Andreas Floer

* [Wikipedia entry](http://en.wikipedia.org/wiki/Andreas_Floer)

## related entries

* [[Floer homology]]

category: people


Andreas Gustavsson

See also [[BLG model]].

* [on the arXiv](http://arxiv.org/find/hep-th/1/au:+Gustavsson/0/1/0/all/0/1)
* Andreas Gustavsson, _Algebraic structures on parallel M2-branes_ Nucl. Phys. B811, 66--76 (2009)[arXiv:0709.1260](https://arxiv.org/abs/0709.1260)
* Andreas Gustavsson, _One-loop corrections to Bagger–Lambert theory_, Nuclear Physics B 807, n. 1-2 (2009) 315--333 [doi](https://doi.org/10.1016/j.nuclphysb.2008.09.003)

category: people


Andreas Holmstrom

I am a PhD student at University of Cambridge, interested primarily in [[homotopy theory]] and [[arithmetic geometry]].

I'm blogging at [Motivic stuff](http://homotopical.wordpress.com/)

## related $n$Lab entries

* [[Cohomology Theory Database]]

category: people


Andreas Höring

* [webpage](http://math.unice.fr/~hoering/)

category: people


Andreas J. Winter

* [institute page](https://www.icrea.cat/Web/ScientificStaff/andreas-winter-556)

* [Wikipedia entry](https://en.wikipedia.org/wiki/Andreas_Winter)

## Selected writings

On ([[quantum entanglement|entangled]]) [[quantum states]] [as resources in](quantum+information#ReferencesQuantumResources) [[quantum information theory]]/[[quantum computation]], not unlike the idea of resources in [[linear logic]]:

* [[Charles H. Bennett]], *A resource-based view of quantum information*, Quantum Information & Computation **4** 6 (2004) 460–466 [[doi:10.5555/2011593.2011598](https://dl.acm.org/doi/abs/10.5555/2011593.2011598)]

* Igor Devetak; Aram W. Harrow; [[Andreas J. Winter]], *A Resource Framework for Quantum Shannon Theory*, IEEE Transactions on Information Theory **54** 10 (2008) [[doi:10.1109/TIT.2008.928980](https://doi.org/10.1109/TIT.2008.928980)]

category: people

[[!redirects Andreas Winter]]


Andreas Juhl

* [webpage](http://www2.mathematik.hu-berlin.de/~ajuhl/)

## related $n$Lab entries

* [[conformal geometry]]

category: people


Andreas Karch

* [webpage](http://faculty.washington.edu/akarch/)

## Selected writings

On [[geometric engineering of quantum field theory]]:

* [[Andreas Karch]], _Field Theory Dynamics from Branes in String Theory_, PhD thesis (1998) ([doi:10.18452/14371](https://doi.org/10.18452/14371))

On [[gravity]] in [[Randall-Sundrum models]]:

* [[Andreas Karch]], [[Lisa Randall]], *Locally Localized Gravity*, JHEP 0105:008 (2001) [[arXiv:hep-th/0011156](https://arxiv.org/abs/hep-th/0011156), [doi:10.1088/1126-6708/2001/05/008](https://doi.org/10.1088/1126-6708/2001/05/008)]

* [[Andreas Karch]], *Randall-Sundrum Branes and Holography*, talk at *[[Strings 2022]]* [[indico:4940841](https://indico.cern.ch/event/1085701/contributions/4940841)]

On [[AdS/CFT]] as [[open/closed string duality]] and early discussion of the concept of [[probe branes]] in [[AdS/CFT]]:

* [[Andreas Karch]], [[Lisa Randall]], _Open and Closed String Interpretation of SUSY CFT's on Branes with Boundaries_, JHEP 0106:063, 2001 ([arXiv:hep-th/0105132](https://arxiv.org/abs/hep-th/0105132))

Introducing the concept of [[flavor branes]] for [[geometric engineering of QFT|geometric engineering]] of [[flavour physics]] in [[intersecting D-brane models]] ([[AdS/QCD]]):

* [[Andreas Karch]], [[Emanuel Katz]],  _Adding flavor to AdS/CFT_, JHEP 0206:043, 2002 ([arxiv:hep-th/0205236](https://arxiv.org/abs/hep-th/0205236))

On [[confinement]] via [[AdS-QCD]]:

* {#KKSS06} [[Andreas Karch]], [[Emanuel Katz]], Dam T. Son, Mikhail A. Stephanov, _Linear Confinement and AdS/QCD_, Phys. Rev. D74:015005, 2006 ([arXiv:hep-ph/0602229](https://arxiv.org/abs/hep-ph/0602229))

On [[Seiberg duality]] for [[gauge group]]s which are [[exceptional Lie group]]s:

* [[Jacques Distler]], [[Andreas Karch]], _$N=1$ Dualities for Exceptional Gauge Groups and Quantum Global Symmetries_ ([arXiv:hep-th/9611088](http://arxiv.org/abs/hep-th/9611088))

On [[M-theory on S1/G_HW times H/G_ADE]]:

* {#BrunnerKarch97} [[Ilka Brunner]], [[Andreas Karch]], _Branes at Orbifolds versus Hanany Witten in Six Dimensions_, JHEP 9803:003, 1998 ([arXiv:hep-th/9712143](https://arxiv.org/abs/hep-th/9712143))

On [[mirror symmetry]]:

* [[Mina Aganagic]], [[Kentaro Hori]], [[Andreas Karch]], [[David Tong]], _Mirror Symmetry in 2+1 and 1+1 Dimensions_, JHEP 0107:022,2001 ([arXiv:hep-th/0105075](http://arxiv.org/abs/hep-th/0105075))

On [[NS5-branes]] and [[orientifolds]] with [[RR-field tadpole cancellation]]:

* {#FengHeKarchUranga01} Bo Feng, [[Yang-Hui He]], [[Andreas Karch]], [[Angel Uranga]], _Orientifold dual for stuck NS5 branes_, JHEP 0106:065, 2001 ([arXiv:hep-th/0103177](https://arxiv.org/abs/hep-th/0103177))

On [[AdS-CFT in condensed matter physics]]:

[[Andreas Karch]] writes [here](http://www.math.columbia.edu/~woit/wordpress/?p=9426#comment-226376):

> These anomalous transport coefficients have first been calculated in AdS/CFT. The relevant references are [8], [9] and [10] in the Son/Surowka paper. In the AdS/CFT calculations these particular transport coefficients only arise due to Chern-Simons terms, which are the bulk manifestation of the field theory anomalies. At that point it was obvious to many of us that there should be a purely field theory based calculation, only using anomalies, that can derive these terms. Son and Surowka knew about this. They were sitting next door to me when they started these calculations. Many of us tried to find these purely field theory based arguments and failed. Son and Surowka succeeded.

> If you ask anyone serious about applying AdS/CFT to strongly coupled field theories why they are doing this, they would (hopefully) give you an answer along the lines of "AdS/CFT provides us with toy models of strongly coupled dynamics. While the field theories that have classical AdS duals are rather special, we can still learn important qualitative insights and find new ways to think about strongly coupled field theories." Once AdS/CFT stumbles on a new phenomenon in these solvable toy models, we want to go back to see whether we can understand it without the crutch of having to rely on AdS/CFT. Any result that only applies in theories with holographic dual is somewhat limited in its applications. In this sense, anomalous transport is a poster child for what AdS/CFT can be used for: a new phenomenon that had been missed completely by people studying field theory gets uncovered by studying these toy models. Once we knew what to look for, a purely field theoretic argument was found that made the AdS/CFT derivation obsolete.

> This is applied AdS/CFT as it should be. Solvable examples exhibit new connections which then can be proven to be correct more generally and are not limited to the toy models that were used to uncover them.

On the [[K-theory classification of topological phases of matter]] translating under [[AdS/CFT duality in solid state physics]]  to the [[K-theory classification of D-brane charge]] in [[string theory]], allowing a dual description of the topological phases even at [[non-perturbative effects|strong coupling]] via [[AdS/CFT duality]]:

* Carlos Hoyos-Badajoz, Kristan Jensen, [[Andreas Karch]], _A Holographic Fractional Topological Insulator_, Phys. Rev. D82:086001, 2010 ([arXiv:1007.3253](https://arxiv.org/abs/1007.3253))

* [[Andreas Karch]], Joseph Maciejko, [[Tadashi Takayanagi]], _Holographic fractional topological insulators in 2+1 and 1+1 dimensions_,  Phys. Rev. D 82, 126003 (2010) ([arXiv:1009.2991](https://arxiv.org/abs/1009.2991))

Argument that "islands" can resolve the [[black hole information paradox]] only for massive gravity:

* [[Hao Geng]], [[Andreas Karch]], *Massive Islands*,  J. High Energ. Phys. **2020** 121 (2020) [[arXiv:2006.02438](https://arxiv.org/abs/2006.02438),doi:10.1007/JHEP09(2020)121]

* [[Hao Geng]], [[Andreas Karch]], [[Carlos Perez-Pardavila]], [[Suvrat Raju]], [[Lisa Randall]], [[Marcos Riojas]], [[Sanjit Shashi]], *Inconsistency of islands in theories with long-range gravity*, J. High Energ. Phys. **2022** 182 (2022) [doi:10.1007/JHEP01(2022)182]

and on what to do about it:

* [[Hao Geng]], [[Andreas Karch]], [[Carlos Perez-Pardavila]], [[Suvrat Raju]], [[Lisa Randall]], [[Marcos Riojas]], [[Sanjit Shashi]], *Information Transfer with a Gravitating Bath*, SciPost Phys. **10** 103 (2021)  \[arXiv:2012.04671, [doi:10.21468/SciPostPhys.10.5.103](https://scipost.org/10.21468/SciPostPhys.10.5.103)\]

category: people


Andreas Kriegl

* [webiste](http://www.mat.univie.ac.at/~kriegl/)

category: people


Andreas Kübel

* [MathsGenealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=197208)

## Selected writings

On [[equivariant de Rham cohomology]] with emphasis on [[characteristic forms]]

* [[Andreas Kübel]], [[Andreas Thom]], _Equivariant characteristic forms in the Cartan model and Borel equivariant cohomology_ ([arXiv:1508.07847](https://arxiv.org/abs/1508.07847))

and application to [[ordinary equivariant differential cohomology]]:

* [[Andreas Kübel]], [[Andreas Thom]], _Equivariant Differential Cohomology_, Trans. Amer. Math. Soc. 370 (2018), 8237-8283  ([arXiv:1510.06392](https://arxiv.org/abs/1510.06392), [doi:10.1090/tran/7315](https://doi.org/10.1090/tran/7315))

category: people

[[!redirects Andreas Kuebel]]

[[!redirects Andreas Kubel]]


Andreas Nuyts

* [personal page](https://anuyts.github.io/)

## Selected writings

On [[universal algebra]]:

* [[Andreas Nuyts]], _Understanding Universal Algebra Using Kleisli-Eilenberg-Moore-Lawvere Diagrams_, (2022) [[pdf](https://anuyts.github.io/files/keml-diagrams.pdf)]

On [[modal type theory]]:

* [[Daniel Gratzer]], [[G. Alex Kavvos]], [[Andreas Nuyts]], [[Lars Birkedal]]: _Multimodal Dependent Type Theory_, Logical Methods in Computer Science **17** 3 (2021) lmcs:7713 [[arXiv:2011.15021](https://arxiv.org/abs/2011.15021), doi:10.46298/lmcs-17(3:11)2021]

category: people

[[!redirects anuyts]]


Andreas P. Schnyder

* [Institute page](https://www.fkf.mpg.de/556169/20_Schnyder)

* [GoogleScholar page](https://scholar.google.com/citations?user=35_fuGcAAAAJ&hl=en)

## Selected writings

Precursor to the [[K-theory classification of topological phases of matter]]:

* [[Andreas P. Schnyder]], [[Shinsei Ryu]], [[Akira Furusaki]], [[Andreas W. W. Ludwig]], *Classification of topological insulators and superconductors in three spatial dimensions*, Phys. Rev. B **78** 195125 (2008) $[$[doi:10.1103/PhysRevB.78.195125](https://doi.org/10.1103/PhysRevB.78.195125), [arXiv:0803.2786](https://arxiv.org/abs/0803.2786)$]$

On ([[symmetry protected topological phase|symmetry protected]]) [[topological phases of matter]]:

* [[Ching-Kai Chiu]], [[Jeffrey C.Y. Teo]], [[Andreas P. Schnyder]] [[Shinsei Ryu]], *Classification of topological quantum matter with symmetries*, Rev. Mod. Phys. **88** 035005 (2016) $[$[arXiv:1505.03535](https://arxiv.org/abs/1505.03535), [doi:10.1103/RevModPhys.88.035005](https://doi.org/10.1103/RevModPhys.88.035005)$]$

On [[topological semi-metals]]:

* {#ChiuSchnyder14} [[Ching-Kai Chiu]], [[Andreas P. Schnyder]], *Classification of reflection-symmetry-protected topological semimetals and nodal superconductors*, Phys. Rev. B **90** 205136 (2014) $[$[doi:10.1103/PhysRevB.90.205136](https://doi.org/10.1103/PhysRevB.90.205136)$]$

* {#Schnyder18} [[Andreas P. Schnyder]], *Accidental and symmetry-enforced band crossings in topological semimetals*, lecture notes (2018) $[$[pdf](https://www.fkf.mpg.de/6431357/topo_lecture_notes_schnyder_TMS18.pdf), [[Schnyder-Semimetals-2018.pdf:file]]$]$

* {#Schnyder20} [[Andreas P. Schnyder]], *Topological semimetals*, lecture notes (2020) $[$[pdf](https://www.fkf.mpg.de/7143520/topological_semimetals.pdf), [[Schnyder-Semimetals-2020.pdf:file]]$]$

category: people

[[!redirects Andreas Schnyder]]


Andreas Recknagel

Andreas Recknagel is lecturer at King's college in London

* [website](http://www.kcl.ac.uk/schools/nms/maths/people/academic/recknagel)

## Selected writings

* {#FroehlichGrandjeanRecknagel97} [[Jürg Fröhlich]], Oliver Grandjean, [[Andreas Recknagel]], section 7 of _Supersymmetric quantum theory, non-commutative geometry, and gravitation_  Lecture Notes Les Houches (1995) ([arXiv:hep-th/9706132](http://arxiv.org/abs/hep-th/9706132)).

