Jean Nuyts

* [spire page](https://inspirehep.net/authors/995317)

## Selected writings

On [[electric-magnetic duality]] ([[S-duality]]):

* {#GNO77} [[Peter Goddard]], [[Jean Nuyts]], [[David Olive]], *Gauge Theories And Magnetic Charge*, Nucl. Phys. B **125** (1977) 1-28 [doi:10.1016/0550-3213(77)90221-8, [spire:111435](https://inspirehep.net/literature/111435)]

category:people


Jean Pradines

Jean Pradines is a French mathematician, who for many years was at the Université Paul Sabatier, Toulouse. He was a student of [[Charles Ehresmann]] and continued many of the themes of Ehresmann's work in differential geometry.

* [genealogy](http://genealogy.math.ndsu.nodak.edu/id.php?id=98595)

## Related pages

* [[internal category]]

* [[Lie algebroid]]

##Publications of interest

* [In Ehresmann's footsteps: from group geometries to groupoid geometries](http://arxiv.org/pdf/0711.1608.pdf)

* [Groupoïdes de Lie et Feuilletages](http://semioweb.msh-paris.fr/f2ds/docs/feuilletages/Jean_Pradines5.pdf) (Lie groupoids and foliations).

category: people


Jean Renault

* [webpage](http://www.univ-orleans.fr/mapmo/membres/renault/)

## Related entries

* [[groupoid algebra]]

category: people


Jean Thierry-Mieg

* [InSpire page](https://inspirehep.net/authors/986225)

## Selected writings

On antisymmetric rank-2 [[field (physics)|fields]] (2-form field, [[Kalb-Ramond fields]]):

* [[Peter D. Jarvis]], [[Jean Thierry-Mieg]], *Antisymmetric tensor fields: actions, symmetries and first order Duffin-Kemmer-Petiau formulations* [[arXiv:2311.01675](https://arxiv.org/abs/2311.01675)]

* [[Jean Thierry-Mieg]], [[Peter D. Jarvis]], *Conformal invariance of antisymmetric tensor field theories in any even dimension* [[arXiv:2311.01701](https://arxiv.org/abs/2311.01701)]

category: people


Jean Vuillemin

* [persona page](https://www.di.ens.fr/~jv/)

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

## Selected writings

On [[exact real computer arithmetic]]:

* [[Jean Vuillemin]], *Exact real computer arithmetic with continued fractions*, in *LFP '88: Proceedings of the 1988 ACM conference on LISP and functional programming* (1988) 14–27 [[doi:10.1145/62678.62681](https://doi.org/10.1145/62678.62681)]

category: people


Jean Zinn-Justin

* [Wikipedia entry](https://en.wikipedia.org/wiki/Jean_Zinn-Justin)

## related $n$Lab entries

* [[BRST complex]]

* [[resurgence]]

category: people


Jean-Benoît Bost

[[!redirects Jean-Benoit Bost]]

* [webpage](http://www.math.u-psud.fr/~bost/Accueil.html)

## Selected writings

Introducing the [[Bost-Connes system]]:

* {#BostConnes95} [[Jean-Benoit Bost]]; [[Alain Connes]], *Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory*, Selecta Mathematica, New Series **1** 3 (1995) 411-457 [[doi:10.1007/BF01589495](https://doi.org/10.1007/BF01589495), ISSN 1022-1824, [pdf](https://web.archive.org/web/20110806043925/https://alainconnes.org/docs/bostconnesscan.pdf)]

## Related entries

* [[Arakelov geometry]]

* [[Bost-Connes system]]

category: people


Jean-Claude Thomas

* [webpage](https://perso.math.univ-angers.fr/spip.php?article28)

## Selected writings

On [[rational homotopy theory]]:

* {#FelixHalperinThomas00} [[Yves Félix]], [[Stephen Halperin]], [[Jean-Claude Thomas]], _Rational Homotopy Theory_, Graduate Texts in Mathematics, 205, Springer-Verlag, 2000 ([doi:10.1007/978-1-4613-0105-9](https://link.springer.com/book/10.1007/978-1-4613-0105-9))

* {#FelixHalperinThomas15} [[Yves Félix]], [[Steve Halperin]], [[Jean-Claude Thomas]], _Rational Homotopy Theory II_, World Scientific 2015 ([doi:10.1142/9473](https://doi.org/10.1142/9473))

  (this second volume generalizes to the case of non-[[simply connected topological spaces]])

On the [[rational cohomology]] of [[configuration spaces of points]]:

* [[Yves Félix]], [[Jean-Claude Thomas]], _Rational Betti numbers of configuration spaces_, Topology and its Applications, Volume 102, Issue 2, 8 April 2000, Pages 139-149 (doi:10.1016/S0166-8641(98)00148-5)

On the [[cobar construction]]:

* [[Yves Felix]], [[Stephen Halperin]], [[Jean-Claude Thomas]], _Adams' Cobar Equivalence_, Transactions of the American Mathematical Society
Vol. 329, No. 2 (1992), pp. 531-549 ([jstor:2153950](https://www.jstor.org/stable/2153950))

category:people


Jean-Eric Pin

 Jean-Éric Pin is a French mathematician based in the
Institut de Recherche en Informatique Fondamentale (IRIF), and University Paris-Diderot. He has made important discoveries in combinatorics, semigroup theory, and the theory of languages.

* [Webpage](https://www.irif.fr/~jep/).

* [Research themes](https://www.irif.fr/~jep/node1.html) (in French)

## Selected publications

On [[tropical semirings]]:

* [[Jean-Eric Pin]], _Tropical semirings_, [Hal preprint, hal-00113779](https://hal.archives-ouvertes.fr/hal-00113779/file/Tropical.pdf).

category:people


Jean-François Pommaret

* [personal page](http://cermics.enpc.fr/~pommaret/home.html)

## Selected writings

On [[partial differential equations]] (via [[jet bundles]], [[jet groups]], ...):

* [[Jean-François Pommaret]], *Partial Differential Equations and Group Theory*, Springer (1994) [[doi:10.1007/978-94-017-2539-2](https://doi.org/10.1007/978-94-017-2539-2)]

category: people

[[!redirects Jean-Francois Pommaret]]


Jean-Louis Koszul

* [Wikipedia entry](http://en.wikipedia.org/wiki/Jean-Louis_Koszul)

## Selected writings

On [[group actions]] in [[TopologicalSpaces]] ("[[transformation groups]]", "[[topological G-spaces]]"):

* {#Koszul65} [[Jean-Louis Koszul]], _Lectures on Groups of Transformations_, Tata Institute 1965 ([pdf](http://www.math.tifr.res.in/~publ/ln/tifr32.pdf), [[KoszulGroupsOfTransformations.pdf:file]])

## Related entries

* [[Koszul-Malgrange theorem]]

* [[Koszul duality]]

* [[Koszul algebra]]

* [[Koszul complex]]

* [[Koszul-Tate resolution]]

category: people

[[!redirects Koszul]]


Jean-Louis Loday

__Jean-Louis Loday__ (1946-2012) was a French mathematician who, at the time of his passing, was _Directeur de Recherche au CNRS_ based in Strasbourg. He is well known for his work in [[algebraic K-theory]], in the development of [[cyclic homology]] and more recently for work on [[operads]] and [[Leibniz algebras]].

* [Wikipedia entry](https://en.wikipedia.org/wiki/Jean-Louis_Loday)

* [SMF notice of decease](http://smf.emath.fr/content/d%C3%A9c%C3%A8s-de-jean-louis-loday)

* [old webpage](https://web.archive.org/web/20110823075214/http://www-irma.u-strasbg.fr/~loday/)

## Selected writings

On [[cyclic homology]] ([[cyclic objects]], [[cyclic spaces]], ... ):

* [[Jean-Louis Loday]], *Cyclic Homology*, Grundlehren **301**, Springer 1992 ([doi:10.1007/978-3-662-21739-9](https://link.springer.com/book/10.1007/978-3-662-21739-9))

On [[homotopy types with finite homotopy groups]]:

* [[Jean-Louis Loday]], _Spaces with finitely many nontrivial homotopy groups_, J.Pure Appl. Alg., 24, (1982), 179--202.

On [[operads]]:

* [[Jean-Louis Loday]], *Algebras, Operads, Combinads*, talk at HOGT Lille (2012) [[[Loday-OperadsCombinads.pdf:file]]]

* [[Jean-Louis Loday]], [[Bruno Vallette]], *Algebraic Operads*, Grundlehren der mathematischen Wissenschaften **346**, Springer 2012 ([ISBN 978-3-642-30362-3](https://www.springer.com/gp/book/9783642303616), [pdf](https://pure.mpg.de/rest/items/item_3121746_1/component/file_3121747/content))

On the relation between [[free loop spaces]]/[[cyclic loop spaces]] and [[Hochschild homology]]/[[cyclic homology]]:

* {#Loday11}[[Jean-Louis Loday]], _Free loop space and homology_, Chapter 4 in: Janko Latchev, Alexandru Oancea (eds.): *Free Loop Spaces in Geometry and Topology*, IRMA Lectures in Mathematics and Theoretical Physics **24**, EMS 2015 ([arXiv:1110.0405](https://arxiv.org/abs/1110.0405), [ISBN:978-3-03719-153-8](https://bookstore.ams.org/emsilmtp-24/))

Other:

* Jean-Louis Loday, [[Teimuraz Pirashvili]], _Universal enveloping algebras of Leibniz algebras and (co)homology_, Math. Ann. __296__, 139-158 (1993), [pdf](http://www-irma.u-strasbg.fr/~loday/PAPERS/LodayPira1993%28Leibniz%29.pdf)

* Jean-Louis Loday, [[Teimuraz Pirashvili]], _The tensor category of linear maps_, Georg. Math. J. vol. 5, n.3 (1998) 263--276.

* D. Guin-Walery and [[J.-L. Loday]], 1981, _Obstructions à l'excision en K-théorie algèbrique_, in Evanston Conference on Algebraic K-theory, 1980, volume 854 of Lecture Notes in Maths., 179 – 216, Springer.

category: people

[[!redirects J-L. Loday]]
[[!redirects J.-L. Loday]]
[[!redirects Loday]]


Jean-Louis Tu

* [webpage](http://www.math.univ-metz.fr/~tu/)

## Selected writings

On [[twisted equivariant K-theory]] via [[bundle gerbes]] over [[differentiable stacks]]:

* [[Jean-Louis Tu]], [[Ping Xu]], [[Camille Laurent-Gengoux]], _Twisted K-theory of differentiable stacks_, Annales Scientifiques de l’École Normale Supérieure Volume 37, Issue 6, November–December 2004, Pages 841-910 ([arXiv:math/0306138](https://arxiv.org/abs/math/0306138), [doi:10.1016/j.ansens.2004.10.002](https://doi.org/10.1016/j.ansens.2004.10.002))

On [[fiber bundles]] and [[principal bundles]] over [[Lie groupoids]] (e.g. [[orbifolds]]):

* [[Camille Laurent-Gengoux]], [[Jean-Louis Tu]], [[Ping Xu]], _Chern-Weil map for principal bundles over groupoids_, Math. Z. 255, 451–491 (2007) ([arXiv:math/0401420](https://arxiv.org/abs/math/0401420), [doi:10.1007/s00209-006-0004-4](https://doi.org/10.1007/s00209-006-0004-4))

On the [[twisted equivariant Chern character]] in [[orbifold K-theory]] (including the twist by [[inner local systems]]):

* [[Jean-Louis Tu]], [[Ping Xu]], _Chern character for twisted K-theory of orbifolds_, Advances in Mathematics Volume 207, Issue 2, 20 December 2006, Pages 455-483 ([arXiv:math/0505267](https://arxiv.org/abs/math/0505267), [doi:10.1016/j.aim.2005.12.001](https://doi.org/10.1016/j.aim.2005.12.001))

On the [[cohomology ring]]-structure of [[twisted equivariant K-theory]]:

* [[Jean-Louis Tu]], [[Ping Xu]], *The ring structure for equivariant twisted K-theory*, J. Reine Angew. Math. 635 (2009), 97–148 ([arXiv:math/0604160](https://arxiv.org/abs/math/0604160), [doi:10.1515/CRELLE.2009.077](https://doi.org/10.1515/CRELLE.2009.077))

category: people


Jean-Louis Verdier

**Jean-Louis Verdier** was a student of [[Alexandre Grothendieck]].  He introduced, at the suggestion of Grothendieck, the notions of [[derived categories]] and [[triangulated categories]] in his thesis.

* [Wikipedia](http://en.wikipedia.org/wiki/Jean-Louis_Verdier)

* [Mathematical genealogy](http://www.genealogy.math.ndsu.nodak.edu/id.php?id=31267)

## Selected writings

On [[derived categories]] of [[abelian categories]] and on [[triangulated categories]]:

* [[Verdier, Jean-Louis]], _Des Catégories Dérivées des Catégories Abéliennes_, Astérisque **239** (1996) [[doi:10.24033/ast.364](https://smf.emath.fr/publications/des-categories-derivees-des-categories-abeliennes), [numdam:AST_1996__239__R1_0](http://www.numdam.org/issues/AST_1996__239__R1_0), [pdf](http://www.numdam.org/item/AST_1996__239__R1_0.pdf)]

He also worked on [[Verdier duality]] of derived categories of [[abelian sheaves]]:

* Jean-Louis Verdier, _Dualité dans la cohomologie des espaces localement compacts_. Séminaire Bourbaki, 9 (1964-1966), Exp. No. 300, 13 p. Available at [NUMDAM](http://www.numdam.org/item?id=SB_1964-1966__9__337_0).

