title stringlengths 1 131 | url stringlengths 33 167 | content stringlengths 0 637k |
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Amalendu Krishna | https://ncatlab.org/nlab/source/Amalendu+Krishna |
* [Wikipedia entry](https://de.wikipedia.org/wiki/Amalendu_Krishna)
* [institute home page](http://www.tifr.res.in/People_Finder/compcode.php?param1=39)
## related $n$Lab entries
* [[algebraic K-theory]]
category: people |
amalgamation | https://ncatlab.org/nlab/source/amalgamation |
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#### Limits and colimits
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Traditionally:
* **in [[group theory]]**
1. the term *[[amalgamated free product of groups]]* refers to what really are *[[pushouts]]* ... |
amalgamation property | https://ncatlab.org/nlab/source/amalgamation+property |
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### Context
#### Model theory
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#Contents#
* table of contents
{:toc}
## Idea
A class of [[structures in model theory]] has the __amalgamation property__ if for any three structu... |
amalgamation theory | https://ncatlab.org/nlab/source/amalgamation+theory |
## Related concepts
* [[amalgamation]]
* [[amalgamated free product of groups]]
* [[amalgamation property]]
[[!redirects amalgamation theoies]] |
Amanda Peet | https://ncatlab.org/nlab/source/Amanda+Peet |
* [webpage](http://ap.io/home/about-prof-peet/)
## Selected writings
On [[S-branes]]:
* {#KruczenskiMyersPeet02} [[Martin Kruczenski]], [[Robert Myers]], [[Amanda Peet]], _Supergravity S-Branes_, JHEP 0205 (2002) 039 ([arXiv:hep-th/0204144](https://arxiv.org/abs/hep-th/0204144))
On [[D-brane polarization]... |
Amar Hadzihasanovic | https://ncatlab.org/nlab/source/Amar+Hadzihasanovic | * [website](https://www.irif.fr/~ahadziha/)
## Selected writings
On [[string diagrams]] and [[quantum entanglement]]:
* [[Amar Hadzihasanovic]], _The algebra of entanglement and the geometry of composition_, ([arXiv:1709.08086](https://arxiv.org/abs/1709.08086))
On [[rewriting]] in [[higher categories]]
... |
Amaria Javed | https://ncatlab.org/nlab/source/Amaria+Javed |
member of [[CQTS]]
* [GoogleScholar page](https://scholar.google.ae/citations?user=NTzY1lUAAAAJ&hl=en)
## Selected writings
on [[solitons]] in [[photonic crystals]]:
* [[Amaria Javed]], Alaa Shaheen U. Al Khawaja, *Amplifying optical signals with discrete solitons in waveguide arrays*, Physics Letters A *... |
amazing right adjoint | https://ncatlab.org/nlab/source/amazing+right+adjoint | [[!redirects fractional exponential]]
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#### Differential geometry
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#### Compact objects
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#Conten... |
Ambidexterity in K(n)-Local Stable Homotopy Theory | https://ncatlab.org/nlab/source/Ambidexterity+in+K%28n%29-Local+Stable+Homotopy+Theory |
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#### Stable Homotopy theory
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This page collects some links related to
* [[Michael Hopkins]], [[Jacob Lurie]]:
**Ambidexterity in $K(n)$-Local Stable Ho... |
ambidextrous adjunction | https://ncatlab.org/nlab/source/ambidextrous+adjunction |
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### Context
#### Category theory
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#### 2-Category theory
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#Contents#
* table of contents
{:toc}
## Definition
... |
ambient category | https://ncatlab.org/nlab/source/ambient+category | An ambient category $C$ is just a category from which [[internalization|internal structures]] take their objects and structure morphisms.