## Related $n$Lab entries

* [[supersymmetric quantum mechanics]]

* [[2-spectral triple]]

category: people


Andreas Thom

* [webpage](https://tu-dresden.de/mn/math/geometrie/thom/)

## Selected writings

On [[equivariant de Rham cohomology]] with emphasis on [[characteristic forms]]

* [[Andreas Kübel]], [[Andreas Thom]], _Equivariant characteristic forms in the Cartan model and Borel equivariant cohomology_ ([arXiv:1508.07847](https://arxiv.org/abs/1508.07847))

and application to [[ordinary equivariant differential cohomology]]:

* [[Andreas Kübel]], [[Andreas Thom]], _Equivariant Differential Cohomology_, Trans. Amer. Math. Soc. 370 (2018), 8237-8283  ([arXiv:1510.06392](https://arxiv.org/abs/1510.06392), [doi:10.1090/tran/7315](https://doi.org/10.1090/tran/7315))

category: people


Andreas W. W. Ludwig

* [institute page](https://www.physics.ucsb.edu/people/andreas-ludwig)

## Selected writings

Precursor to the [[K-theory classification of topological phases of matter]]:

* [[Andreas P. Schnyder]], [[Shinsei Ryu]], [[Akira Furusaki]], [[Andreas W. W. Ludwig]], *Classification of topological insulators and superconductors in three spatial dimensions*, Phys. Rev. B **78** 195125 (2008) $[$[doi:10.1103/PhysRevB.78.195125](https://doi.org/10.1103/PhysRevB.78.195125), [arXiv:0803.2786](https://arxiv.org/abs/0803.2786)$]$

category: people

[[!redirects Andreas W. Ludwig]]
[[!redirects Andreas Ludwig]]


Andreas Wallraff

* [research group](https://qudev.phys.ethz.ch/Andreas-Wallraff)

* [Wikipedia page](https://en.m.wikipedia.org/wiki/Andreas_Wallraff)

## Selected writings

On [[experiment|experimental]] realization of [[quantum error correction]]:

* [[Markus Müller]], [[Andreas Wallraff]] et al., *Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code*, Nature **605** (2022) 669–674 [[arXiv:2112.03708](https://arxiv.org/abs/2112.03708), [doi:10.1038/s41586-022-04566-8](https://doi.org/10.1038/s41586-022-04566-8)]

category: people


Andreas Wipf

* [webpage](https://www.tpi.uni-jena.de/qfphysics/homepage/wipf/)

## selected writings

* [[Andreas Wipf]], _Chapter 10: Berezin integral_ ([pdf](https://www.tpi.uni-jena.de/qfphysics/homepage/wipf/lectures/pfad/pfad10.pdf))

  (on the [[Berezin integral]])

## related $n$Lab entries

* [[Berezin integral]]

category: people


Andreas Čap

[[!redirects Andreas Cap]]

* [webpage](http://www.mat.univie.ac.at/~cap/)

## Related entries

* [[parabolic geometry]]

  * [[conformal geometry]]

  * [[CR geometry]]

* [[Cartan connection]]

* [[twistor space]]

category: people


Andree Ehresmann

## Andrée Charles Ehresmann

Andrée Charles Ehresmann is a category theorist and the editor in chief of the journal [[Cahiers de Topologie et Géométrie Différentielle Catégoriques]], founded by her late husband [[Charles Ehresmann]]. Andrée Ehresmann's early papers were published under her maiden name Andrée Bastiani, and during a transition period under the hyphenated surname Bastiani-Ehresmann.

* [website](http://ehres.pagesperso-orange.fr/index.htm)
* [French Wikipedia](http://fr.wikipedia.org/wiki/Andr%C3%A9e_Ehresmann)

## Related entries

* [[Michal-Bastiani smooth map]]
* [[sketch]]
* [[monoidal closed category]]

## Selected writings

On [[internalization]] of [[mathematical structures]] via [[sketches]]:

* [[Andrée Bastiani]], [[Charles Ehresmann]], _Categories of sketched structures_, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 13 (1972) no. 2, pp. 104-214 ([numdam:CTGDC_1972__13_2_104_0](http://www.numdam.org/item/?id=CTGDC_1972__13_2_104_0))

category: people

[[!redirects Andrée Charles Ehresmann]]
[[!redirects Andrée Ehresmann]]
[[!redirects Andree Ehresmann]]
[[!redirects A. Ehresmann]]
[[!redirects Bastiani]]
[[!redirects Andree Bastiani]]
[[!redirects Andrée Bastiani]]


Andree Lischewski

* [webpage](http://www.math.hu-berlin.de/~diffgeo/index.php?seite=lischewski)

## related $n$Lab pages

* [[superconformal geometry]]

category: people


Andrei Constantin

* [webpage](https://www2.physics.ox.ac.uk/contacts/people/constantin)

* [Institute page](https://www.bnc.ox.ac.uk/about-brasenose/academic-staff/423-mr-andrei-constantin)

## Selected writings

On [[heterotic string theory|heterotic]] [[string phenomenology]] with [[heterotic line bundle models]]:

* [[Lara Anderson]], [[Andrei Constantin]], [[James Gray]], [[Andre Lukas]], [[Eran Palti]], _A Comprehensive Scan for Heterotic $SU(5)$ GUT models_, JHEP01(2014)047 ([arXiv:1307.4787](https://arxiv.org/abs/1307.4787))

* [[Evgeny Buchbinder]], [[Andrei Constantin]], [[Andre Lukas]], _The Moduli Space of Heterotic Line Bundle Models: a Case Study for the Tetra-Quadric_, 	JHEP03 (2014) 025 ([arXiv:1311.1941](https://arxiv.org/abs/1311.1941))

Survey:

* [[Andrei Constantin]], _Heterotic line bundle models_, talk at _[New Developments in Gravity, Cosmology and Strings 2013](https://www.theorie.physik.uni-muenchen.de/activities/workshops/archive_13/ppcsst/)_, Munich 2013 ([pdf](https://www.theorie.physik.uni-muenchen.de/activities/workshops/archive_13/ppcsst/constantin.pdf), [[ConstantiHeteroticLineBundles.pdf:file]])

On computation of [[Yukawa couplings]] in [[heterotic string theory]]:

* Stefan Blesneag, [[Evgeny Buchbinder]], [[Andrei Constantin]], [[Andre Lukas]], [[Eran Palti]], _Matter Field Kähler Metric in Heterotic String Theory from Localisation_ ([arXiv:1801.09645](https://arxiv.org/abs/1801.09645))

On realizations of the [[MSSM]] [[standard model of particle physics]] in [[heterotic string theory]]:

* {#CHE18} [[Andrei Constantin]], [[Yang-Hui He]], [[Andre Lukas]], _Counting String Theory Standard Models_, Physics Letters B Volume 792, 10 May 2019, Pages 258-262 ([arXiv:1810.00444](https://arxiv.org/abs/1810.00444))

category: people


Andrei Khrennikov

* [institute page](https://lnu.se/en/staff/andrei.khrennikov/)

## Selected writings

On [[Bell's inequalities]] and highlighting their preconception in classical [[probability theory]] due to [[Boole -- The Laws of Thought|Boole's "Laws of Thought"]], as pointed out by [Pitowsky 1989](Bell's+inequalities#Pitowsky89a):

* {#Khrennikov07} [[Andrei Khrennikov]], *Bell's inequality: Physics meets Probability* [[arXiv:0709.3909](https://arxiv.org/abs/0709.3909)]

* {#Khrennikov08} [[Andrei Khrennikov]], *Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?*, Entropy **10** 2 (2008) 19-32 [[doi:10.3390/entropy-e10020019](https://doi.org/10.3390/entropy-e10020019)]

category: people


Andrei Linde

* [webpage](http://www.stanford.edu/dept/physics/people/faculty/linde_andrei.html)

* [Wikipedia entry](http://en.wikipedia.org/wiki/Andrei_Linde)

## Related entries

* [[cosmic inflation]]

category: people


Andrei Marshakov

* [Institute page](https://faculty.skoltech.ru/people/andreimarshakov)

* [InSpire page](https://inspirehep.net/authors/998700)

## Selected writings

On [[Seiberg-Witten theory]] in  relation to [[integrable systems]]:

* [[Alexander Gorsky]], [[Igor Krichever]], [[Andrei Marshakov]], [[Andrei Mironov]], [[Andrey Morozov]], *Integrability and Seiberg-Witten Exact Solution*, Phys. Lett. B **355** (1995) 466-474 [[arXiv:hep-th/9505035](https://arxiv.org/abs/hep-th/9505035), doi:10.1016/0370-2693(95)00723-X]

* [[Andrei Marshakov]], *Seiberg-Witten Curves and Integrable Systems* [[arXiv:hep-th/9903252](https://arxiv.org/abs/hep-th/9903252)]

category: people


Andrei Micu

* [webpage](http://www.theory.nipne.ro/~amicu/cv.html)

## Selected writings

For [[heterotic string theory]] [[M-theory on Sp(1)-manifolds|on Sp(1)-manifolds]]:

* [[Jan Louis]], Danny Martinez-Pedrera, [[Andrei Micu]], _Heterotic compactifications on SU(2)-structure backgrounds_, JHEP 0909:012, 2009 ([arXiv:0907.3799](https://arxiv.org/abs/0907.3799))

On [[M-theory on G2-manifolds]]:

* {#HouseMicu04} Thomas House, [[Andrei Micu]], _M-theory Compactifications on Manifolds with $G_2$ Structure_ ([arXiv:hep-th/0412006](http://arxiv.org/abs/hep-th/0412006))

On [[M-theory on 8-manifolds]], [[F-theory on Spin(7)-manifolds]] and [[G-structures]]:

* Cezar Condeescu, [[Andrei Micu]], [[Eran Palti]], _M-theory Compactifications to Three Dimensions with M2-brane Potentials_, JHEP 04 (2014) 026 ([arxiv:1311.5901](https://arxiv.org/abs/1311.5901))

category: people


Andrei Mironov

* [mathscinet page](https://mathscinet.ams.org/mathscinet/MRAuthorID/262237)

## Selected writings

On [[Seiberg-Witten theory]] in  relation to [[integrable systems]]:

* [[Alexander Gorsky]], [[Igor Krichever]], [[Andrei Marshakov]], [[Andrei Mironov]], [[Andrey Morozov]], *Integrability and Seiberg-Witten Exact Solution*, Phys. Lett. B **355** (1995) 466-474 [[arXiv:hep-th/9505035](https://arxiv.org/abs/hep-th/9505035), doi:10.1016/0370-2693(95)00723-X]

On the [[AGT correspondence]]:

* [[Andrei Mironov]], [[Andrey Morozov]], [[Sh. Shakirov]], *A direct proof of AGT conjecture at $\beta = 1$*, JHEP 1102:067 (2011) [[arXiv:1012.3137](https://arxiv.org/abs/1012.3137), doi:10.1007/JHEP02(2011)067]

On [[topological quantum computation]] with [[Chern-Simons theory]] (e.g. with [[su(2)-anyons]]):

* [[Dmitry Melnikov]], [[Andrei Mironov]], [[Sergey Mironov]], [[Alexei Morozov]], [[Andrey Morozov]], _Towards topological quantum computer_, Nucl. Phys. B926 (2018) 491-508 [[arXiv:1703.00431](https://arxiv.org/abs/1703.00431), [doi:10.1016/j.nuclphysb.2017.11.016](https://doi.org/10.1016/j.nuclphysb.2017.11.016)]

category: people


Andrei Moroianu

* [webpage](http://moroianu.perso.math.cnrs.fr/)

## Selected writings

On [[Kähler manifolds]]:

* {#Moroianu07} [[Andrei Moroianu]], _Lectures on Kähler Geometry_, Cambridge University Press 2007 ([arXiv:math/0402223](https://arxiv.org/abs/math/0402223) [doi:10.1017/CBO9780511618666](https://doi.org/10.1017/CBO9780511618666), [pdf](https://moroianu.perso.math.cnrs.fr/tex/kg.pdf))

On [[quaternion-Kähler manifolds]]:

* {#Moroianu} [[Andrei Moroianu]], [[Uwe Semmelmann]], _Killing Forms on Quaternion-Kähler Manifolds_, Annals of Global Analysis and Geometry, November 2005, Volume 28, Issue 4, pp 319–335 ([arXiv:math/0403242](https://arxiv.org/abs/math/0403242), [doi:10.1007/s10455-005-1147-y](https://doi.org/10.1007/s10455-005-1147-y))

## Related entries

* [[Chern connection]]

category: people


Andrei Okounkov

* [webpage](http://www.math.columbia.edu/~okounkov/)

* Yen Duong, *[A Profile of Andrei Okounkov](https://www.simonsfoundation.org/2021/06/10/connecting-the-family-tree-of-mathematics/)*, Simons Foundation News, June 06, 2021