* Jean-Louis Verdier, _A duality theorem in the etale cohomology of schemes_. Lecture notes. Summer Institute on Algebraic Geometry. Woods Hole 1964.

On a formalization and proof of the [[McKay correspondence]] via [[equivariant K-theory]]:

* {#GSV83} [[Gérard Gonzalez-Sprinberg]], [[Jean-Louis Verdier]], _Construction géométrique de la correspondance de McKay_, Ann. Sci. ́École Norm. Sup. **16** 3 (1983) 409–449 ([numdam:ASENS_1983_4_16_3_409_0](http://www.numdam.org/item?id=ASENS_1983_4_16_3_409_0))

## Related pages

* [[SGA]]

* [[Verdier site]]

* [[hypercover]]

* [[Verdier duality]]

* [[Grothendieck context]]

* [[ind-object]], [[strict ind-object]]

* [[triangulated category]]

* [[enhanced triangulated category]]

* [[Karoubian category]]

* [[comparison lemma]]

* [[pro-object]]

* [[McKay correspondence]]

category: people

[[!redirects Verdier]]
[[!redirects J.-L. Verdier]]
[[!redirects J. L. Verdier]]
[[!redirects Verdier, Jean-Louis]]


Jean-Loup Gervais

* [Wikipedia entry](https://en.wikipedia.org/wiki/Jean-Loup_Gervais)

* [InSpire page](https://inspirehep.net/authors/1008543)

## Selected writings

Early discussion of [[quantization]] of the [[Polyakov action]] for the [[bosonic string]] with attention to the [[Liouville field]]:

* [[Jean-Loup Gervais]], [[André Neveu]], *The dual string spectrum in Polyakov's quantization (I)*, Nuclear Physics B **199** 1 (1982) 59-76 [doi:10.1016/0550-3213(82)90566-1]

* [[Jean-Loup Gervais]], [[André Neveu]], *Dual string spectrum in Polyakov's quantization (II). Mode separation*, Nuclear Physics B **209** 1 (1982) 125-145 [doi:10.1016/0550-3213(82)90105-5]

category: people


Jean-Luc Brylinski

Jean-Luc Brylinski is a French mathematician now working in the USA. He has developed [[gerbes]] in a differential geometric context.

* [Wikipedia entry](http://en.wikipedia.org/wiki/Jean-Luc_Brylinski)

## Selected writings

On [[loop spaces]], [[characteristic classes]] and [[geometric quantization]] (and on [[bundle gerbes]] and on [[Deligne cohomology]]):

* {#Brylinski93} [[Jean-Luc Brylinski]], *Loop spaces, characteristic classes and geometric quantization*, Birkhäuser (1993) [[doi:10.1007/978-0-8176-4731-5](https://link.springer.com/book/10.1007/978-0-8176-4731-5)]

On the [[cyclic homology]] of the [[groupoid convolution algebra]] of [[étale groupoid|étale]] [[Lie groupoids]], hence of [[orbifolds]]:

* [[Jean-Luc Brylinski]], [[Victor Nistor]], *Cyclic cohomology of étale groupoids*,  K-theory 8.4 (1994): 341-365 ([pdf](https://www.researchgate.net/profile/Victor-Nistor/publication/226520448_Cyclic_cohomology_of_etale_groupoids/links/5509d9d30cf20ed529e227b0/Cyclic-cohomology-of-etale-groupoids.pdf), [[BrylinskiNistor_CyclicCohomology.pdf:file]])

## Related $n$Lab entries

many (...)

category: people
[[!redirects J.-L. Brylinski]]


Jean-Marc Andreoli

* [webpage](http://www.xrce.xerox.com/About-XRCE/People/Jean-Marc-Andreoli)

##Related concepts

* [[focusing]]
* [[polarity in type theory]]

category: people


Jean-Marc Cordier

**Jean-Marc Cordier** (died 7 May 2014) was a French mathematician, working at LAMFA, Université de Picardie Jules Verne, Amiens.