If $C$ has extra structure, like being ([[semi-abelian category|semi]]-)[[abelian category|abelian]] or a [[site]], then one can do extra things; this is made precise through the co... |
ambimorphic object > history | https://ncatlab.org/nlab/source/ambimorphic+object+%3E+history | < [[ambimorphic object]]
[[!redirects ambimorphic object -- history]] |
Ambrus Kaposi | https://ncatlab.org/nlab/source/Ambrus+Kaposi |
* [website](https://akaposi.github.io/)
## Selected writings
* [[Thorsten Altenkirch]], [[Ambrus Kaposi]], *Type Theory in Type Theory using Quotient Inductive Types*, POPL17 (2017) [[pdf](http://www.cs.nott.ac.uk/~psztxa/publ/tt-in-tt.pdf)]
On [[higher inductive-inductive types]]:
* {#Kapos... |
amenable category | https://ncatlab.org/nlab/source/amenable+category | An **amenable category** is an [[additive category]] in which all [[idempotent]]s split. |
amenable topological groupoid | https://ncatlab.org/nlab/source/amenable+topological+groupoid |
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#### Topology
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#Contents#
* table of contents
{:toc}
## Definition
([AD-Renault 00](#AD-Renault00))
Recall... |
Amer Iqbal | https://ncatlab.org/nlab/source/Amer+Iqbal |
* [Wikipedia entry](https://en.wikipedia.org/wiki/Amer_Iqbal)
## Selected writings
On [[string junctions]] in relation to [[Lie algebras]] and [[Lie algebra representations]]:
* Oliver DeWolfe, Tamas Hauer, [[Amer Iqbal]], [[Barton Zwiebach]], _Uncovering the Symmetries on $[p,q]$ 7-branes: Beyond the Ko... |
Amihay Hanany | https://ncatlab.org/nlab/source/Amihay+Hanany |
Amihay Hanany is professor for theoretical [[physics]] at Imperial College London.
* [webpage](http://www.imperial.ac.uk/people/a.hanany)
## Selected writings
On [[small instantons]] as [[NS5-branes]]/[[M5-branes]] in [[E8]]-[[heterotic string theory]]/[[heterotic M-theory]]:
* {#GanorHanany96} [[Ori Gano... |
Amir Dembo | https://ncatlab.org/nlab/source/Amir+Dembo |
* [webpage](http://statweb.stanford.edu/~adembo/)
## related $n$Lab entries
* [[probability theory]]
category: people |
Amir-Kian Kashani-Poor | https://ncatlab.org/nlab/source/Amir-Kian+Kashani-Poor |
* [webpage](www.phys.ens.fr/~kashani/index.html)
## related $n$Lab entries
* [[topological recursion]]
* [[topological string]]
* [[matrix model]]
category: people |
Amirhossein Tajdini | https://ncatlab.org/nlab/source/Amirhossein+Tajdini |
* [InSpire page](https://inspirehep.net/authors/1889144)
* [ResearchGate page](https://www.researchgate.net/scientific-contributions/Amirhossein-Tajdini-2116760582)
## Selected writings
Review of the claim that the proper application of [[holographic entanglement entropy]] to the discussion of [[Bekenstein-H... |
Amit Giveon | https://ncatlab.org/nlab/source/Amit+Giveon |
* [webpage](http://old.phys.huji.ac.il/~hep/amit.giveon.html)
## Selected writings
On [[geometric engineering of QFT]] in [[intersecting D-brane models]] subject to the [[s-rule]]:
* [[Amit Giveon]], [[David Kutasov]], _Brane Dynamics and Gauge Theory_, Rev. Mod. Phys. 71:983-1084, 1999 ([arXiv:hep-th/98... |
Amit Patel | https://ncatlab.org/nlab/source/Amit+Patel |
* [institute page](https://www.math.colostate.edu/~akp/)
* [personal page](http://akpatel.org/)
## Selected writings
Introducing [[well groups]]:
* {#EMP11} [[Herbert Edelsbrunner]], [[Dmitriy Morozov]], [[Amit Patel]], *Quantifying Transversality by Measuring the Robustness of Intersections*, Foundations... |
Amit Sever | https://ncatlab.org/nlab/source/Amit+Sever |
* [Institute page](https://en-exact-sciences.tau.ac.il/profile/asever)
## Selected writings
On [[Wilson line]]-[[quantum observables]] and [[bosonization]] in [[Chern-Simons theory|Chern-Simons]]/matter theory (such as the [[ABJM model]]):
* [[Amit Sever]], _Line Operators in Chern-Simons-Matter Theories and... |
Amit Sharma | https://ncatlab.org/nlab/source/Amit+Sharma |
* [MathGenealogy page](https://www.mathgenealogy.org/id.php?id=214520)
## Selected writings
On [[compact closed category|compact closure]] in [[homotopical algebra]] and relating to the [Barrat-Priddy theorem](stable+cohomotopy#AsAlgebraicKTheoryOverTheFieldWithOneElement):
* [[Amit Sharma]], *Compact closed... |
Amitai Regev | https://ncatlab.org/nlab/source/Amitai+Regev |
* [Wikipedia entry](https://en.wikipedia.org/wiki/Amitai_Regev)
## Selected writings
Expressing the number of [[standard Young tableaux]] with at most 3 rows through [[Catalan numbers]] and [[Motzkin numbers]]:
* [[Amitai Regev]], *Asymptotic values for degrees associated with strips of young diagrams*, Adva... |
Amitsur complex | https://ncatlab.org/nlab/source/Amitsur+complex |
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#### Algebra
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#### Homological algebra
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#### Locality and descent
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amnestic functor | https://ncatlab.org/nlab/source/amnestic+functor |
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#### Category theory
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# Amnestic functors
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{: toc}
## Idea
A [[strict functor]] is _amnestic_ if its [[domain]] has no more duplication of [[... |
Amnon Neeman | https://ncatlab.org/nlab/source/Amnon+Neeman | # Amnon Neeman
* [web site](http://wwwmaths.anu.edu.au/~neeman/)
## Selected writing
On [[triangulated categories]]:
* {#Neeman01} [[Amnon Neeman]], *Triangulated Categories*, Annals of Mathematics Studies **213**, Princeton University Press (2001) [[ISBN:9780691086866](https://press.princeton.edu/ti... |
Amnon Yekutieli | https://ncatlab.org/nlab/source/Amnon+Yekutieli |
Here are abstracts of a few papers of mine that connect to higher category theory, with links to the full texts. I will be glad to discuss this material.