## Selected writings

On [[dimers]] in [[quantum many-body physics]]:

* [[Richard Kenyon]], [[Andrei Okounkov]], *What is... a dimer?*, Notices of the AMS, Vol. 52 No 3 (2005) ([pdf](https://www.ams.org/notices/200503/what-is.pdf))

On [[pillowcase orbifolds]]:

* {#EskinOkounkov05} [[Alex Eskin]], [[Andrei Okounkov]], _Pillowcases and quasimodular forms_, In: Ginzburg V. (ed.) _Algebraic Geometry and Number Theory_, Progress in Mathematics, vol 253. Birkhäuser 2006
 ([arXiv:math/0505545](https://arxiv.org/abs/math/0505545), [doi:10.1007/978-0-8176-4532-8_1](https://doi.org/10.1007/978-0-8176-4532-8_1))

On the [[Gromov-Witten/Donaldson-Thomas correspondence]]:

* [[Davesh Maulik]], [[Nikita Nekrasov]], [[Andrei Okounkov]], [[Rahul Pandharipande]], _Gromov–Witten theory and Donaldson–Thomas theory, I_. Compositio Mathematica. 142 (5): 1263–1285. (2003) ([arXiv:math/0312059](https://arxiv.org/abs/math/0312059). [doi:10.1112/S0010437X06002302](http://www.journals.cambridge.org/abstract_S0010437X06002302))

* [[Davesh Maulik]], [[Alexei Oblomkov]], [[Andrei Okounkov]], [[Rahul Pandharipande]], _Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds_ ([arXiv:0809.3976](https://arxiv.org/abs/0809.3976v1))

On the [[representation theory of the symmetric group]] via the [[Gelfand-Tsetlin basis]]/[[seminormal representation]]:

On the [[representation theory of the symmetric group]] via the [[seminormal representation]]:

* {#VershikOkounkov04} [[Anatoly Vershik]], [[Andrei Okounkov]], *A New Approach to the Representation Theory of the Symmetric Groups*,
Part I: Selecta Mathematica, New Series **2**, 581-605 ([arXiv:math/0503040](https://arxiv.org/abs/math/0503040), [doi:10.1007/BF02433451](https://doi.org/10.1007/BF02433451));
Part II (incorporates Part I in revised and improved form):
Russian version: [Записки научных семинаров ПОМИ 307 (2004), 57–98](ftp://ftp.pdmi.ras.ru/pub/publicat/znsl/v307/p057.ps.gz) (Zapiski nauchnyh seminarov POMI 307 (2004), 57–98);
English version: Journal of Mathematical Sciences 131 (2005), 5471–5494 ([doi:10.1007/s10958-005-0421-7](https://doi.org/10.1007/s10958-005-0421-7)).

Discussion of [[Witten indices]] and [[K-theory|K-theoretic]] [[enumerative geometry]] (with [[Hilbert schemes]]):

* [[Andrei Okounkov]], _Lectures on K-theoretic computations in enumerative geometry_ ([arXiv:1512.07363](https://arxiv.org/abs/1512.07363))

On [[Lie theory]]:

* {#Okounkov18} [[Andrei Okounkov]], _New worlds for Lie theory_, talk at [ICM 2018](http://www.icm2018.org/portal/en/home) ([pdf](http://www.math.columbia.edu/~okounkov/icm.pdf))

On [[equivariant elliptic cohomology]] of [[quiver varieties]] in relation to the [[AGT correspondence]]:

* [[Mina Aganagic]], [[Andrei Okounkov]], _Elliptic stable envelopes_ ([arXiv:1604.00423](https://arxiv.org/abs/1604.00423))

* [[Andrei Okounkov]], _Inductive construction of stable envelopes and applications, I. Actions of tori. Elliptic cohomology and K-theory_ ([arXiv:2007.09094](https://arxiv.org/abs/2007.09094))

following the analogous non-elliptic discussion in:

* [[Davesh Maulik]], [[Andrei Okounkov]], _Quantum Groups and Quantum Cohomology_, Asterisque 408(2019) ([arXiv:1211.1287](https://arxiv.org/abs/1211.1287), [ISBN: 978-2-85629-900-5](https://bookstore.ams.org/ast-408))

Review in:

* Andrey Smirnov, _Stable envelopes for $A_n$, $\widehat A_n$-quiver varieties_, 2019 ([pdf](https://math.mit.edu/events/quantum/a_smirnov.pdf))

## Related $n$Lab entries

* [[geometric Langlands correspondence]]

* [[Lie theory]]

category: people


Andrei Parnachev

* [personal page](https://www.maths.tcd.ie/~parnachev/group.html)

* [GoogleScholar page](https://scholar.google.nl/citations?user=QLOl2EYAAAAJ&hl=en)

## Selected wrirings

On [[topological entanglement entropy]] in terms of [[holographic entanglement entropy]]:

* Ari Pakman, [[Andrei Parnachev]], *Topological Entanglement Entropy and Holography*, JHEP 0807: 097 (2008) ([arXiv:0805.1891](https://arxiv.org/abs/0805.1891))

* [[Andrei Parnachev]], Napat Poovuttikul, *Topological Entanglement Entropy, Ground State Degeneracy and Holography*, Journal of High Energy Physics volume 2015, Article number: 92 (2015) ([arXiv:1504.08244](https://arxiv.org/abs/1504.08244))

category: people


Andrei Rodin

* [webpage](http://philomatica.org)

## Some writings

* Andrei Rodin, _Axiomatic Method and Category Theory_ ([arXiv:1210.1478](http://arxiv.org/abs/1210.1478))

  on [[foundations]] in [[categorical logic]] in view of [[homotopy type theory]] and other modern developments

* Andrei Rodin, _On Constructive Axiomatic Method_, [arXiv:1408.3591](http://arxiv.org/abs/1408.3591)

On models of homotopy type theory:

* [[Andrei Rodin]], *Models of HoTT and the Constructive View of Theories*, in: *[[Reflections on the Foundations of Mathematics]]*, Synthese Library **407** Springer (2019)  [[doi:10.1007/978-3-030-15655-8_9](https://doi.org/10.1007/978-3-030-15655-8_9), [pdf](https://philomatica.org/wp-content/uploads/2013/01/MH1.pdf)]

category: people


Andrei Sakharov

* [Wikipedia entry](http://en.wikipedia.org/wiki/Andrei_Sakharov)

## related $n$Lab entries

* [[baryogenesis]]

* [[rubber-sheet analogy of gravity]]

category: people


Andrei Suslin

# Andrei Suslin

* [Faculty profile](http://www.math.northwestern.edu/people/facultyProfiles/andrei.suslin.html)

* [Wikipedia (English)](http://en.wikipedia.org/wiki/Andrei_Suslin)

category:people

[[!redirects Andrei Suslin]]
[[!redirects A. Suslin]]
[[!redirects A Suslin]]
[[!redirects Suslin]]
[[!redirects Andrei Souslin]]
[[!redirects A. Souslin]]
[[!redirects A Souslin]]
[[!redirects Souslin]]
[[!redirects Андре́й Александро́вич Су́слин]]
[[!redirects Андрей Александрович Суслин]]
[[!redirects Андреи Александрович Суслин]]
[[!redirects Андрей A. Суслин]]
[[!redirects Андреи A. Суслин]]
[[!redirects Андрей A Суслин]]
[[!redirects Андреи A Суслин]]
[[!redirects Андрей Суслин]]
[[!redirects Андреи Суслин]]
[[!redirects А. A. Суслин]]
[[!redirects А A Суслин]]
[[!redirects А.A. Суслин]]
[[!redirects АA Суслин]]
[[!redirects А. Суслин]]
[[!redirects А Суслин]]
[[!redirects Суслин]]


Andrei Tyurin

* [webpage](http://u.math.biu.ac.il/~leyenson/tyurin/)

## Selected writings

On [[Bohr-Sommerfeld leaves]] in [[geometric quantization]] with application to [[conformal blocks]]:

* [[Andrei Tyurin]], *On Bohr-Sommerfeld bases*, Izvestiya: Mathematics **64** 5 (2000) 1033–1064 [[arXiv:math/9909084](https://arxiv.org/abs/math/9909084), [doi:10.1070/IM2000v064n05ABEH000308](https://iopscience.iop.org/article/10.1070/IM2000v064n05ABEH000308), [pdf](https://www.mathnet.ru/links/d8ad7540137cf2f33c44ab3e9455d392/im308_eng.pdf)]

category: people

[[!redirects Andrey Tyurin]]


Andrei V. Prasolov

Andrei V. Prasolov (Андрей Прасолов)
is a Professor at the Department of Mathematics and Statistics of
the Arctic University of Norway.

[website](https://en.uit.no/ansatte/person?p_document_id=40972)

## Related entries

* [[cosheaf]]


Andrei Zelevinsky

**Andrei Zelevinsky** has main interests in [[representation theory]], [[algebraic geometry]], polyhedral and algebraic combinatorics and Lie theory (not in the sense as in $n$lab, but in the common sense of the circle of questions relating [[Lie algebras]], [[Lie groups]], Kac-Moody groups, quantum groups etc.). With [[Sergey Fomin]], he created a theory of [[cluster algebra]]s. He studied multidimensional generalizations of [[hypergeometric function|hypergeometric functions]], arrangements of hyperplanes, bases for [[quantum groups]], quantum determinants and minors, Grassmanians, flag and Schubert varieties etc.

* [[I. M. Gelfand]], [[Mikhail Kapranov|M. M. Kapranov]], A. Zelevinsky, _Discriminants, [[resultants]], and multidimensional determinants_, Birkhäuser 1994, 523 pp.

* [[Sergey Fomin]], Andrei Zelevinsky, _Cluster algebras. I. Foundations_, J. Amer. Math. Soc. __15__ (2002) no. 2, 497--529 [math.RT/0104151](http://arxiv.org/abs/math/0104151); _Cluster algebras. II. Finite type classifications._ Invent. Math. __154__ (2003) no. 1, 63--121 -- classification of cluster algebras of finite type via root systems [math.RA/0208229](https://arxiv.org/abs/math/0208229).

* [[Arkady Berenstein]], Andrei Zelevinsky, _Quantum cluster algebras_, [math.QA/0404446](http://arxiv.org/abs/math/0404446)

* A. Zelevinsky's [homepage](http://www.math.neu.edu/zelevinsky/andrei.html)

category: people
[[!redirects A. Zelevinsky]]


Andrej Bauer

* [home page](http://andrej.com/)

* [blog](http://math.andrej.com/)

## Selected writings

On [[propositional truncation]] in [[dependent type theory]]:

* [[Steve Awodey]], [[Andrej Bauer]], *Propositions as $[$Types$]$*, Journal of Logic and Computation, **14**  (2004) 447-471 [[doi:10.1093/logcom/14.4.447](https://doi.org/10.1093/logcom/14.4.447), [pdf](http://andrej.com/papers/brackets_letter.pdf)]

On the [[Dedekind real numbers]] via [[abstract Stone duality]]:

* [[Andrej Bauer]], [[Paul Taylor]], *The Dedekind reals in abstract Stone duality*, Mathematical Structures in Computer Science **19** 4 (2009) 757-838 [[doi:10.1017/S0960129509007695](https://doi.org/10.1017/S0960129509007695)]

* [[Andrej Bauer]], *Efficient Computation with Dedekind Reals*, talk at *[Computability and complexity in analysis 2008](https://math.andrej.com/2008/08/24/efficient-computation-with-dedekind-reals/)* and at *[Mathematics, Algorithms and Proofs 2008](http://cdsagenda5.ictp.trieste.it/full_display.php?smr=0&ida=a07167)* (2008) [[web](https://math.andrej.com/2008/08/24/efficient-computation-with-dedekind-reals/), slides: [pdf](https://math.andrej.com/wp-content/uploads/2008/08/slides-map2008.pdf), extended abstract: [pdf](https://math.andrej.com/wp-content/uploads/2008/08/abstract-cca2008.pdf)]

On the [[HoTT book real numbers]]:

* [[Andrej Bauer]], *The real numbers in homotopy type theory*, talk at *[Computability and Complexity in Analysis](http://cca-net.de/cca2016/)*, Faro (2016) [[pdf](https://math.andrej.com/wp-content/uploads/2016/06/hott-reals-cca2016.pdf), [[Bauer-RealsInHoTT.pdf:file]]]

On [[dependent type theory]]:

* {#BauerHaselwarterLumsdaine20} [[Andrej Bauer]], [[Philipp G. Haselwarter]], [[Peter LeFanu Lumsdaine]], *A general definition of dependent type theories* [[arXiv:2009.05539](https://arxiv.org/abs/2009.05539)]

category: people


Andrej Ščedrov

* [personal page](https://www.cis.upenn.edu/~scedrov/)

## Selected writings

On [[classifying toposes]] and [[forcing]]:

* [[Andreas Blass]], [[Andrej Ščedrov]], *Classifying topoi and finite forcing*, Journal of Pure and Applied Algebra **28** (1983) 111-140 [doi:10.1016/0022-4049(83)90085-3]

* [[Andrej Ščedrov]], *Forcing and classifying topoi*, Memoirs of the American Mathematical Society (1984) [[AMS:memo-48-295](https://bookstore.ams.org/memo-48-295/5)]

[[!redirects Andrej Scedrov]]


Andres Collinucci

* [inspire page](https://inspirehep.net/authors/1023466)

* [institute page](https://www.theorie.physik.uni-muenchen.de/MATH/members/former_mem/former_asc/collinucci_andres/index.html)