He obtained his doctorat d'état es' Sciences from Paris 7 in 1987. His research has centred on problems of homotopy coherence, homotopy limits and their application to Steenrod-Sitnikov homology, and strong shape theory.

## Selected writings

On [[profunctors]] with application to [[shape theory]]:

* [[Dominique Bourn]], [[Jean-Marc Cordier]], _Distributeurs et théorie de la forme_, Cah. Top. Géom. Diff. Cat. **21** no.2 (1980) pp.161-189. ([numdam:CTGDC_1980__21_2_161_0](http://www.numdam.org/item/CTGDC_1980__21_2_161_0), [pdf](http://archive.numdam.org/ARCHIVE/CTGDC/CTGDC_1980__21_2/CTGDC_1980__21_2_161_0/CTGDC_1980__21_2_161_0.pdf))

On [[homotopy coherent diagrams]] and their [[homotopy limits]]/[[homotopy colimits]]

* J.-M. Cordier, _Sur la notion de diagramme homotopiquement cohérent_, Proc. 3éme Colloque sur les Catégories, Amiens (1980), Cah. Top. Géom. Diff., 23,(1982) 93 -112.

* J.-M. Cordier, _Sur les limites homotopiques de diagrammes homotopiquement cohérents_, Comp. Math., 62 (1987) 367-388.

* J.-M. Cordier, _Homologie de Steenrod-Sitnikov et limite homotopique algèbrique_, manuscripta math 59 (1987) 35-52.

together with several other joint papers with [[Dominique Bourn]] and [[Tim Porter]].

category: people
[[!redirects J.-M. Cordier]]
[[!redirects Cordier]]


Jean-Marc Fontaine

* [Wikipedia entry](http://en.wikipedia.org/wiki/Jean-Marc_Fontaine)

## related $n$Lab entries

* [[function field analogy]]

* [[perfectoid space]]

category: people


Jean-Marc Richard

* [spire page](https://inspirehep.net/authors/991820)

## Selected writings

On [[tetraquarks]] completely made of [[heavy quarks]] (specifically: [[charm quarks]]):

* [[Jean-Marc Richard]], *About the $J/\psi J/\psi$ peak of LHCb: fully-charmed tetraquark?*, Science Bulletin Volume 65, Issue 23, 15 December 2020, Pages 1954-1955 ([arXiv:2008.01962](https://arxiv.org/abs/2008.01962), [doi:10.1016/j.scib.2020.08.020](https://doi.org/10.1016/j.scib.2020.08.020))

* [[Jean-Marc Richard]], *Fully-heavy tetraquarks and other heavy multiquarks*, Nuclear and Particle Physics Proceedings 00 (2021) 1–5 ([arXiv:2105.02503](https://arxiv.org/abs/2105.02503))

category: people


Jean-Marie Maranda

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=17855)

(brief comments on Maranda may be found in [Marquis & Reyes, 2009](logic#MarquisReyes09))

## Selected writings

A list of publications may be found in Berthiaume's Prologue to *A generalization of the notion of fundamental construction* [[pdf](http://www.labmath.uqam.ca/~annales/volumes/01-1/PDF/033-035.pdf)].

The observation that [[colimits]] can be constructed from [[coproducts]] and [[coequalisers]]:

* [[J.-M. Maranda]], *Some remarks on limits in categories*. Canadian Mathematical Bulletin **5** 2 (1962) 133-146 [[doi:10.4153/CMB-1962-015-0](https://doi.org/10.4153/CMB-1962-015-0)]

Introducing the notion of *[[enriched categories]]* (and that of *[[strict 2-categories]]*, as an example, and that of [[adjunctions]] in general strict 2-categories):

* {#Maranda65} [[Jean-Marie Maranda]], Def. 1 in: *Formal categories*, Canadian Journal of Mathematics **17** (1965) 758-801 [[doi:10.4153/CJM-1965-076-0](https://doi.org/10.4153/CJM-1965-076-0), [pdf](https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A7C463460EB8CAC64C2CA340F870CF80/S0008414X00039729a.pdf/formal-categories.pdf)]

On the [[universal property]] of the [[Kleisli category]] under  [[monad morphisms]]:

* {#Maranda66} [[Jean-Marie Maranda]], *On Fundamental Constructions and Adjoint Functors*, Canadian Mathematical Bulletin **9** 5  (1966) 581-591 [[doi:10.4153/CMB-1966-072-9](https://doi.org/10.4153/CMB-1966-072-9)]

On "monads of superior degree":