### 1. Twisted Deformation Quantization of Algebraic Varieties ###
Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce th... |
ample sheaf | https://ncatlab.org/nlab/source/ample+sheaf |
## Definition
### General
(...)
### In complex geometry
In [[complex analytic geometry]] a [[line bundle]] is ample precisely if its [[Chern class]] is represented by a [[Kähler form]].
See also at _[[positive line bundle]]_.
## References
* Wikipedia, _[Ample line bundle](http://en.wikipedia.org/wiki/Ample_l... |
amplimorphism | https://ncatlab.org/nlab/source/amplimorphism |
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#### Algebra
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#### Operator algebra
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[[!include AQFT and operator algebra contents]]
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#Contents#
* table of contents
{:toc}
## Idea
The concept of _amplimorphism_ i... |
amplitude | https://ncatlab.org/nlab/source/amplitude |
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#### Harmonic analysis
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* table of contents
{:toc}
## Idea
The _amplitude_ of a [[wave]] is a measure for its maximal change with [[space]] and [[t... |
amplituhedron | https://ncatlab.org/nlab/source/amplituhedron |
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### Context
#### Physics
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* table of contents
{:toc}
## Idea
The [[scattering amplitudes]] in [[Yang-Mills theory]] are traditionally expressed as sums of typically very many... |
Amélia Liao | https://ncatlab.org/nlab/source/Am%C3%A9lia+Liao |
* [Website](https://amelia.how/)
## Talks
On [[univalent categories]] in [[homotopy type theory]]:
* [[Amélia Liao]], *Univalent Category Theory*, [[Homotopy Type Theory Electronic Seminar Talks]], 6 October 2022, ([slides](https://www.uwo.ca/math/faculty/kapulkin/seminars/hottestfiles/Liao-2022-10-06-HoTTES... |
An Descheemaeker | https://ncatlab.org/nlab/source/An+Descheemaeker |
* [Institute page I](https://www.kuleuven.be/wieiswie/nl/person/00011206)
* [Institute page II (publications)](https://kuleuven.academia.edu/AnDescheemaeker)
## Selected writing
On relative [[completions of groups]]:
* [[Carles Casacuberta]], [[An Descheemaeker]], *Relative group completions*, Journal of ... |
an elementary treatment of Hilbert spaces | https://ncatlab.org/nlab/source/an+elementary+treatment+of+Hilbert+spaces | +-- {: .rightHandSide}
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## Purpose of this page
The purpose of this page is to examine how much of the theory of [... |
An Essay on the Foundations of Geometry | https://ncatlab.org/nlab/source/An+Essay+on+the+Foundations+of+Geometry |
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#### Philosophy
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* [[Bertrand Russell]],
_An Essay on the Foundations of Geometry_,
Cambridge 1897,
[online version](http://bertrandrussellsocietylibrary.org/... |
An Exercise in Kantization | https://ncatlab.org/nlab/source/An+Exercise+in+Kantization | ## Motivation
Once, [[Johan Alm]] wrote some very neat notes:
* [Quantization as a Kan Extension](http://ncatlab.org/nlab/files/Kantization09May27.pdf)
A discussion is available at the [$n$Café](https://golem.ph.utexas.edu/category/2009/05/alm_on_quantization_as_a_kan_e.html). The paper proves an aspect of the... |
An Huang | https://ncatlab.org/nlab/source/An+Huang |
* [webpage](http://people.brandeis.edu/~anhuang/)
* [institute page](http://www.brandeis.edu/facultyguide/person.html?emplid=e225bcb771bc4cefeed959ca4b802ac0055303e5)
## selected writings
* {#HuangStoicaYau19} [[An Huang]], [[Bogdan Stoica]], [[Shing-Tung Yau]], _General relativity from $p$-adic strings_ ([a... |
An Introduction to Homological Algebra | https://ncatlab.org/nlab/source/An+Introduction+to+Homological+Algebra |
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This entry provides a hyperlinked index for the textbook
* [[Charles Weibel]],
**An Introduction to Homological Algebra**
C... |