## Selected writings

On [[shifted C-field flux quantization]] in [[F-theory]]:

* [[Andres Collinucci]], [[Raffaele Savelli]], *On Flux Quantization in F-Theory*,  J. High Energ. Phys. **2012** 15 (2012)   [[arXiv:1011.6388](https://arxiv.org/abs/1011.6388), doi:10.1007/JHEP02(2012)015]

* [[Andres Collinucci]], [[Raffaele Savelli]], *On Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups*,  J. High Energ. Phys. **2012** 94 (2012) [[arXiv:1203.4542](https://arxiv.org/abs/1203.4542), doi:10.1007/JHEP08(2012)094]

category: people


Andrew Baker

* [webpage](http://www.maths.gla.ac.uk/~ajb/)

## Selected writings

On [[ring spectra]]:

* {#BakerRichter04} [[Andrew Baker]], [[Birgit Richter]] _Structured ring spectra_, London Mathematical Society Lecture Notes Series 315, Springer 2004 ([ISBN:9780521603058](https://www.cambridge.org/de/academic/subjects/mathematics/algebra/structured-ring-spectra?format=PB))

## Related entries

* [[brave new algebra]]

category: people

[[!redirects Andy Baker]]


Andrew Blumberg

* [website](http://www.math.utexas.edu/users/blumberg/)

## Selected writings

On [[∞-groups of units]], [[Thom spectra]] and [[twisted generalized cohomology]]:

* {#ABGHR08} [[Matthew Ando]], [[Andrew Blumberg]], [[David Gepner]], [[Michael Hopkins]], [[Charles Rezk]], _Units of ring spectra and Thom spectra_ ([arXiv:0810.4535](http://arxiv.org/abs/0810.4535))

* [[Matthew Ando]], [[Andrew Blumberg]], [[David Gepner]], [[Michael Hopkins]], [[Charles Rezk]], _Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory_, Journal of Topology, Volume7, Issue 4, December 2014 ([arXiv:1403.4320](https://arxiv.org/abs/1403.4320), [arXiv:10.1112/jtopol/jtu009](https://doi.org/10.1112/jtopol/jtu009))

* {#ABGHR14} [[Matthew Ando]], [[Andrew Blumberg]], [[David Gepner]], [[Michael Hopkins]], [[Charles Rezk]], _An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology_, Journal of Topology Volume 7, Issue 3 2014 Pages 869–893  ([arXiv:1403.4325](http://arxiv.org/abs/1403.4325), [doi:10.1112/jtopol/jtt035](https://doi.org/10.1112/jtopol/jtt035))

Specifically on [[twisted K-theory]] and twisted [[tmf]]:

* {#ABG10} [[Matthew Ando]], [[Andrew Blumberg]], [[David Gepner]], _Twists of K-theory and TMF_, in Robert S. Doran, Greg Friedman, [[Jonathan Rosenberg]], _Superstrings, Geometry, Topology, and $C^*$-algebras_, Proceedings of Symposia in Pure Mathematics 81, American Mathematical Society 2010 ([arXiv:1002.3004](http://arxiv.org/abs/1002.3004), [ISBN:978-0-8218-4887-6](https://bookstore.ams.org/pspum-81))

On [[noncommutative motives]] in terms of [[algebraic K-theory]]:

* {#BlumbergGepnerTabuada10} [[Andrew Blumberg]], [[David Gepner]], [[Gonçalo Tabuada]], _A universal characterization of higher algebraic K-theory_,  Geometry and Topology 17 (2013) 733–838 ([arXiv:1001.2282](http://arxiv.org/abs/1001.2282))

On the [[equivariant stable homotopy theory]] of [[cyclotomic spectra]]:

* {#BlumbergMandell13} [[Andrew Blumberg]], [[Michael Mandell]], _The homotopy theory of cyclotomic spectra_, Geom. Topol. **19** (2015) 3105-3147 [[arXiv:1303.1694](http://arxiv.org/abs/1303.1694), [doi:10.2140/gt.2015.19.3105](https://doi.org/10.2140/gt.2015.19.3105)]

On [[equivariant homotopy theory]]:

* Andrew Blumberg, _Equivariant homotopy theory_, 2017 ([pdf](https://www.ma.utexas.edu/users/a.debray/lecture_notes/m392c_EHT_notes.pdf), [GitHub](https://github.com/adebray/equivariant_homotopy_theory))

On [[persistent homotopy theory]] and its [[stability of persistence diagrams|stability theorem]]:

* {#BlumbergLesnick17} [[Andrew J. Blumberg]], [[Michael Lesnick]], *Universality of the Homotopy Interleaving Distance* $[$[arXiv:1705.01690](https://arxiv.org/abs/1705.01690)$]$

On the [[Arnold conjecture]] and [[Morava K-theory]]:

* [[Mohammed Abouzaid]], [[Andrew J. Blumberg]], _Arnold Conjecture and Morava K-theory_, ([arXiv:2103.01507](https://arxiv.org/abs/2103.01507))

## Related entries

* [[twisted cohomology]]

* [[equivariant homotopy theory]], [[Bredon cohomology]]

category: people

[[!redirects Andrew J. Blumberg]]
[[!redirects Andrew J Blumberg]]
[[!redirects A. Blumberg]]


Andrew Brooke-Taylor

* [personal page](http://www1.maths.leeds.ac.uk/~pmtadb/)

* [institute page](https://eps.leeds.ac.uk/maths/staff/4010/dr-andrew-brooke-taylor)

## Selected writings

On [[products]] of [[CW-complexes]]:

* {#BrookeTaylor17} [[Andrew Brooke-Taylor]], *Products of CW complexes -- the full story*, 2017 ([pdf](http://www.math.helsinki.fi/logic/arctic/2017/Slides/BrookeTaylor_arctic2017.pdf), [[Brooke-Taylor_ProductsOfCWComplexes.pdf:file]])

category: people


Andrew C. Doherty

* [institute page](https://www.sydney.edu.au/science/about/our-people/academic-staff/andrew-doherty.html)

* [GoogleScholar page](https://scholar.google.com/citations?user=F3fXFXwAAAAJ&hl=en)

## Selected writings

On [[quantum circuits]] for [[quantum computation]] as ([[geodesic]], if optimal) [computational paths](computation#ReferencesConceptualizationViaPathLifting):

* {#NielsenDowlingGuDoherty06} [[Michael A. Nielsen]], [[Mark R. Dowling]], [[Mile Gu]], [[Andrew C. Doherty]], *Quantum Computation as Geometry*, Science, **311** 5764 (2006) 1133-1135 [[doi:10.1126/science.1121541](https://doi.org/10.1126/science.1121541), [arXiv:quant-ph/0603161](https://arxiv.org/abs/quant-ph/0603161)]

* [[Mark R. Dowling]], [[Michael A. Nielsen]], *The geometry of quantum computation*, Quantum Information & Computation **8** 10 (2008) 861–899 [[doi:10.5555/2016985.2016986](https://dl.acm.org/doi/abs/10.5555/2016985.2016986), [arXiv:quant-ph/0701004](https://arxiv.org/abs/quant-ph/0701004)]

On [[quantum error correction]]:

* Mackenzie H. Shaw, [[Andrew C. Doherty]], Arne L. Grimsmo, *Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes* [[arXiv:2210.14919](https://arxiv.org/abs/2210.14919)]

category: people

[[!redirects Andrew Doherty]]


Andrew C. Tang

* [InSpire page](https://inspirehep.net/authors/986616)

## Selected writings

On [[discretized light-cone quantization]] in [[quantum electrodynamics]]:

* [[Andrew C. Tang]], *Discretized light cone quantization: Application to quantum electrodynamics*, PhD thesis, Stanford (1990) [[spire:296776](https://inspirehep.net/literature/296776), [pdf](https://inspirehep.net/files/5ef318e56c87e7561d36559f54895bd1), [[Tang-DLCQ.pdf:file]]]

* {#TangBrodskyPauli91} [[Andrew C. Tang]], [[Stanley J. Brodsky]], [[Hans-Christian Pauli]], *Discretized light-cone quantization: Formalism for quantum electrodynamics*, Phys. Rev. D **44** (1991) 1842 [[doi:10.1103/PhysRevD.44.1842](https://doi.org/10.1103/PhysRevD.44.1842)]

category: people

[[!redirects Andrew Tang]]


Andrew Childs

* [personal page](https://www.cs.umd.edu/~amchilds/)

* [Wikipedia entry](https://en.wikipedia.org/wiki/Andrew_Childs)

## Selected writings

On [[adiabatic quantum computation]]:

* [[Andrew Childs]], [[Edward Farhi]], [[John Preskill]], *Robustness of adiabatic quantum computation*, Phys.Rev. A **65** (2002) 012322 [[arXiv:quant-ph/0108048](https://arxiv.org/abs/quant-ph/0108048), [doi:10.1103/PhysRevA.65.012322](https://doi.org/10.1103/PhysRevA.65.012322)]

* [[Andrew Childs]],  *Overview of adiabatic quantum computation*, talk at *[CIFAR](https://cifar.ca/research-programs/quantum-information-science/) Workshop on Quantum Information Processing* (2013) [[pdf](https://www.cs.umd.edu/~amchilds/talks/cifar13-tutorial.pdf), [[Childs-AdiabaticQuantumComputation.pdf:file]]]

category: people


Andrew Gleason

Andrew Gleason was the Hollis Professor of Mathematics and Natural Philosophy at Harvard University.

* [Wikipedia entry](https://en.wikipedia.org/wiki/Andrew_M._Gleason)

* [biography](http://www-history.mcs.st-and.ac.uk/Biographies/Gleason.html) (detailed)

* [biography](http://en.wikipedia.org/wiki/Andrew_Gleason) (brief)

## Selected writings

On [[extremally disconnected topological spaces]] as [[projective objects]]:

* {#Gleason58} [[Andrew M. Gleason]], _Projective topological spaces_ , Ill. J. Math. **2** no.4A (1958) pp.482-489. ([euclid:ijm/1255454110](https://projecteuclid.org/euclid.ijm/1255454110))

On [[equivariant Tietze extension theorems]] and on the [[slice theorem]]:

* {#Gleason50} [[Andrew Gleason]], _Spaces with a compact Lie group of transformations_,  Proc. Amer. Math. Soc. 1 (1950), 35-43 ([doi:10.1090/S0002-9939-1950-0033830-7](https://doi.org/10.1090/S0002-9939-1950-0033830-7))

On [[Gleason's theorem]]:

* {#Gleason57} [[Andrew Gleason]], _Measures on the closed subspaces of a Hilbert space_, Journal of Mathematics and Mechanics,  Indiana Univ. Math. J. **6** 4 (1957), 885-893 [[IUMJ:56050](http://www.iumj.indiana.edu/IUMJ/FULLTEXT/1957/6/56050), [pdf](http://www.iumj.indiana.edu/IUMJ/FTDLOAD/1957/6/56050/pdf)]

## Related $n$Lab entries

* [[Gleason's theorem]]

* [[Kochen-Specker theorem]]

* [[von Neumann algebra]]

* [[quantum state]]

* [[Stone Spaces]]

* [[equivariant Tietze extension theorem]]

category: people

[[!redirects Andrew M. Gleason]]


Andrew Hanson

* [Wikipedia entry](https://en.wikipedia.org/wiki/Andrew_J._Hanson)

## Selected writings

Introducing [[gravitational instantons]]:

* [[Tohru Eguchi]], [[Andrew Hanson]], _Gravitational instantons_, General Relativity and Gravitation volume 11, pages 315–320 (1979) ([doi:10.1007/BF00759271](https://doi.org/10.1007/BF00759271))

On [[topology]]/[[homotopy theory]] and [[differential geometry]] in [[gauge theory]] and [[gravity]] (such as in [[fiber bundles in physics]]):

* [[Tohru Eguchi]], [[Peter Gilkey]], [[Andrew Hanson]], _Gravitation, gauge theories and differential geometry_, Physics Reports Volume 66, Issue 6, December 1980, Pages 213-393 (doi:10.1016/0370-1573(80)90130-1)

category: people


Andrew Hodges

* [webpage](http://www.maths.ox.ac.uk/people/profiles/andrew.hodges)

* [twistor diagram page](http://www.twistordiagrams.org.uk)

## Related entries

* [[twistor]]

category: people


Andrew Hubery

* [webpage](http://wwwmath.uni-paderborn.de/~hubery/)

## related $n$Lab entries

* [[triangulated category]]

category: people


Andrew Kent

Andrew Kent is professor at *[NYU Center for Quantum Phenomena](https://as.nyu.edu/departments/physics/research/center-for-quantum-phenomena.html)*

* [institute page](https://as.nyu.edu/faculty/andrew-d-kent.html)

* [research lab page](https://physics.nyu.edu/kentlab/)

## Selected writings

On magnetic [[skyrmions]] in [[experiment]] and for [[computing]]:

* [[Andrew Kent]] et al. *Skyrmionics -- Computing and memory technologies based on topological excitations in magnets*, Journal of Applied Physics **130** (2021) 070908 [[arXiv:2101.09947](https://arxiv.org/abs/2101.09947), [doi:10.1063/5.0046950](https://doi.org/10.1063/5.0046950)]

Survey and exposition:

* [[Andrew Kent]], *A new spin on magnetism with applications in information processing*, talk at *[[CQTS]]* (Nov 2022) [[[Kent-CQTS-Nov2022.pdf:file]], [video](https://drive.google.com/file/d/1LTz2y6KrJytps94rlS6o0BET6rmzPFU_/view)]

category: people

[[!redirects Andy Kent]]


Andrew Kresch

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=55112)

