when from William or from the other possibilities discussed in 2–4 below. However, there has been much confusion over the centuries.Northern English : topographic name for someone who lived by a ravine or deep glen, Middle English gil(l), Old Norse gil ‘ravine’.Scottish and Irish : reduced Anglicized form of Gaelic Mac Gille (Scottish), Mac Giolla (Irish), patronymics from an occupational name for a servant or a short form of the various personal names formed by attaching this element to the name of a saint. See McGill. The Old Norse personal name Gilli is probably of this origin, and may lie behind some examples of the name in northern England.Scottish and Irish : reduced Anglicized form of Gaelic Mac An Ghoill (see Gall 1).Norwegian : habitational name from any of three farmsteads in western Norway named Gil, from Old Norse gil ‘ravine’.Dutch : cognate of Giles.Jewish (Israeli) : ornamental name from Hebrew gil ‘joy’.German : from a vernacular short form of the medieval personal name Aegidius (see Gilger).Indian (Panjab) : Sikh name, probably from Panjabi gil ‘moisture’, also meaning ‘prosperity’. There is a Jat tribe that bears this name; the Ramgarhia Sikhs also have a clan called Gill.
Boy/Male
Indian
Singularity
SINGULARITY THEORY
SINGULARITY THEORY
Biblical
Shamer, prison; bush; lees; thorn
Female
Greek
(Ἀλκμήνη) Greek name ALKMENE means "might of the moon." In mythology, this is the name of the mortal mother of Herakles by Zeus.
Female
Scottish
Pet form of English/Scottish Anstice, ANSTEY means "resurrection."
Girl/Female
Arabic, Muslim
Good Fortune
Girl/Female
Tamil
Rajdulari | ராஜதà¯à®²à®¾à®°à¯€
Dear princess
Boy/Male
Gaelic
Slender; fair. Form of Caelan.
Boy/Male
Tamil
New
Boy/Male
Indian, Punjabi, Sikh
Glorious Victory
Boy/Male
Hindu, Indian
Knowledge
Girl/Female
Greek
Lover of man.
SINGULARITY THEORY
SINGULARITY THEORY
SINGULARITY THEORY
SINGULARITY THEORY
SINGULARITY THEORY
v. t.
To make singular or single; to distinguish.
n.
Possession of a particular or exclusive privilege, prerogative, or distinction.
n.
Singularity; strangeness; eccentricity; irregularity; uncouthness; as, the oddness of dress or shape; the oddness of an event.
n.
The quality or state of being singular; some character or quality of a thing by which it is distinguished from all, or from most, others; peculiarity.
n.
Narrowness or illiberality of opinion; prejudice; exclusiveness; as, the insularity of the Chinese or of the aristocracy.
pl.
of Singularity
n.
The philosophical explanation of phenomena, either physical or moral; as, Lavoisier's theory of combustion; Adam Smith's theory of moral sentiments.
n.
A genus of tropical apocynaceous shrubs having singularly twisted flowers. One species (Strophanthus hispidus) is used medicinally as a cardiac sedative and stimulant.
n.
The quality or state of being odd; singularity; queerness; peculiarity; as, oddity of dress, manners, and the like.
n.
One who affects singularity.
n.
The quality or state of being peculiar; individuality; singularity.
adv.
Singularly; peculiarly.
n.
Anything singular, rare, or curious.
adv.
So as to express one, or the singular number.
adv.
In a singular manner; in a manner, or to a degree, not common to others; extraordinarily; as, to be singularly exact in one's statements; singularly considerate of others.
n.
Celibacy.
n.
The quality or state of being angular; angularness.
n.
The state or quality of being an island or consisting of islands; insulation.
adv.
Strangely; oddly; as, to behave singularly.