Ana Canas da Silva | https://ncatlab.org/nlab/source/Ana+Canas+da+Silva |
* [webpage](https://people.math.ethz.ch/~acannas/)
## related $n$Lab entries
* [[geometric quantization]]
* [[geometric quantization by push-forward]]
category: people |
Ana Cannas da Silva | https://ncatlab.org/nlab/source/Ana+Cannas+da+Silva |
* [webpage](http://www.math.ethz.ch/~acannas/)
* [Wikipedia entry](https://en.wikipedia.org/wiki/Ana_Cannas_da_Silva)
## Selected writings
On [[geometric quantization]]:
* [[Ana Cannas da Silva]], [[Yael Karshon]], [[Susan Tolman]], *Quantization of Presymplectic Manifolds and Circle Actions*, Transactio... |
Ana-Maria Raclariu | https://ncatlab.org/nlab/source/Ana-Maria+Raclariu |
* [website](https://perimeterinstitute.ca/people/ana-maria-raclariu)
## Selected publications
On [[celestial holography]]:
* [[Nima Arkani-Hamed]], Monica Pate, [[Ana-Maria Raclariu]], [[Andrew Strominger]], *Celestial Amplitudes from UV to IR*, JHEP 08 (2021) 062 ([arXiv:2012.04208](https://arxiv.org/abs/20... |
anabelian geometry | https://ncatlab.org/nlab/source/anabelian+geometry |
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## Idea
In _anabelian geometry_ one studies how much information about a [[space]] $X$ (specifically: an [[a... |
anabelian group | https://ncatlab.org/nlab/source/anabelian+group |
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#### Group Theory
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* table of contents
{:toc}
## Idea
An _anabelian group_ is a group that is "far from being an [[abelian group]]" in a precise sense:
## Definition
... |
anabelioid | https://ncatlab.org/nlab/source/anabelioid | \tableofcontents
\section{Introduction}
An anabelioid is a category intended to play the role of a 'generalised geometric object' in algebraic/arithmetic geometry. Its definition is simple: a finite product of [[Galois category|Galois categories]], or in other words of [[classifying topos|classifying topoi]] of [... |
anabicategory | https://ncatlab.org/nlab/source/anabicategory | An **anabicategory** is a particular notion of _weak [[2-category]]_ appropriate in the absence of the [[axiom of choice]] (including in many [[internal category|internal]] contexts). It is derived from the notion of [[bicategory]] by replacing the composition functors $\circ: B(y,z) \times B(x,y) \to B(x,z)$ with [[a... |
anafunction | https://ncatlab.org/nlab/source/anafunction | # Anafunctions
* table of contents
{: toc}
## Idea
An *anafunction* is a [[relation]] between two [[sets]] $A,B$ such that to each [[element]] of $A$ there corresponds exactly one element of $B$. It can (usually) equivalently be defined as a [[span]] $A \leftarrow F \to B$ of functions whose first leg $F\to ... |
anafunctor | https://ncatlab.org/nlab/source/anafunctor |
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#### Category theory
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# Anafunctors
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{:toc}
## Ide... |
anafunctor category | https://ncatlab.org/nlab/source/anafunctor+category | Given [[category|categories]] $C$ and $D$, the _anafunctor category_ $D^C$ has [[anafunctor|anafunctors]] $F: C \to D$ as [[object|objects]] and [[ananatural transformation|ananatural transformations]] between these as [[morphism|morphisms]].
This is the appropriate notion of [[functor category]] to use in the absence... |
analogy | https://ncatlab.org/nlab/source/analogy |
#Contents#
* table of contents
{:toc}
## Examples
* [[function field analogy]]
* [[MKR analogy]]
* [[rubber-sheet analogy of gravity]]
## Related concepts
[[!include mathematical statements --- contents]]
## References
* Wikipedia, _[Analogy](http://en.wikipedia.org/wiki/Analogy)_
[[!re... |
analyser | https://ncatlab.org/nlab/source/analyser | Before the modern theory of [[operad]]s was (re)invented there was a variant introduced earlier in
* M. Lazard, _Lois de groupes et analyseurs_, Ann. École Norm. Sup. __72__ (1955), pp. 299–400.
under the name __analyser__ which is often even nowdays referred by its original French version *analyseur*.