## Selected writings

* {#Kresch09} [[Andrew Kresch]], _On the geometry of Deligne-Mumford stacks_ ([doi:10.5167/uzh-21342](https://doi.org/10.5167/uzh-21342), [pdf](https://www.zora.uzh.ch/id/eprint/21342/1/geodm.pdf)), in:  D. Abramovich, A. Bertram, L. Katzarkov, R. Pandharipande, M. Thaddeus (eds.) _Algebraic Geometry: Seattle 2005_, Proceedings of Symposia in Pure Mathematics 80, Providence, Rhode Island: American Mathematical Society 2009, 259-271 ([pspum-80-1](https://bookstore.ams.org/pspum-80-1))

  (on [[Deligne-Mumford stacks]] and [[orbifolds]])

## Related $n$Lab entries

* [[Deligne-Mumford stack]]

* [[orbifold]]

category: people


Andrew Lenard

Professor Emeritus in Mathematics, University of Indiana

* [webpage](http://www.math.indiana.edu/people/profile.phtml?id=lenard)

##Related concepts

* [[stability of matter]]

category: people


Andrew Lewis

* [webpage](http://www.mast.queensu.ca/~andrew/)

## related $n$Lab entries

* [[jet bundle]]

category: people


Andrew Lucas

* [webpage](https://www.colorado.edu/physics/andrew-lucas)

## Selected writings

On [[AdS/CFT in condensed matter physics]]:

* {#HartnollLucasSachdev16} [[Sean Hartnoll]], [[Andrew Lucas]], [[Subir Sachdev]], _Holographic quantum matter_, MIT Press 2018 ([arXiv:1612.07324](https://arxiv.org/abs/1612.07324), [publisher](https://mitpress.ublish.com/book/holographic-quantum-matter))

* Mike Blake, Yingfei Gu, [[Sean A. Hartnoll]], Hong Liu, [[Andrew Lucas]], Krishna Rajagopal, [[Brian Swingle]], [[Beni Yoshida]], *Snowmass White Paper: New ideas for many-body quantum systems from string theory and black holes* [[arXiv:2203.04718](https://arxiv.org/abs/2203.04718)]

category: people


Andrew M. Steane

* [personal page](https://users.physics.ox.ac.uk/~Steane/)

## Selected writings

Introducing the notion of [[quantum error correcting codes]]:

* [[Andrew M. Steane]], *Error Correcting Codes in Quantum Theory*, Phys. Rev. Lett. 77, 793 1996 ([doi:10.1103/PhysRevLett.77.793](https://doi.org/10.1103/PhysRevLett.77.793))

category: people

[[!redirects Andrew Steane]]


Andrew MacFie

[[!redirects amacfie]]

category:people


Andrew Neitzke

* [webpage](http://www.ma.utexas.edu/users/neitzke/)

## Selected writings

On a [[mysterious duality]]:

* {#INV01} [[Amer Iqbal]], [[Andrew Neitzke]], [[Cumrun Vafa]], _A mysterious duality_, ([arXiv:hep-th/0111068](https://arxiv.org/abs/hep-th/0111068))

On [[topological string theory]]:

* {#NeitzkeVafa04} [[Andrew Neitzke]], [[Cumrun Vafa]], _Topological strings and their physical applications_, talk at [Simons Workshop in Mathematics and Physics 2004](http://insti.physics.sunysb.edu/conf/simonsworkII/) ([hep-th/0410178](http://xxx.lanl.gov/abs/hep-th/0410178))

On [[topological M-theory]]:

* [[Robbert Dijkgraaf]], [[Sergei Gukov]], [[Andrew Neitzke]], [[Cumrun Vafa]], *Topological M-theory as Unification of Form Theories of Gravity*, Adv. Theor. Math. Phys. **9** (2005) 603-665 [[arXiv:hep-th/0411073](http://arxiv.org/abs/hep-th/0411073), [doi:10.4310/ATMP.2005.v9.n4.a5](https://dx.doi.org/10.4310/ATMP.2005.v9.n4.a5)]

* {#Neitzke2005} [[Andrew Neitzke]], *Elements of topological M-theory* (2005) [[[Neitzke-TopologicalMTheory.pdf:file]]]

On [[QFTs with defects]]:

* [[Andrew Neitzke]], *Some uses of defects in quantum field theory* (2016?) [[html](https://gauss.math.yale.edu/~an592/talks/html/defects-aspen/talk.html)]

Discussion of [[topological quantum field theory]] with an eye towards [[supersymmetry|supersymmetric]] field theory, in terms of the [[ordinary homology]] of [[configuration spaces of points]] (see also at _[[correlators as differential forms on configuration spaces of points]]_):

* [[Christopher Beem]], [[David Ben-Zvi]], [[Mathew Bullimore]], [[Tudor Dimofte]], [[Andrew Neitzke]], _Secondary products in supersymmetric field theory_ ([arXiv:1809.00009](https://arxiv.org/abs/1809.00009))

On [[spectral networks]] and [[Chern-Simons theory with complex gauge group]]:

* [[Daniel S. Freed]], [[Andrew Neitzke]], *3d spectral networks and classical Chern-Simons theory* [[arXiv:2208.07420](https://arxiv.org/abs/2208.07420)]

category: people


Andrew Pitts

__Andrew Mawdesley Pitts__ is a professor of theoretical computer science at Cambridge. His thesis was on the theory of [[tripos]]es; he studies semantic of programming languages, type theory, symbolic computation etc.

* [webpage](http://www.cl.cam.ac.uk/~amp12)

## Selected writings

* _Nontrivial power types can't be subtypes of polymorphic types_, [ps.gz](http://www.cl.cam.ac.uk/~amp12/papers/nontpt/nontpt.ps.gz)

* _The theory of [[triposes]]_, 1981, thesis, [pdf](http://www.cl.cam.ac.uk/~amp12/papers/thet/thet.pdf)

* _Tripos theory in retrospect_, [pdf](http://www.cl.cam.ac.uk/~amp12/papers/tritr/tritr.pdf)

On [[categorical semantics]] and the [[categorical model of dependent types]]:

* [[Andrew M. Pitts]], *Categorical logic*, in *[[Handbook of Logic in Computer Science]]* **5** Oxford Univ. Press (2000) 39-128 [[doi:10.1093/oso/9780198537816.003.0002](https://doi.org/10.1093/oso/9780198537816.003.0002), [pdf](https://www.cl.cam.ac.uk/~amp12/papers/catl/catl.pdf), [MR1859470](http://www.ams.org/mathscinet-getitem?mr=1859470)]

On [[denotational semantics]] and [[domain theory]]:

* [[Andrew M. Pitts]], *Lecture Notes on Denotational Semantics* (2012) [[pdf](https://www.cl.cam.ac.uk/teaching/1112/DenotSem/dens-notes-bw.pdf), [[Pitts-DenotationalSemantics.pdf:file]]]

On [[quotient types]], [[inductive types]] and [[inductive-inductive types]]:

* [[Marcelo P. Fiore]], [[Andrew M. Pitts]], [[S. C. Steenkamp]], *Quotients, inductive types, and quotient inductive types*, Logical Methods in Computer Science **18** 2 (2022) lmcs:7076  [[arXiv:2101.02994](https://arxiv.org/abs/2101.02994), doi:10.46298/lmcs-18(2:15)2022]

[[!redirects Andrew M. Pitts]]
[[!redirects Andrew Mawdesley Pitts]]
[[!redirects A. M. Pitts]]
[[!redirects Andy Pitts]]
[[!redirects A. Pitts]]

category: people


Andrew Putman

* [webpage](http://www3.nd.edu/~andyp/)

## related $n$Lab entries

* [[cobordism ring]]

* [[homotopy groups of spheres]]

category: people


Andrew Ranicki

Andrew Ranicki is professor for mathematics at Edinburgh University. He works on [[algebraic topology]].

* [webpage](http://www.maths.ed.ac.uk/~aar/)

* [Wikipedia entry](http://de.wikipedia.org/wiki/Andrew_Ranicki)

category: people
[[!redirects A. Ranicki]]


Andrew Salch

* [webpage](https://clasprofiles.wayne.edu/profile/dy8211)

## Selected writings

On [[L-complete modules]]:

* {#Salch16} [[Andrew Salch]], Approximation of subcategories by abelian subcategories ([arXiv:2011.01827](https://arxiv.org/abs/2011.01827))

category: people


Andrew Snowden

* [personal page](http://www-personal.umich.edu/~asnowden/)

* [MathematicsGenealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=138771)

* [GoogleScholar page](https://scholar.google.com/citations?user=V_lAuVcAAAAJ&hl=en)

## Selected writings

On the [[Mordell conjecture]]:

* {#BhattSnowden} [[Bhargav Bhatt]], [[Andrew Snowden]] (org.): _Faltings' proof of the Mordell conjecture_ (seminar notes, 2016) [[pdf](https://web.math.princeton.edu/~takumim/Mordell.pdf), [[BhattSnowden-FaltingsProofofMordell.pdf:file]]]

category: people


Andrew Stacey

From 2009 to 2014 Andrew Stacey was the local system administrator of the nLab.

## Selected writings

On [[cohomology operations]]:

* [[Andrew Stacey]], [[Sarah Whitehouse]], _The Hunting of the Hopf Ring_,     Homology Homotopy Appl. Volume 11, Number 2 (2009), 75-132. ([arXiv:0711.3722](https://arxiv.org/abs/0711.3722), [euclid:hha/1251832594](https://projecteuclid.org/euclid.hha/1251832594))

specifically on [[ordinary cohomology]]:

* [[Andrew Stacey]], [[Sarah Whitehouse]], _Stable and unstable operations in mod $p$ cohomology theories_, Algebr. Geom. Topol. Volume 8, Number 2 (2008), 1059-1091 ([arXiv:math/0605471](https://arxiv.org/abs/math/0605471), [euclid:agt/1513796856](https://projecteuclid.org/euclid.agt/1513796856))

## Related $n$Lab entries

* [[Froelicher space|Frölicher spaces]]
* [[Isbell envelope]]
* [[Tall-Wraith monoid]]
* [[an elementary treatment of Hilbert spaces]]
* [[algebraic theories in functional analysis]]
* [[davidroberts:which smooth paths do I use]]
* [[davidroberts:topological fundamental bigroupoid]]
* [[smooth loop space]]
* [[schedule]]

category: people


Andrew Strominger

* [webpage](http://www.physics.harvard.edu/people/facpages/strominger.html)

## Selected writings

On [[NS5-branes]] in ([[dual heterotic string theory|dual]]) [[heterotic string theory]] and their interpretation as [[Yang-Mills instantons]] (see also at _[[half M5-branes]]_):

* {#Strominger90} [[Andrew Strominger]], _Heterotic solitons_, Nucl. Phys. B343 (1990) 167-184 (doi:10.1016/0550-3213(90)90599-9) Erratum: Nucl. Phys. B353 (1991) 565-565 (doi:10.1016/0550-3213(91)90349-3) ([spire:27900](http://inspirehep.net/record/27900))

On microscopic explanation of [[Bekenstein-Hawking entropy]] via [[geometric engineering of QFT|geometric engineering]] of [[black holes in string theory]] as [[bound states of D-branes]]:

* {#StromingerVafa96} [[Andrew Strominger]], [[Cumrun Vafa]], _Microscopic Origin of the Bekenstein-Hawking Entropy_, Phys. Lett. B379: 99-104, 1996 ([arXiv:hep-th/9601029](http://arxiv.org/abs/hep-th/9601029))

Discussion of [[black hole entropy]] of [[D2-D6 brane bound states]] as [[black holes in string theory]]:

* [[Juan Maldacena]], [[Andrew Strominger]], _Statistical Entropy of Four-Dimensional Extremal Black Holes_, Phys. Rev. Lett. 77:428-429, 1996 ([arXiv:hep-th/9603060](https://arxiv.org/abs/hep-th/9603060))

On [[KK-compactification|dimensional reduction]] of [[black rings]] in [[D=5 gravity]] to [[black holes]] in [[D=4 gravity]]:

* [[Davide Gaiotto]], [[Andrew Strominger]], [[Xi Yin]], _5D Black Rings and 4D Black Holes_, JHEP 0602:023, 2006 ([arXiv:hep-th/0504126](https://arxiv.org/abs/hep-th/0504126))

On [[Kerr black holes]] in the context of the [[holographic principle]] and the [[AdS-CFT correspondence]]:

* [[Monica Guica]], [[Thomas Hartman]], Wei Song, [[Andrew Strominger]], _The Kerr/CFT Correspondence_, Phys. Rev. D **80** (2009) 124008 [[arXiv:0809.4266](http://arxiv.org/abs/0809.4266), [doi:10.1103/PhysRevD.80.124008](https://doi.org/10.1103/PhysRevD.80.124008)]

On the [[M5-brane elliptic genus]]:

* [[Davide Gaiotto]], [[Andrew Strominger]], [[Xi Yin]], _The M5-Brane Elliptic Genus: Modularity and BPS States_, JHEP 0708:070, 2007 ([hep-th/0607010](https://arxiv.org/abs/hep-th/0607010))

On the [[Navier-Stokes equation]] in view of the [[fluid/gravity correspondence]]:

* {#BKLS12} Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, [[Andrew Strominger]], _From Navier-Stokes To Einstein_, J. High Energ. Phys. (2012) 2012: 146 ([arXiv:1101.2451](https://arxiv.org/abs/1101.2451))

On [[celestial amplitudes]]:

* [[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/2012.04208))

On the [[soft graviton theorem]] in the [[BFSS matrix model]]:

* Noah Miller, [[Andrew Strominger]], Adam Tropper, Tianli Wang, *Soft Gravitons in the BFSS Matrix Model* [[arXiv:2208.14547](https://arxiv.org/abs/2208.14547)]

category: people


Andrew Sutherland

* [webpage](http://math.mit.edu/~drew/)

## Related $n$Lab entries

* [[number theory]]

category: people


Andrew Swan

* [webpage](https://awswan.github.io/)

## Selected writings

On the [[Nielsen-Schreier theorem]] in [[homotopy type theory]]/[[univalent foundations]]:

* {#Swan20} [[Andrew Swan]], _On the Nielsen-Schreier Theorem in Homotopy Type Theory_ ([arXiv:2010.01187](https://arxiv.org/abs/2010.01187))

On [[path types]] and [[identity types]]:

* [[Andrew Swan]], *Separating Path and Identity Types in Presheaf Models of Univalent Type Theory*, ([arXiv:1808.00920](https://arxiv.org/abs/1808.00920))

On [[Lifschitz realizability]]:

* [[Michael Rathjen]], [[Andrew Swan]], *Lifschitz Realizability as a Topological Construction*. The Journal of Symbolic Logic, Volume 85, Issue 4, December 2020, pp. 1342 - 1375. [[doi:10.1017/jsl.2021.1](https://doi.org/10.1017/jsl.2021.1), [arXiv:1806.10047](https://arxiv.org/abs/1806.10047)]

## Talks

* [[Andrew Swan]], *Double negation stable h-propositions in cubical sets*, [[Homotopy Type Theory Electronic Seminar Talks]], 9 February 2023 ([slides](https://www.uwo.ca/math/faculty/kapulkin/seminars/hottestfiles/Swan-2023-02-09-HoTTEST.pdf), [video](https://www.youtube.com/watch?v=lNNrmuUQzkw))

category: people


Andrew Wiles

Andrew Wiles is professor for pure [[mathematics]] at Oxford.