* [[J.-M. Maranda]], *Constructions fondamentales de dégré supérieur* (1970) 1-16 [[doi:10.1515/crll.1970.243.1](https://doi.org/10.1515/crll.1970.243.1)]

category: people

[[!redirects Jean Maranda]]

[[!redirects Jean M. Maranda]]
[[!redirects Jean-M. Maranda]]

[[!redirects J.-M. Maranda]]
[[!redirects J. M. Maranda]]


Jean-Marie Souriau

* [wikipedia entry](http://en.wikipedia.org/wiki/Jean-Marie_Souriau)

* [Souriau's works](http://sites.univ-provence.fr/souriau90/Souriau90/Works.html)

## Selected writings

Introducing [[geometric quantization]]:

* {#Souriau69} [[Jean-Marie Souriau]], _[Structure des systemes dynamiques](http://www.jmsouriau.com/structure_des_systemes_dynamiques.htm)_, Dunod, Paris (1970)

  Translated and reprinted as (see section V.18 for geometric quantization):

  [[Jean-Marie Souriau]], _Structure of dynamical systems - A symplectic view of physics_, Brikhäuser (1997) ([doi:10.1007/978-1-4612-0281-3](https://link.springer.com/book/10.1007/978-1-4612-0281-3))

* {#Souriau74} [[Jean-Marie Souriau]], _Modèle de particule à spin dans le champ électromagnétique et gravitationnel_, Annales de l'I.H.P. Physique théorique, 20 no. 4 (1974), p. 315-364  ([numdam](http://www.numdam.org/item?id=AIHPA_1974__20_4_315_0))

On [[diffeological groups]] (and introducing [[diffeological spaces]]) in [[mathematical physics]] in general and in [[geometric quantization]] in particular:

* {#Souriau79} [[Jean-Marie Souriau]], _Groupes différentiels_, in _Differential Geometrical Methods in Mathematical Physics_ (Proc. Conf., Aix-en-Provence/Salamanca, 1979), Lecture Notes in Math. 836, Springer, Berlin, (1980), pp. 91–128. ([doi:10.1007/BFb0089728](https://doi.org/10.1007/BFb0089728), [mr:607688](http://www.ams.org/mathscinet-getitem?mr=607688))

* {#Souriau84} [[Jean-Marie Souriau]], _Groupes différentiels et physique mathématique_,  In: Denardo G., Ghirardi G., Weber T. (eds.) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 201. Springer 1984 ([doi:10.1007/BFb0016198](https://doi.org/10.1007/BFb0016198))

On [[thermodynamics]] and [[general relativity]]:

* {#IglesiasSouriau84} [[Patrick Iglesias-Zemmour]], [[Jean-Marie Souriau]] _Heat, cold and Geometry_, in: M. Cahen et al (eds.) Differential geometry and mathematical physics, 37-68, D. Reidel 1983 ([web](http://www.jmsouriau.com/Heat_Cold_And_Geometry_1983.htm), [pdf](http://www.jmsouriau.com/Publications/JMSouriau-PIglesias-HeatColdAndGeometry1983.pdf), [doi:978-94-009-7022-9_5](https://doi.org/10.1007/978-94-009-7022-9_5))

On [[symplectic geometry]] of [[phase spaces]]:

* [[Jean-Marie Souriau]], _Structure of dynamical systems. A symplectic view of physics_ . Translated from the French by C. H. Cushman-de Vries. Translation edited and with a preface by R. H. Cushman and G. M. Tuynman. Progress in Mathematics, 149. Birkhäuser Boston, Inc., Boston, MA, 1997

On [[thermodynamics]]:

* [[Jean-Marie Souriau]], _Thermodynamique et géométrie_,  Lecture Notes in Math. 676 (1978), 369–397 ([scan](http://www-lib.kek.jp/cgi-bin/kiss_prepri.v8?KN=197810025))

## Related entries

* [[symplectic manifold]]

* [[moment map]]

* [[geometric quantization]]

  * [[quantomorphism group]]

* [[diffeological space]]

* [[diffeological group]]

category: people


Jean-Michel Bismut

* [Wikipedia entry](http://en.wikipedia.org/wiki/Jean-Michel_Bismut)

## Selected writings

Introducing the [[Bismut-Chern character]]:

* [[Jean-Michel Bismut]], *Index Theorem and Equivariant Cohomology on the Loop Space*, Comm. in Math. Phys. **98** (1985) 213-237 [[doi:10.1007/BF01220509](https://doi.org/10.1007/BF01220509), [euclid](https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-98/issue-2/Index-theorem-and-equivariant-cohomology-on-the-loop-space/cmp/1103942357.full)]