Th... |
analysis | https://ncatlab.org/nlab/source/analysis |
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#### Analysis
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... |
analysis - contents | https://ncatlab.org/nlab/source/analysis+-+contents |
**[[analysis]]** ([[differential calculus|differential]]/[[integral calculus|integral]] [[calculus]], [[functional analysis]], [[topology]])
[[epsilontic analysis]]
[[infinitesimal analysis]]
[[computable analysis]]
_[[Introduction to Topology -- 1|Introduction]]_
## Basic concepts
[[triangle inequality]]
[[me... |
Analysis Situs | https://ncatlab.org/nlab/source/Analysis+Situs |
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... |
analytic (∞,1)-functor | https://ncatlab.org/nlab/source/analytic+%28%E2%88%9E%2C1%29-functor |
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#### Goodwillie calculus
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* table of contents
{:toc}
## Idea
In the context of [[Goodwillie calculus]] an [[(∞,1)-functor]] is called _analytic_ i... |
analytic affine line | https://ncatlab.org/nlab/source/analytic+affine+line |
#Contents#
* table of contents
{:toc}
## Idea
The analytic affine line is a [[Berkovich analytic space]] that is the analog of the [[affine line]] in [[analytic geometry]].
It is the [[analytic spectrum]] of the [[polynomial]] ring over the given base [[field]].
## References
* [[Jérôme Poineau]], _An introductio... |
analytic completion of a ring | https://ncatlab.org/nlab/source/analytic+completion+of+a+ring | [[!redirects analytic completion]]
#Contents#
* table of contents
{:toc}
## Idea
For $A$ a [[commutative ring]] and $p$ a [[prime number]], then there is the [[formal completion|topological completion]] at $(p)$, the _[[p-completion]]_ $A_p^\wedge \coloneqq \underset{\leftarrow}{\lim}_n A/(p^n A)$. The _ana... |
analytic continuation | https://ncatlab.org/nlab/source/analytic+continuation |
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#### Complex geometry
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{:toc}
## Idea
In [... |
analytic function | https://ncatlab.org/nlab/source/analytic+function |
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#### Analysis
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# Analytic functions
* table of contents
{: toc}
## Idea
An _anal... |
analytic geometry | https://ncatlab.org/nlab/source/analytic+geometry |
> This entry is about [[geometry]] based on the study of _[[analytic functions]]_, hence about [[analytic varieties]].
> This is unrelated to "analytic geometry" in the sense of methods in the geometry of $n$-dimensional [[Euclidean space]] involving *[[coordinate]] calculations* (as opposed to [[synthetic geomet... |
analytic geometry -- contents | https://ncatlab.org/nlab/source/analytic+geometry+--+contents |
**[[analytic geometry]] ([[complex analytic geometry|complex]], [[rigid analytic geometry|rigid]], [[global analytic geometry|global]])**
[[geometry]]+[[analysis]]/[[analytic number theory]]
## Basic concepts
[[analytic function]]
[[analytic space]], [[analytic variety]], [[Berkovich space]]
* [[polydisc]]
* [[a... |
analytic geometry ingredients -- table | https://ncatlab.org/nlab/source/analytic+geometry+ingredients+--+table |
| [[algebra|algebraic structure]] | [[group]] | [[ring]] | [[field]] | [[vector space]] | [[associative algebra|algebra]] |
|---|-----------|-----------|-------------------|--------------|---|
| (submultiplicative) [[norm]] | [[normed group]] | [[normed ring]] | [[normed field]] | [[normed vector space]] | [[... |
analytic Langlands program | https://ncatlab.org/nlab/source/analytic+Langlands+program | [[!redirects analytic langlands program]]
#Contents#
* table of contents
{:toc}
## Idea
The aim of analytic version of the [[Langlands program]] is to find a theory of analytic motives that gives a full correspondence between all (not only algebraic) automorphic representations and all analytic motives.
T... |
analytic manifold | https://ncatlab.org/nlab/source/analytic+manifold |
#Contents#
* table of contents
{:toc}
## Idea
An **analytic manifold** is a [[manifold]] with [[analytic function|analytic]] transition functions over some [[field]]. The most widely studied are real-analytic and complex analytic manifolds.
Analytic manifolds are studied in [[analytic geometry]].