* [webpage](https://www.maths.ox.ac.uk/people/andrew.wiles)

* [Wikipedia entry](http://en.wikipedia.org/wiki/Andrew_Wiles)

Wiles is famous for havin proved the [[Taniyama-Shimura conjecture]], also known as the [[modularity theorem]].

## Selected writings

On the [[modularity theorem]]:

* {#Wiles95} [[Andrew Wiles]], *Modular Elliptic Curves and Fermat's Last Theorem*, Annals of Mathematics Second Series, **141** 3 (1995) 443-551 $[$[doi:10.2307/2118559](https://doi.org/10.2307/2118559)$]$

* {#TaylorWiles95} [[Richard Taylor]], [[Andrew Wiles]], *Ring-Theoretic Properties of Certain Hecke Algebras*, Annals of Mathematics Second Series **141** 3 (1995) 553-572 $[$[doi:10.2307/2118560 ](https://doi.org/10.2307/2118560 )$]$

category: people


Andrews–Curtis conjecture

+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
###Context###
#### Group Theory
+-- {: .hide}
[[!include group theory - contents]]
=--
=--
=--

#Contents#
* table of contents
{:toc}

## Idea

A conjecture about [[group presentation|presentations]] of the [[trivial group]].

## Related concepts

* [[combinatorial group theory]]

## References

The original article:

* J. J. Andrews, M. L. Curtis, *Free groups and handlebodies*, Proc. Amer. Math. Soc. **16** (1965) 192-195 [[ams:S0002-9939-1965-0173241-8](https://www.ams.org/journals/proc/1965-016-02/S0002-9939-1965-0173241-8)]

See also:

* Wikipedia, *[Andrews–Curtis conjecture](https://en.wikipedia.org/wiki/Andrews%E2%80%93Curtis_conjecture)*

[[!redirects Andrews-Curtis conjecture]]


Andrey Kolmogorov

* [Wikipedia entry](http://en.wikipedia.org/wiki/Andrey_Kolmogorov)

## Selected writings

On [[intuitionistic logic]]:

* [[Andrey Kolmogorov]], *Zur Deutung der intuitionistischen Logik*, Math. Z. **35** (1932) 58-65 [[doi:10.1007/BF01186549](https://link.springer.com/article/10.1007/BF01186549)]

Introducing [[chain homology]]/[[cochain cohomology]] and [[singular homology]]/[[singular cohomology]]:

* [[Andrei Kolmogoroff]], _Über die Dualität im Aufbau der kombinatorischen Topologie_, Recueil Mathématique 1(43) (1936), 97–102.  ([mathnet](http://mi.mathnet.ru/msb5361))

* [[Andrei Kolmogoroff]], _Homologiering des Komplexes und des lokal-bicompakten Raumes_, Recueil Mathématique 1(43) (1936), 701–705.  [mathnet](http://mi.mathnet.ru/msb5475).

## Related $n$Lab entries

* [[probability theory]]

* [[probability space]]

* [[random variable]]

* [[Kolmogorov complexity]]

* [[cohomology]]

category: people

[[!redirects Kolmogorov]]
[[!redirects A. N. Kolmogorov]]
[[!redirects Andrei Kolmogoroff]]
[[!redirects Андрей Николаевич Колмогоров]]
[[!redirects Андрей Колмогоров]]
[[!redirects Колмогоров]]
[[!redirects А. Колмогоров]]
[[!redirects А. Н. Колмогоров]]


Andrey Lazarev

__Andrey Lazarev__ is a mathematician at the University of Lancaster. His research is at the interface of [[mathematical physics]] and pure mathematics, including [[algebraic topology]], [[homological algebra]] and [[deformation theory]], [[noncommutative geometry]] and [[conformal field theory]].

* [homepage](https://www.maths.lancs.ac.uk/~lazarev/)

## Selected writings

* [[Joseph Chuang]], Andrey Lazarev, _L-infinity maps and twistings_, [arxiv/0912.1215](http://arxiv.org/abs/0912.1215);

* [[Joseph Chuang]], Andrey Lazarev,_Abstract Hodge decomposition and minimal models for cyclic algebras_, [arxiv./0810.2393](http://arxiv.org/abs/0810.2393),

* [[Joseph Chuang]], Andrey Lazarev,_Feynman diagrams and minimal models for operadic algebras_, [arxiv/0802.3507](http://arxiv.org/abs/0802.3507),

* [[Joseph Chuang]], Andrey Lazarev,_Dual Feynman transform for modular operads_, [arxiv/0704.2561](http://arxiv.org/abs/0704.2561)

* Alastair Hamilton, Andrey Lazarev, _Characteristic classes of $A_\infty$-algebras_, [arxiv/0801.0904](http://arxiv.org/abs/0801.0904); _Symplectic $A_\infty$-algebras and string topology operations_, Amer. Math. Soc. Transl. (2), Vol. 224, 2008, 147--157, [arxiv/0707.4003](http://arxiv.org/abs/0707.4003); _Symplectic $C_\infty$-algebras_, Mosc. Math. J. 8 (2008), no. 3, 443--475, 615, [arxiv/0707.3951](http://arxiv.org/abs/0707.3951); _Cohomology theories for homotopy algebras and noncommutative geometry_, Algebr. Geom. Topol. __9__ (2009), 1503--1583, [arxiv/0707.3937](http://arxiv.org/abs/0707.3937); _Graph cohomology classes in the [[BV-BRST formalism|Batalin-Vilkovisky formalism]]_, J.Geom.Phys. __59__:555-575, 2009, [arxiv/0701825](http://arxiv.org/abs/math/0701825); _Characteristic classes of A-infinity algebras_, [math.QA/0608395](http://arxiv.org/abs/math/0608395)

* Andrey Lazarev, _The Stasheff model of a simply-connected manifold and the string bracket_, [math.AT/0512596](http://arxiv.org/abs/math/0512596)

* A. Lazarev, A. A. Voronov, _Graph homology: Koszul and Verdier duality_, [math.QA/0702313](http://arxiv.org/abs/math/0702313)

* [[Jonathan Block]], Andrey Lazarev, _André-Quillen cohomology and rational homotopy of function spaces_, [math.KT/0306406](http://arxiv.org/abs/math/0306406)

* [[Andrey Lazarev]], Def. 5.1 in: *Maurer-Cartan moduli and models for function spaces* ([arxiv:1109.3715](http://arxiv.org/abs/1109.3715))

* [[Joseph Chuang]], [[Andrey Lazarev]], Def. 1.6 in: *Combinatorics and formal geometry of the master equation*,  Lett. Math. Phys. **103** (2013) 79–112  ([arXiv:1205.5970](https://arxiv.org/abs/1205.5970), [doi:10.1007/s11005-012-0586-1](https://doi.org/10.1007/s11005-012-0586-1))

On [[Koszul duality]] duality:

* [[Julian Holstein]], [[Andrey Lazarev]], *Categorical Koszul duality*, Advances in Mathematics **409** B (2022) 108644 [[arXiv:Koszul duality2006.01706](https://arxiv.org/pdf/2006.01705.pdf), [doi:10.1016/j.aim.2022.108644](https://doi.org/10.1016/j.aim.2022.108644)]

On the [[Riemann-Hilbert correspondence]]:

* [[Joseph Chuang]], [[Julian Holstein]], [[Andrey Lazarev]] _Maurer–Cartan moduli and theorems of Riemann–Hilbert type_, Applied Categorical Structures **29** (2021) 685–728 [[doi:10.1007/s10485-021-09631-3](https://doi.org/10.1007/s10485-021-09631-3)]

category: people

## Related entries

* [[L-infinity algebra]]

* [[Maurer-Cartan equation]]

[[!redirects A. Lazarev]]


Andrey Markov

Андрей Андреевич Марков (Andrey Andreyevich Markov) (1856--1922) was a mathematician, the father of [[Andrey Markov Jr]].

He worked on probability and statistics, particularly [[Markov chains]].

category: people

[[!redirects Andrey Markov]]
[[!redirects Andrey Markov Sr]]
[[!redirects Andrey Markov Sr.]]
[[!redirects Andrei Markov]]
[[!redirects Andrei Markov Sr]]
[[!redirects Andrei Markov Sr.]]
[[!redirects Andrej Markov]]
[[!redirects Andrej Markov Sr]]
[[!redirects Andrej Markov Sr.]]
[[!redirects Andrey Andreyevich Markov]]
[[!redirects Andrey Andreyevich Markov Sr]]
[[!redirects Andrey Andreyevich Markov Sr.]]
[[!redirects Andrei Andreievich Markov]]
[[!redirects Andrei Andreievich Markov Sr]]
[[!redirects Andrei Andreievich Markov Sr.]]
[[!redirects Andrei Andreevich Markov]]
[[!redirects Andrei Andreevich Markov Sr]]
[[!redirects Andrei Andreevich Markov Sr.]]
[[!redirects Andrej Andreevich Markov]]
[[!redirects Andrej Andreevich Markov Sr]]
[[!redirects Andrej Andreevich Markov Sr.]]
[[!redirects Markov]]
[[!redirects Markov Sr]]
[[!redirects Markov Sr.]]
[[!redirects Андрей Андреевич Марков]]
[[!redirects Андрей Андреевич Марков Sr]]
[[!redirects Андрей Андреевич Марков Sr.]]
[[!redirects Андрей Андреевич Марков старший]]
[[!redirects Андрей Андреевич Марков (старший)]]
[[!redirects Андрей Марков]]
[[!redirects Андрей Марков Sr]]
[[!redirects Андрей Марков Sr.]]
[[!redirects Андрей Марков старший]]
[[!redirects Андрей Марков (старший)]]
[[!redirects Марков]]
[[!redirects Марков Sr]]
[[!redirects Марков Sr.]]
[[!redirects Марков старший]]
[[!redirects Марков (старший)]]


Andrey Markov Jr

Андрей Андреевич Марков (Andrey Andreyevich Markov) Jr (1903--1979) was a mathematician, the son of [[Andrey Markov Sr]].