On [[quantum anomalies]] via [[index theory]]:

* [[Jean-Michel Bismut]], [[Daniel Freed]], _The analysis of elliptic families. I. Metrics and connections on determinant bundles_ , Comm. Math. Phys. 106 (1986), no. 1, 159–176 ([doi:10.1007/BF01210930](https://doi.org/10.1007/BF01210930), [euclid:1104115586](https://projecteuclid.org/euclid.cmp/1104115586))

* [[Jean-Michel Bismut]], [[Daniel Freed]], _The analysis of elliptic families. II. Dirac operators, eta invariants, and the holonomy theorem_ , Comm. Math. Phys. 107 (1986), no. 1, 103–163 ([doi:10.1007/BF01206955](https://doi.org/10.1007/BF01206955), [euclid:1104115934](https://projecteuclid.org/euclid.cmp/1104115934))

category: people


Jean-Michel Kantor

* [webpage](http://webusers.imj-prg.fr/~jean-michel.kantor/)

## related $n$Lab entries

* [[structuralism]]

category: people


Jean-Michel Raimond

* [Wikipedia entry](https://en.wikipedia.org/wiki/Jean-Michel_Raimond)

## Selected writings

On [[quantum physics]]:

* [[Serge Haroche]], [[Jean-Michel Raimond]], *Exploring the Quantum: Atoms, Cavities, and Photons*, Oxford University Press (2006) [[doi:10.1093/acprof:oso/9780198509141.001.0001](https://doi.org/10.1093/acprof:oso/9780198509141.001.0001)]

category: people


Jean-Noël Fuchs

* [institute page](https://www.lptmc.jussieu.fr/users/fuchs)

## Selected writings

Models for [[Chern insulators]] akin to the [[Haldane model]]:

* Doru Sticlet, [[Frédéric Piéchon]], [[Jean-Noël Fuchs]], Pavel Kalugin, Pascal Simon, *Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index*, Phys. Rev. B **85** 165456 (2012) [[arXiv:1201.6613](https://arxiv.org/abs/1201.6613), [doi:10.1103/PhysRevB.85.165456](https://doi.org/10.1103/PhysRevB.85.165456)]

* [[Marwa Mannaï]], [[Jean-Noël Fuchs]], [[Frédéric Piéchon]], [[Sonia Haddad]], *Stacking-induced Chern insulator* [[arXiv:2208.02491](https://arxiv.org/abs/2208.02491)]

On [[electronic band structure]] with focus on [[topological phases of matter]]:

* [[Jérôme Cayssol]], [[Jean-Noël Fuchs]], *Topological and geometrical aspects of band theory*, J. Phys. Mater. **4** (2021) 034007 ([arXiv:2012.11941](https://arxiv.org/abs/2012.11941), [doi:10.1088/2515-7639/abf0b5](https://doi.org/10.1088/2515-7639/abf0b5))

category: people


Jean-Philippe Vert

* [personal page](http://members.cbio.mines-paristech.fr/~jvert/)

## Selected writings

On [[kernel methods]] in [[machine learning]]:

* [[Julien Mairal]], [[Jean-Philippe Vert]], *Machine Learning with Kernel Methods*, lecture notes 2017 ([webpage](http://members.cbio.mines-paristech.fr/~jvert/svn/kernelcourse/course/2021mva/index.html), [pdf](http://members.cbio.mines-paristech.fr/~jvert/svn/kernelcourse/slides/master2017/master2017.pdf), [[MairalVertKernelMethods.pdf:file]])

Proof that the [[Mallows kernel]] and [[Kendall kernel]] are [[positive definite bilinear form|positive definite]]:

* [[Yunlong Jiao]], [[Jean-Philippe Vert]], *The Kendall and Mallows Kernels for Permutations*, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 40, no. 7, pp. 1755-1769, 1 July 2018 ([doi:10.1109/TPAMI.2017.2719680](https://doi.org/10.1109/TPAMI.2017.2719680), [hal:01279273](https://hal.archives-ouvertes.fr/hal-01279273/document))

Discussion of weighted variants:

* [[Yunlong Jiao]], [[Jean-Philippe Vert]], *The Weighted Kendall and High-order Kernels for Permutations*, Proceedings of the 35th International Conference on Machine Learning, PMLR 80:2314-2322, 2018 ([arXiv:1802.08526](https://arxiv.org/abs/1802.08526), [mlr:v80/jiao18a](http://proceedings.mlr.press/v80/jiao18a.html), [hal:hal-01717385](https://hal.inria.fr/hal-01717385))

category: people


Jean-Pierre Demailly

* [webpage](http://www-fourier.ujf-grenoble.fr/~demailly/)

category: people


Jean-Pierre Jouanolou

_Jean-Pierre Jouanolou_ is working in [[algebraic geometry]], [[commutative algebra]] and [[algebraic K-theory]]; he was a student of [[Alexandre Grothendieck]]. There is a famous cover of the [[projective space]] by [[quadric]]s called [[Jouanolou cover]].