## Re... |
analytic Markov's principle | https://ncatlab.org/nlab/source/analytic+Markov%27s+principle |
#Contents#
* table of contents
{:toc}
## Definition ##
The **analytic Markov's principle** states that the [[pseudo-order]] on the [[Dedekind real numbers]] is a [[stable relation]]: for all [[real numbers]] $r \in \mathbb{R}$ and $s \in \mathbb{R}$, $\neg \neg (r \lt s)$ implies $r \lt s$.
This is equiva... |
analytic monad | https://ncatlab.org/nlab/source/analytic+monad | ## Idea
Analytic monads are [[monads]] on [[Set]] that correspond to [[operads]] in [[Set]].
## Definition
More precisely, an [[operad]] $O$ in [[Set]] induces a [[monad]] $T$
on [[Set]]:
$$T(S)=\coprod_{n\ge0} O_n \times_{\Sigma_n} S^n.$$
Such a monad $T$ is equipped with a canonical weakly [[cartesian n... |
analytic motives | https://ncatlab.org/nlab/source/analytic+motives | Analytic motives give a common generalization of classical homotopy theory (Ayoub's analytic motives over C), algebraic motivic homotopy theory (strict analytic motives over Z with the trivial non-archimedean norm), and Ayoub's non-archimedean motives.
The basic idea is to extend motivic homotopy theory to a general b... |
analytic motivic homotopy theory | https://ncatlab.org/nlab/source/analytic+motivic+homotopy+theory | #Contents#
* table of contents
{:toc}
## Idea
Analytic motivic homotopy theory is an analytic generalization of [[motivic homotopy theory]] that gives back classical homotopy theory when one works with analytic varieties over $\mathbb{C}$ and motivic homotopy theory when one works with strict analytic varieties over ... |
analytic number theory | https://ncatlab.org/nlab/source/analytic+number+theory |
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###Context###
#### Analytic geometry
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* table of contents
{:toc}
## Idea
The branch of [[number theory]] that uses [[analysis]]. Related to [[global analytic geometry]] as [[nu... |
analytic philosophy | https://ncatlab.org/nlab/source/analytic+philosophy |
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### Context
#### Philosophy
+-- {: .hide}
[[!include philosophy - contents]]
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#Contents#
* table of contents
{:toc}
## Idea
_Analytic philosophy_ is a school of [[philosophy]] emphasizing clarity of argument, [[formal logic]],... |
analytic ring | https://ncatlab.org/nlab/source/analytic+ring | #Contents#
* table of contents
{:toc}
## Definition
\begin{definition}([ScholzeLCM](#ScholzeLCM), Def. 7.1)
In [[condensed mathematics]], a _pre-analytic ring_ is a [[condensed ring]] $\underline{A}$ together with a [[functor]] $S\mapsto\mathcal{A}[S]$ from [[extremally disconnected topological spaces]] to $... |
analytic space | https://ncatlab.org/nlab/source/analytic+space |
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### Context
#### Analytic geometry
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#### Complex geometry
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# Analytic spaces
* table of contents
{: toc}
## Idea
Analytic spaces are... |
analytic spectrum | https://ncatlab.org/nlab/source/analytic+spectrum |
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### Context
#### Analytic geometry
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[[!include analytic geometry -- contents]]
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#Contents#
* table of contents
{:toc}
## Idea
The concept of _analytic spectrum_ is a realization of the concept of [[spectrum (geometry)]] in the cont... |
analytic torsion | https://ncatlab.org/nlab/source/analytic+torsion |
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###Context###
#### Riemannian geometry
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[[!include Riemannian geometry - contents]]
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#Contents#
* table of contents
{:toc}
## Idea
What is called _analytic torsion_ or _Ray-Singer torsion_ ([Ray-Singer 73](#RaySinger... |
analytic variety | https://ncatlab.org/nlab/source/analytic+variety |
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### Context
#### Analytic geometry
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[[!include analytic geometry -- contents]]
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#### Complex geometry
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# Analytic varieties
* table of contents
{: toc}
## Idea
Analytic varieti... |
analytic versus synthetic | https://ncatlab.org/nlab/source/analytic+versus+synthetic |
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#### Philosophy
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#Contents#