He founded the school of [[Russian constructivism]]; [[Markov's principle]] is named after him.  He also worked on the [[foundations]] of [[classical mathematics]], including a proof that the classification of $4$-[[manifolds]] is undecidable.

category: people

[[!redirects Andrey Andreyevich Markov Jr]]
[[!redirects Andrey Andreyevich Markov Jr.]]
[[!redirects Andrei Andreievich Markov Jr]]
[[!redirects Andrei Andreievich Markov Jr.]]
[[!redirects Andrei Andreevich Markov Jr]]
[[!redirects Andrei Andreevich Markov Jr.]]
[[!redirects Andrej Andreevich Markov Jr]]
[[!redirects Andrej Andreevich Markov Jr.]]
[[!redirects Andrey Markov Jr]]
[[!redirects Andrey Markov Jr.]]
[[!redirects Andrei Markov Jr]]
[[!redirects Andrei Markov Jr.]]
[[!redirects Andrej Markov Jr]]
[[!redirects Andrej Markov Jr.]]
[[!redirects A A Markov Jr]]
[[!redirects A. A. Markov Jr]]
[[!redirects A A Markov Jr.]]
[[!redirects A. A. Markov Jr.]]
[[!redirects A Markov Jr]]
[[!redirects A. Markov Jr]]
[[!redirects A Markov Jr.]]
[[!redirects A. Markov Jr.]]
[[!redirects Андрей Андреевич Марков Jr]]
[[!redirects Андрей Андреевич Марков Jr.]]
[[!redirects Андрей Андреевич Марков младший]]
[[!redirects Андрей Андреевич Марков (младший)]]
[[!redirects Андрей Марков Jr]]
[[!redirects Андрей Марков Jr.]]
[[!redirects Андрей Марков младший]]
[[!redirects Андрей Марков (младший)]]
[[!redirects А А Марков Jr]]
[[!redirects А. А. Марков Jr]]
[[!redirects А А Марков Jr.]]
[[!redirects А. А. Марков Jr.]]
[[!redirects A A Марков младший]]
[[!redirects A. A. Марков младший]]
[[!redirects A A Марков (младший)]]
[[!redirects A. A. Марков (младший)]]
[[!redirects A Марков Jr]]
[[!redirects A. Марков Jr]]
[[!redirects A Марков Jr.]]
[[!redirects A. Марков Jr.]]
[[!redirects A Марков младший]]
[[!redirects A. Марков младший]]
[[!redirects A Марков (младший)]]
[[!redirects A. Марков (младший)]]


Andrey Morozov

* [InSpire page](https://inspirehep.net/authors/1071335)

## Selected writings

On [[Seiberg-Witten theory]] in  relation to [[integrable systems]]:

* [[Alexander Gorsky]], [[Igor Krichever]], [[Andrei Marshakov]], [[Andrei Mironov]], [[Andrey Morozov]], *Integrability and Seiberg-Witten Exact Solution*, Phys. Lett. B **355** (1995) 466-474 [[arXiv:hep-th/9505035](https://arxiv.org/abs/hep-th/9505035), doi:10.1016/0370-2693(95)00723-X]

On the [[AGT correspondence]]:

* [[Andrei Mironov]], [[Andrey Morozov]], [[Shamil Shakirov]], *A direct proof of AGT conjecture at $\beta = 1$*, JHEP 1102:067 (2011) [[arXiv:1012.3137](https://arxiv.org/abs/1012.3137), doi:10.1007/JHEP02(2011)067]

On [[topological quantum computation]] with [[Chern-Simons theory]]:

* [[Dmitry Melnikov]], [[Andrei Mironov]], [[Sergey Mironov]], [[Alexei Morozov]], [[Andrey Morozov]], _Towards topological quantum computer_, Nucl. Phys. B926 (2018) 491-508 ([arXiv:1703.00431](https://arxiv.org/abs/1703.00431), [doi:10.1016/j.nuclphysb.2017.11.016](https://doi.org/10.1016/j.nuclphysb.2017.11.016))

On universality of [[braid representation|braid]] [[quantum gates]] of [[su(2)-anyons]] at higher [[Chern-Simons level|level]] $k$ (and also for $SU(N)$-anyons with $N \gt 2$):

* [[Nikita Kolganov]], [[Sergey Mironov]], [[Andrey Morozov]], *Large $k$ topological quantum computer*, Nuclear Physics B
**987** (2023) 116072 [[arXiv:2105.03980](https://arxiv.org/abs/2105.03980), [doi:10.1016/j.nuclphysb.2023.116072](https://doi.org/10.1016/j.nuclphysb.2023.116072)]

category: people


Andrey Tikhonov

Андрей Николаевич Тихонов was a Russian mathematician and geophysicist, known for his contributions to [[topology]] and [[functional analysis]], but also [[mathematical physics]].

Concepts named after him include _[[Tychonoff space]]_, _[[Tychonoff product]]_, _[[Tychonoff's theorem]]_.

Beware that spelling varies, other common uses are _Tihonov_ and _Tikhonov_. The original _Тихонов_, becomes _Tihonov_ in the transliteration used in slavistics or _Andrey Nikolayevich Tikhonov_ in modern English (BGN/PCGN) transliteration. But notice that he himself originally published in German as _A.N. Tychonoff_ (e.g. [Tychonoff 30](#Tychonoff30), [Tychonoff 35](#Tychonoff35)).

* [Wikipedia entry](http://en.wikipedia.org/wiki/Andrey_Nikolayevich_Tychonoff)

## Writings

* {#Tychonoff30} _Über die topologische Erweiterung von Räumen_, Mathematische Annalen, December 1930, Volume 102, Issue 1, pp 544–561

* {#Tychonoff35} _Ein Fixpunktsatz_, Mathematische Annalen, December 1935, Volume 111, Issue 1, pp 767–776

## Related entries

* [[Tychonoff space]]

* [[Tychonoff product]]

* [[Tychonoff's theorem]]

category: people

[[!redirects Andrey Nikolayevich Tikhonov]]
[[!redirects Tychonoff]]
[[!redirects A. N. Tychonoff]]
[[!redirects Andrey Tychonoff]]
[[!redirects Андрей Николаевич Тихонов]]
[[!redirects Андрей Тихонов]]
[[!redirects Тихонов]]


Andrey Todorov

* [Wikipedia entry](http://de.wikipedia.org/wiki/Andrey_Todorov)
* [[Bogomolov-Tian-Todorov theorem]]
* [[Ludmil Katzarkov]], [[Maxim Kontsevich]], [[Tony Pantev]], _Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models_,  J. Differential Geom. 105(1): 55--117 [doi](https://doi.org/10.4310/jdg/1483655860)

category: people


Andries E. Brouwer

* [personal page](https://www.win.tue.nl/~aeb/)

## Selected writins

On [[lattice (discrete subgroup)|lattice theory]]:

* [[Andries E. Brouwer]], _Lattices_, Course notes (2002) $[$[pdf](http://www.win.tue.nl/~aeb/latt/lattices.pdf)$]$

category: people

[[!redirects Andries Brouwer]]


AndriusKulikauskas

Thank you for creating this space for research.

### [[big picture]]: My research at N Lab ###

At n Lab, I am interested to do a variety of personal and collaborative research projects regarding the [[big picture]] in mathematics.

### Category theory ###

I have twice tried to learn category theory and now will try for the third time.  I am interested to learn it as a potential language for expressing an "algebra of perspectives".  Also, I think it is essential for understanding the "big picture" in mathematics as I'm hoping to do.

Learning category theory

* I've found the Catster videos especially helpful.
* I'm reading Wikipedia pages.
* I watched a series of video lectures on algebraic topology and that provided practical context.

## My main interest ##

Since childhood I have wished to know everything and apply that knowledge usefully.  I have written a summary of my findings, [The Truth, From Relative to Absolute](http://www.selflearners.net/wiki/Truth/Book), which explains how to go from relative truth to absolute truth.

I am now writing a detailed book which I hope to finish next year. It will be a manual for investigators of the big questions in life. I want that to include big questions in math and physics.  In particular, I want to explain how math and physics arise from more fundamental pre-mathematical perspectives.

### My mathematical background ###

In educating myself, I earned Bachelor's degrees in Math and Physics in 1986 from the University of Chicago and a Ph.D. in Math from UCSD in 1993.  I took two courses on recursive function theory from Robert Soare at the University of Chicago.

For my Ph.D., my main interest was to study algebraic combinatorics as "the basement of math" from which mathematical objects arise, or so I thought.  In algebraic combinatorics the symmetric functions are central because they are the generating functions for relabeling objects.  I was particularly interested to know why among the infinitely many bases for the symmetric functions as a vector space there seemed to be six bases of particular interest to humans: the monomial, elementary, homogeneous, power, Schur and forgotten bases.  I never answered this question.   However, I realized that the determinant and trace of a generic matrix were symmetric functions of eigenvalues, and similarly, for my Ph.D. thesis, [Symmetric functions of the eigenvalues of a matrix](http://www.selflearners.net/uploads/AndriusKulikauskasThesis.pdf) I calculated in terms of the matrix entries all six of these bases at the eigenvalues of a generic matrix.  The usual symmetric functions are recovered by considering a diagonal matrix.  Thus I had found a general framework for all of combinatorics in terms of matrix edges building up walks, signed cycles, words, Lyndon words, etc.  But I ended my math research to focus on the philosophical questions about life which were my main interest.

## My current interests in Math ##

### [[discovery]] ###

My current questions in math relate to my study in 2010-2011 of "the ways of figuring things out".  I surveyed 200 ways that I had figured things out in my philosophy and organized them into a system of 24 ways, a "house of knowledge".  I came up with an analogous system of 24 ways of figuring things out in mathematics which I wrote up [here](https://groups.google.com/d/msg/mathfuture/50pk00XZCLQ/HnQjrun8ej8J).

George Polya wrote a book "How to Solve It" where he describes several patterns for solving math problems, such as the pattern for "two locii".  For example, consider Euclid's first problem in his Elements: In drawing an equilateral triangle, given the first side AB, how do we draw the other two?  We solve this by drawing two circles of radius "AB" and noting their intersections. Now I noticed, let us consider what is happening in our minds!  We are constructing a lattice of solution sets, namely, the two circles centered on A and B (each circle represents a condition), the points of intersection (they represent the set of both conditions) and the entire plane represents the set of no conditions.  Thus in our minds we have reduced a nontrivial problem into a tiny lattice.  That lattice is a mathematical object!  We are using math to solve math. The math in the mind (the lattice) is much more basic than the math on the paper (the triangle).  But the math in the mind is not defined in some explicit system, as far as we know.  In some sense it is pre-systemic, pre-mathematical.  It is a link between math and some more basic metaphysics.  I went through Paul Zeitz's excellent book "The Art and Craft of Problem Solving" and organized a system of 24 such mental math structures by which we figure things out. The system lets us see or at least imagine some of the origins of math, the distinctions of what is systemic and pre-systemic, what is algebra and what is analysis, what might be the most natural way of defining set theory axioms.  Here are some [200 examples from math](http://www.selflearners.net/ways/index.php?d=Math) of ways of figuring things out:

### Learning math for undersanding physics ###

For my book, I want to show how such a system can be set up fruitfully for any domain, any "world" as Heidegger would say, any "techne" as Aristotle would say.  I think it's important to try to do it for physics.  So I've started going through the lists of physics experiments at Wikipedia.  Also, here in Lithuania, I meet with Thomas Gajdosik, a theoretical physicist.  I can ask him basic questions like, Why doesn't an electron rip itself apart, given that like charges repel?  I've realized that I need to learn a lot of math (Lie groups, Lie algebras) to understand physics.  I need to learn things that I never understood (like tensors).  So I have found some good books (such as "The Road to Reality" by Roger Penrose, available online for free), good video lectures (I like the ones by Fredric Schuller), and I find it very helpful to surf Wikipedia.  I have also downloaded SageMath and will try that out to help me visualize and play with concrete structures.  I feel that with these tools it's possible to grasp the "big picture" in mathematics in a way that was not available in graduate school.

### [[organization]] ###

To get a sense of the big picture, I made a map of the areas of math based on the Mathematics Subject Classification:

![Alt Areas of math based on the Mathematics Subject Classification](http://www.ms.lt/derlius/MatematikosSakosDidelis.png)

I organized them to try to show which area depended on which area. It's just a first try but I wanted to see what was most basic in math.  To my surprise, it seems that geometry must be very basic. So, for example, differential geometry is "calculus + geometry", but what is geometry?  I'm coming to believe that geometry is the way of embedding a lower dimension space into a higher dimension space.  In particular, I think that this is what tensors are all about.  I had been very confused about tensors trying to think of them as arrays of numbers, or "cemeteries" as Fredric Schuller says, critically, "witchcraft".  Now I am learning that the key point of tensors is that they divide a space into two points of view (covariant and contravariant).  The most helpful picture for me is [https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors](this one) from Wikipedia, but especially the example of a nonorthogonal coordinate system for a tetrahedron.  Removing each vector and replacing it with the normal ("the desired orthogonal vector") at the remaining surface yields a second coordinate system, a complementary one.  In other words, we can build up a system "bottom up" by adding dimensions (lines, planes) or we can start with the entire system and work "top down" by removing dimensions, yielding a sequence of hyperplanes. Geometry is what takes place between these two approaches.  The coordinate systems are complementary in the way that love supports life.  I may not be clear but at least it starts to make sense to me.   Also, I started to realize that the natural way to think about both of these coordinate systems is in terms of linear functionals.  One set of linear functionals naturally gives rise to a second set of linear functionals.  Now the latter turn out to be isomorphic to vectors when we are working in finite dimensions. However, it seems that vectors are Not the natural way to think of this.  That's I think another reason why I was confused.  So these are the kinds of matters it would be good to talk with somebody about, especially as regards how they help make sense of the big picture.

### [[premathematics]] ###

I will conclude with a little bit of my own philosophy/metaphysics to show how it can relate to math.  It is a structural thinking but is implicit, not explicit as we take "math" to be.  I start with the concept of "everything" and note that it has (and is given by) the following four properties:

* Everything has no external context.  If you put it in a box, it includes the box.  If you think it, then it includes you.
* Everything has no internal structure.  It may be orderly, it may be chaotic, it is both, it doesn't care.  Consequently, all statements are true of everything: Everything is hot, everything is cold, everything is good, everything is bad.
* Everything is the simplest possible algorithm.  It has no filter: Whatever you think of, you put into everything: the chair, the cup, yourself, God, etc.  This means that everything is a universal concept.  It's the same everything, the same algorithm, although we may put different things in it.  You may have your name for everything (Universe, being, love, etc.) and I may have mine, but we can talk about the same everything, even though we may have different things to say about it.
* Everything is a required concept.  Pragmatically, we all have it. We can't get rid of it.  We couldn't have learned it from the world, because everything that we know in the world is bounded whereas everything is unbounded.  So we must have already had it.

So the concept of "everything" provides an anchor for absolute truth, a preverbal concept that we can think about (as I have above) without necessarily relying on words.  In math we have an impulse to talk about "the set of all sets" and "everything" is similar but more basic, without any particular baggage (like sets) because everything is taken as the starting point.  In math, I think a better way to think about "everything" is "the state of contradiction" in which all statements are true.  The idea is that starting with the state of contradiction, then that state can work backwards to establish the conditions where a noncontradictory system is possible.