* table of contents
{:toc}
## Idea
The analytic-synthetic distinction has a long history stretching back to the ancient Greeks. It has come... |
analytical index | https://ncatlab.org/nlab/source/analytical+index |
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### Context
#### Index theory
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[[!include index theory - contents]]
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#### Integration theory
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[[!include integration theory - contents]]
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=--
#Contents#
* table of contents
{:toc}
## Idea
By [[pseudo-differential operat... |
analytically continued Chern-Simons theory | https://ncatlab.org/nlab/source/analytically+continued+Chern-Simons+theory |
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#### $\infty$-Chern-Simons theory
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#### Quantum field theory
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[[!include functorial quantum field theory - contents]]
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#### Physics
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... |
analytically continued Wess-Zumino-Witten theory | https://ncatlab.org/nlab/source/analytically+continued+Wess-Zumino-Witten+theory |
## Idea
[[WZW model]] for non-compact [[complex Lie groups]] such as $SL(2,\mathbb{C})$
## Related concepts
* [[analytically continued Chern-Simons theory]]
* [[Liouville theory]]
## References
* Nobuyuki Ishibashi, _Extra Observables in Gauged WZW Models_, Nucl.Phys. B379 (1992) 199-219 ([arXiv:hep-th/9110071](... |
analytification | https://ncatlab.org/nlab/source/analytification |
> under construction
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### Context
#### Analytic geometry
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[[!include analytic geometry -- contents]]
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#### Complex geometry
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[[!include complex geometry - contents]]
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#Contents#
* table of contents
{... |
ananatural transformation | https://ncatlab.org/nlab/source/ananatural+transformation |
# Ananatural transformations
* table of contents
{: toc}
## Idea
Just as [[natural transformation|natural transformations]] go between [[functor|functors]], ananatural transformations go between [[anafunctor|anafunctors]].
Given two functors interpreted as anafunctors, the natural transformations and ananatural tra... |
Anand Dessai | https://ncatlab.org/nlab/source/Anand+Dessai |
* [webpage](https://homeweb.unifr.ch/dessaia/pub/)
## Selected writings
On the [[Witten genus]] and the [[Stolz conjecture]]:
* [[Anand Dessai]], _Some geometric properties of the Witten genus_, in: [[Christian Ausoni]], [[Kathryn Hess]], [[Jérôme Scherer]] (eds.) _Alpine Perspectives on Algebraic Topology_,... |
Anand Pillay | https://ncatlab.org/nlab/source/Anand+Pillay | __Anand Pillay__ is a model theorist, now at University of Notre Dame.
* [homepage](https://www3.nd.edu/~apillay) at Notre Dame
Related items: [[geometric stability theory]], [[definable set]], [[differential Galois theory]]
* _Remarks on Galois cohomology and definability_, The Journal of Symbolic Logic __62_... |
Ananda Roy | https://ncatlab.org/nlab/source/Ananda+Roy |
* [personal page](https://sites.rutgers.edu/ananda-roy/)
* [institute page](https://physics.rutgers.edu/people/faculty-list/faculty-profile/roy-ananda)
## Selected writings
On [[topological quantum computation]]:
* [[Ananda Roy]], [[David P. DiVincenzo]], *Topological Quantum Computing*, Lecture notes o... |
Anastasia Volovich | https://ncatlab.org/nlab/source/Anastasia+Volovich |
* [Wikipedia entry](https://en.wikipedia.org/wiki/Anastasia_Volovich)
* [Institute page](https://vivo.brown.edu/display/avolovic)
## Selected writings
On [[twistor string theory]]:
* {#RoibanVolovich04} [[Radu Roiban]], [[Anastasia Volovich]], *All Googly Amplitudes from the B-model in Twistor Space*, Phy... |
Anatoly Libgober | https://ncatlab.org/nlab/source/Anatoly+Libgober |
* [personal page](http://homepages.math.uic.edu/~libgober/)
* [Wikipedia entry](https://en.wikipedia.org/wiki/Anatoly_Libgober)
## Selected writings
On [[braid groups]], [[braid representations]] and some [[knot theory]]:
* [[Joan S. Birman]], [[Anatoly Libgober]] (eds.) *Braids*, Contemporary Mathematics... |
Anatoly Malcev | https://ncatlab.org/nlab/source/Anatoly+Malcev | [[!redirects A. I. Mal'cev]]
Anatoly Malcev (Анато́лий Ива́нович Ма́льцев; [ˈmɐlʲt͡sef]) was a Russian mathematician.