Starting with everything as an anchor, it is possible to divide everything into perspectives.  It turns out that my imagination is quite limited in doing so.  As a freshman in college in 1982-1983 I noticed the following divisions of everything:

* Dividing everything into two perspectives yields a framework for issues of existence.  There is one perspective where opposites coexist, as with free will, so that we can consider the question, whether this chair exists or not? And there is another perspective where all things are the same, as with fate, so that we have an answer: if it exists, then it exists, and if not, then not.
* Dividing everything into three perspectives yields a framework for participation, as with the scientific method: we take a stand, follow through and reflect, and then can take a stand again...
* Dividing everything into four perspectives yields a framework for knowledge, four levels: whether, what, how, why.

In math, starting with a state of contradiction, we can imagine it dividing itself into two perspectives to yield a proof by contradiction: if A, then A (all things are the same) but if Not A, then A anyways (opposites coexist).  Goedel's theorem shows that a state of contradiction can yield a division into three perspectives: completeness, consistency and self-reflectivity.  The division into four is at work in Yates Index Theorem in Recursive function theory where a level in the jump hierarchy knows everything about the level three jumps below.

The division of everything into five perspectives grounds decision making (time and space).  The division of everything into six perspectives grounds morality.  Finally, the division of everything into seven perspectives establishes a self-standing logical system. I take this to be Aristotle's logical square with three sides: All are black, all are white, there exists a black, there exists a white, all are black and there exists a black, all are white and there exists a white, there exists a black and there exists a white.  Adding an eighth perspective "all are black and all are white" makes the entire system empty, and it collapses, returning us to the state of contradiction.  So this is a good sign for me in the sense that it suggests that the philosophy may be finite and it may truly be possible to know everything.

Finally, I find it very helpful to think in terms of God's perspective.  God can be defined as the division of everything into no perspectives, whereas everything is the division of everything into one perspective.  God thus would be that initial state of contradiction from which all is generated.  The question which apparently drives God is: Is God necessary? Would God exist even if God didn't exist?  This yields the two perspectives given by the proof by contradiction.  So we have God who understands, who makes way for his own nonbeing (the world we find ourselves in), in which God arises even so as one who comes to understand.  How do they know they are the same God? Because they understand the same God.  So this is a trinity (the well known Father, Son, Spirit of Christianity).  But this same "game" also takes place from the Son's point of view (which requires 8 perspectives) and the Spirit's point of view (which requires 10 perspectives).  And there are 3 more perspectives that permute these 3 structures.  So there is a total of 24 = 3 + 8 + 10 + 3 perspectives which are the ways I imagine God and which are a closed system ("God's dance") that is the kernel for the more open system that we live in.  These questions are the most important ones for me.  But I want to show that this kind of thinking provides useful insights for math, physics and all of life.


Andrzej Buras

* [Wikipedia entry](https://en.wikipedia.org/wiki/Andrzej_Buras)

* [Institute page](https://www.professoren.tum.de/en/buras-andrzej/)

## Selected writings

On [[flavour physics]] and potential [[flavour anomalies]] in [[kaon]]-[[scattering|decays]]:

* {#Buras16} [[Andrzej Buras]], _The Revival of Kaon Flavour Physics_,  EPJ Web Conf. Volume 129, 2016  ([arXiv:1609.05711](https://arxiv.org/abs/1609.05711), [doi:10.1051/epjconf/201612900050](https://doi.org/10.1051/epjconf/201612900050))

* {#Buras18} [[Andrzej Buras]], _The Return of Kaon Flavour Physics_, Acta Phys. Pol. B 49, 1043 (2018) ([doi:10.5506/APhysPolB.49.1043](https://www.actaphys.uj.edu.pl/index_n.php?I=R&V=49&N=6#1043))

Textbook account:

* {#Buras20}  [[Andrzej Buras]], _Gauge Theory of Weak Decays_, (2020) ([doi:10.1017/9781139524100](https://doi.org/10.1017/9781139524100), [CERN review](https://cerncourier.com/a/the-hitchhikers-guide-to-weak-decays/) by [[Gino Isidori]])

category: people


Andrzej Filinski

* [webpage](http://www.diku.dk/~andrzej/)

category: people


Andrzej Kozlowski

* [Maths Genealogy page](https://www.mathgenealogy.org/id.php?id=175618)

## Selected writings

On [[equivariant bundles]] and [[equivariant cohomology]]:

* [[Andrzej Kozlowski]], _Equivariant Bundles and Cohomology_, Transactions of the American Mathematical Society Vol. 296, No. 1 (Jul., 1986), pp. 181-190 ([jstor:2000568](https://www.jstor.org/stable/2000568))

Identification of the higher [[homotopy groups]] of the [[homotopy of rational maps]] on the [[Riemann sphere]]:

*  [[Martin A. Guest]], [[Andrzej Kozlowski]], M. Murayama, [[Kohhei Yamaguchi]], *The homotopy type of the space of rational functions*, J. Math. Kyoto Univ. 35(4): 631-638 (1995) ([doi:10.1215/kjm/1250518652](https://projecteuclid.org/journals/kyoto-journal-of-mathematics/volume-35/issue-4/The-homotopy-type-of-the-space-of-rational-functions/10.1215/kjm/1250518652.full))

On [[homotopy of rational maps]] between [[real projective spaces]]:

* {#AdamaszekKozlowskiYamaguchi08} [[Michal Adamaszek]], [[Andrzej Kozlowski]], [[Kohhei Yamaguchi]], *Spaces of algebraic and continuous maps between real algebraic varieties*, Quart. J. Math. 62 (2011), 771–790 ([arXiv:0809.4893](https://arxiv.org/abs/0809.4893), [doi:10.1093/qmath/haq029](https://doi.org/10.1093/qmath/haq029))

and from [[real projective space]] to [[complex projective space]]:

* [[Andrzej Kozlowski]], [[Kohhei Yamaguchi]], *Spaces of algebraic maps from real projective spaces into complex projective spaces* ([arXiv:0812.3954](https://arxiv.org/abs/0812.3954)), in: [[Yves Félix]] et al. (eds.) *Homotopy Theory of Function Spaces and Related Topics*, Contemporary Mathematics Volume: 519; 2010 ([ISBN:978-0-8218-4929-3](https://bookstore.ams.org/conm-519))

category: people


Andrzej M. Borzyszkowski

* [GoogleScholar page](https://scholar.google.com/citations?user=CEsh0CQAAAAJ&hl=en)

## Selected writings

On generalized [[congruences]] and [[coequalizers]] in the [[1-category]] [[Cat]] of [[small categories]]:

* {#BednarczykBorzyszkowskiPawlowski99} [[Marek A. Bednarczyk]], [[Andrzej M. Borzyszkowski]], [[Wieslaw Pawlowski]], Section 4 of: *Generalized congruences -- epimorphisms in $\mathcal{C}at$*, Theory and Applications of Categories **5** 11 (1999) 266-280 [[tac:5-11](http://www.tac.mta.ca/tac/volumes/1999/n11/5-11abs.html), [dml:120226](https://eudml.org/doc/120226?lang=fr&limit=5)]

category: people

[[!redirects Andrzej Borzyszkowski]]


Andrzej Tarlecki

* [personal page](https://www.mimuw.edu.pl/~tarlecki/)

* [GoogleScholar page](https://scholar.google.com/citations?user=G3omKXoAAAAJ&hl=en)

## Selected writings

Introducing [[indexed categories]] as a tool of [[categorical semantics]] in [[computer science]], with fundamental results such as the existence and construction of [(co)limits in Grothendieck constructions](Grothendieck+construction#CoLimitsInAGrothendieckConstruction):

* {#TBG91} [[Andrzej Tarlecki]], [[Rod M. Burstall]], [[Joseph A. Goguen]], *Some fundamental algebraic tools for the semantics of computation: Part 3. Indexed categories*, Theoretical Computer Science **91** 2 (1991) 239-264 [doi:10.1016/0304-3975(91)90085-G]

category: people


András Csépai

## Selected writings

On the [[Pontryagin theorem]] (relating [[cobordism classes]] of [[normally framed submanifolds]] to [[Cohomotopy]]-sets), generalized to [[proper maps]] to [[Euclidean spaces]]:

* {#Csepai20} [[András Csépai]], _Stable Pontryagin-Thom construction for proper maps_,  Period Math Hung 80, 259–268 (2020) ([arXiv:1905.07734](https://arxiv.org/abs/1905.07734), [doi:10.1007/s10998-020-00327-0](https://doi.org/10.1007/s10998-020-00327-0))

category: people

[[!redirects Andras Csepai]]


András Kovács

* [personal page](https://andraskovacs.github.io/)

## Selected writings

On [[higher inductive-inductive types]]:

* {#KaposiKovacs} [[Ambrus Kaposi]], [[András Kovács]], *A Syntax for Higher Inductive-Inductive Types*, at *3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)* (2018) 20:1-20:18 [[pdf](http://drops.dagstuhl.de/opus/volltexte/2018/9190/), [doi:10.4230/LIPIcs.FSCD.2018.20](https://doi.org/10.4230/LIPIcs.FSCD.2018.20)]

* [[Ambrus Kaposi]], [[András Kovács]], *Signatures and Induction Principles for Higher Inductive-Inductive Types*, Logical Methods in Computer Science **16** 1 (2020) lmcs:6100 [[arXiv:1902.00297](https://arxiv.org/abs/1902.00297), doi:10.23638/LMCS-16(1:10)2020]

category: people

[[!redirects Andras Kovacs]]


André Haefliger

* [Home page](http://www.unige.ch/math/folks/haefliger/)

* [Wikipedia entry](http://en.wikipedia.org/wiki/Andr%C3%A9_Haefliger)

## Selected writings

* {#Haefliger66} [[André Haefliger]], _Differentiable Embeddings of $S^n$ in $S^{n+q}$ for $q \gt 2$_, Annals of Mathematics Second Series, Vol. 83, No. 3 (May, 1966), pp. 402-436 ([jstor:1970475](https://www.jstor.org/stable/1970475))

* [[M. Bridson]] and [[A. Haefliger]], 1999, _Metric Spaces of Non-Positive Curvature_, number 31 in  Grundlehren der Math. Wiss, Springer.

Introducing [[Haefliger groupoids]]:

* [[André Haefliger]], _Homotopy and integrability_,  In: N.H. Kuiper (ed.) _Manifolds_ — Amsterdam 1970. Lecture Notes in Mathematics, vol 197. Springer 1971 ([doi:10.1007/BFb0068615](https://doi.org/10.1007/BFb0068615))

On [[orbifolds]]:

* [[André Haefliger]], _Groupoides d'holonomie et classifiants_, Astérisque no. 116 (1984), p. 70-97 ([numdam:AST_1984__116__70_0/](http://www.numdam.org/item/AST_1984__116__70_0/))

On [[orbispaces]]:

* {#Haefliger84} [[André Haefliger]], _Groupoides d'holonomie et classifiants_, Astérisque no. 116  (1984), p. 70-97 ([numdam:AST_1984__116__70_0](http://www.numdam.org/item/?id=AST_1984__116__70_0))

* {#Haefliger90} [[André Haefliger]], _Orbi-Espaces_,  In: E. Ghys, P. de la Harpe (eds.), _Sur les Groupes Hyperboliques d’après Mikhael Gromov_, Progress in Mathematics, vol 83. Birkhäuser 1990 ([doi:10.1007/978-1-4684-9167-8_11](https://doi.org/10.1007/978-1-4684-9167-8_11))

* {#Haefliger91} [[André Haefliger]], _Complexes of Groups and Orbihedra_, in: E. Ghys, A. Haefliger, A Verjovsky (eds.), _Proceedings of the Group Theory from a Geometrical Viewpoint_, ICTP, Trieste, Italy , 26 March – 6 April 1990_, World Scientific 1991 ([doi:10.1142/1235](https://doi.org/10.1142/1235))

On [[mapping stacks]] between [[orbifolds]]:

* [[André Haefliger]], _On the space of morphisms between étale groupoids_, In:  P. Robert Kotiuga (ed.) _A Celebration of the Mathematical Legacy of Raoul Bott_ ([arXiv:0707.4673](https://arxiv.org/abs/0707.4673), [ams:crmp-50](https://bookstore.ams.org/crmp-50))

category:people

[[!redirects A. Haefliger]]
[[!redirects Haefliger]]
[[!redirects Andre Haefliger]]


André Henriques

* [personal website](http://andreghenriques.com/)

* [university website](https://www.maths.ox.ac.uk/people/andre.henriques)

## Selected writings:

On [[tmf]]:

* [[Christopher Douglas]], [[John Francis]], [[André Henriques]], [[Michael Hill]], _Topological Modular Forms_, Mathematical Surveys and Monographs Volume 201, AMS 2014  ([ISBN:978-1-4704-1884-7](https://bookstore.ams.org/surv-201))

On [[2d CFT]] as an  [[functorial quantum field theory]] on a [[(infinity,n)-category of cobordisms|2-category of complex cobordisms]]:

* [[André Henriques]], *The complex cobordism 2-category*, 2021 ([video](http://andreghenriques.com/ComplexCob2CatandCentralExt.mp4))

## Related $n$Lab-entries

* [[Lie integration]]

* [[string Lie 2-algebra]], [[string Lie 2-group]]

* [[conformal net]]

* [[Chern-Simons theory]]

* [[orbispace]]

category: people

[[!redirects Andre Henriques]]


André Hirschowitz

* [webpage](http://math.unice.fr/~ah/)

category: people

[[!redirects Andre Hirschowitz]]