## Related entries
* [[Malcev completion]]
* [[Malcev variety]]
* [[Malcev category]]
* [[Kan object]]
* [[maximal compact subgroup]]
## References
[List of publications at ... |
Anatoly Shirshov | https://ncatlab.org/nlab/source/Anatoly+Shirshov | __Anatolij Illarionovič Širšov__ (Anatoly/Anatolii Illarinovich Shirshov, orig. Анатолий Илларионович Ширшов) was an [[algebra|algebraist]] working i... |
Anatoly Vershik | https://ncatlab.org/nlab/source/Anatoly+Vershik |
* [Wikipedia entry](https://en.wikipedia.org/wiki/Anatoly_Vershik)
## Selected writings
On the asymptotic number of [[standard Young tableaux]] (dimension of [[Specht modules]]) with respect to the [[Plancherel measure]]:
* {#VershikKerov85} [[Anatoly Vershik]], [[Sergei Kerov]], *Asymptotic of the largest a... |
Anaxagoras | https://ncatlab.org/nlab/source/Anaxagoras |
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### Context
#### Philosophy
+-- {: .hide}
[[!include philosophy - contents]]
=--
=--
=--
## Hegel on Anaxagoras
In the _[[Science of Logic]]_, [[Hegel]] writes
> [WdL §54](Science+of+Logic#54) Anaxagoras wird als derjenige gepriesen, der zuerst den Ge... |
Anayeli Ramirez | https://ncatlab.org/nlab/source/Anayeli+Ramirez |
* [webpage](https://uniovi.academia.edu/AnayeliRamirez)
## Selected writings
On [[black brane|black]]$\;$[[D6-D8-brane bound states]] in [[massive type IIA string theory]], with [[defect QFT|defect]] [[D2-D4-brane bound states]] inside them realizing [[AdS3-CFT2]] as [[defect field theory]] "inside" [[AdS7-CFT6... |
Anders Kock | https://ncatlab.org/nlab/source/Anders+Kock | Anders Kock is a mathematician at Aarhus University, Denmark. He has proved important results in [[category theory]] and particularly in [[synthetic differential geometry]].
[Homepage](https://users-math.au.dk/kock)
## Selected writings
On the [[2-category]] of [[complete categories]] being [[monadic functor... |
Anders Mörtberg | https://ncatlab.org/nlab/source/Anders+M%C3%B6rtberg |
* [webpage](https://staff.math.su.se/anders.mortberg/)
## Selected writings
On [[affine schemes]] in [[cubical type theory]]:
* [[Anders Mörtberg]], [[Max Zeuner]], *A Univalent Formalization of Affine Schemes* ([arXiv:2212.02902](https://arxiv.org/abs/2212.02902))
Introducing the [[programming language... |
Anders S. Buch | https://ncatlab.org/nlab/source/Anders+S.+Buch |
* [personal page](https://sites.math.rutgers.edu/~asbuch/)
## Selected writings
On [[quantum K-theory rings]]:
* [[Anders S. Buch]], [[Leonardo C. Mihalcea]], *Quantum K-theory of Grassmannians*, Duke Math. J. **156** 3 (2011) 501-538 [[arXiv:0810.0981](https://arxiv.org/abs/0810.0981), [doi:10.1215/0... |
Anderson duality | https://ncatlab.org/nlab/source/Anderson+duality |
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### Context
#### Stable Homotopy theory
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[[!include stable homotopy theory - contents]]
=--
#### Duality
+-- {: .hide}
[[!include duality - contents]]
=--
=--
=--
#Contents#
* table of contents
{:toc}
## Idea
The [[stable... |
Andor Lukacs | https://ncatlab.org/nlab/source/Andor+Lukacs |
* [website](http://www.staff.science.uu.nl/~lukac101/)
category: people |
Andre Geim | https://ncatlab.org/nlab/source/Andre+Geim |
* [Wikipedia entry](https://en.wikipedia.org/wiki/Andre_Geim)
* [institute page](http://www.condmat.physics.manchester.ac.uk/people/academic/geim/)
## Selected writings
Announcing the isolation of [[graphene]]:
* [[Konstantin Novoselov]], [[Andre Geim]], S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos,... |
Andre Hirschowitz | https://ncatlab.org/nlab/source/Andre+Hirschowitz |
* [website](http://math.unice.fr/~ah/)
## related $n$Lab entries
* [[∞-stack]]
* [[schematic homotopy type]]
category: people
[[!redirects Andre Hirschowicz]] |
Andre Kornell | https://ncatlab.org/nlab/source/Andre+Kornell |
* [Institute page](https://math.berkeley.edu/people/grad/andre-kornell)
* [MathematicsGenealogy page](https://www.mathgenealogy.org/id.php?id=220518)
## Selected writings
On [[quantum sets]] with [[quantum relations]]:
* [[Andre Kornell]], *Quantum Sets*, J. Math. Phys. **61** 102202 (2020) [[doi:1... |
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