* [conference](http://www-sop.inria.fr/galaad/conf/jouanolou) honoring Jouanolou
* math [genealogy](http://genealogy.math.ndsu.nodak.edu/id.php?id=90399) page
* J.-P. Jouanolou, _Une suite exacte de Mayer-Vietoris en K-th´eorie alg´ebrique_, Algebraic K-theory, I (Seattle, 1972), 293–316, Lecture Notes in Mathematics __341__, Springer (1973).

category: people


Jean-Pierre Marquis

Jean-Pierre Marquis is a professor in the Département de Philosophie of the Université de Montréal. He has written extensively on the [[philosophy|philosophical]] implications of [[category theory]] and is currently exploring the role of '[[model theory|models]]' in [[homotopy theory]].

* [philpeople.org page](https://philpeople.org/profiles/jean-pierre-marquis-marquis)

## Selected writings

On the history of [[category theory]]:

* [[Jean-Pierre Marquis]], *What is Category Theory?*, in G. Sica (ed.) *What is Category Theory?*, Polimetrica (2006) 221-256 [[[Marquis-CategoryTheory.pdf:file]], [semanticscholar](https://www.semanticscholar.org/paper/What-is-category-theory-Sica/7737401202b220f89ae9c11cf9af65995a4dcf50)]

* [[Jean-Pierre Marquis]], _From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory_, Springer (2009) [[doi:10.1007/978-1-4020-9384-5](https://doi.org/10.1007/978-1-4020-9384-5)]

On the history of [[categorical logic]]:

* {#MarquisReyes09} [[Jean-Pierre Marquis]], [[Gonzalo Reyes]], (2009) _The History of Categorical Logic 1963-1977 ([pdf](https://www.webdepot.umontreal.ca/Usagers/marquisj/MonDepotPublic/HistofCatLog.pdf), [[MarquisReyes_CategoricalLogic.pdf:file]])

category: people


Jean-Pierre Quadrat

Jean-Pierre Quadrat is Directeur de Recherche INRIA-Rocquencourt. He works in areas related to system theory, discrete event systems and dynamical programming.

* [homepage](http://jpquadrat.free.fr/)

category:people


Jean-Pierre Schneiders

* [webpage](http://www.analg.ulg.ac.be/jps/index.html)

## related $n$Lab entries

* [[bornological space]]

category: people

[[!redirects J.-P. Schneiders]]

category: people


Jean-Pierre Serre

**Jean-Pierre Serre** is a French mathematician, Fields medalist and one of the mathematically most influential mathematicians of the 20th century with main contributions to algebraic topology, algebraic and analytic geometry, algebra and number theory. He introduced a number of innovative calculations and concepts in the aparatus of algebraic topology including a number of useful spectral and exact sequences, the notion of Serre fibration, localization with respect to Serre class and so on. In algebraic and analytic geometry he introduced the technique of [[coherent sheaf|coherent sheaves]], along with basic theorems on categories of (quasi)coherent sheaves on affine and projective varieties (Serre's theorem on Proj, affine Serre's theorem, Serre duality...), a deep correspondence between the complex algebraic geometry and analytic geometry (GAGA principle), number of deep results in arithmetic geometry, Galois theory, cohomological study of algebraic varieties, class field theory...

category:people

[[!redirects J-P. Serre]]
[[!redirects J.-P. Serre]]
[[!redirects Serre]]


Jean-Pierre Tignol

* [personal page](https://perso.uclouvain.be/jean-pierre.tignol/Page_personnelle_de_Jean-Pierre_Tignol.html)

* [Wikipedia entry (fr)](https://fr.wikipedia.org/wiki/Jean-Pierre_Tignol)

* [Wikipedia entry (dr)](https://de.wikipedia.org/wiki/Jean-Pierre_Tignol)

## Selected writings

On [[Galois theory]]:

* [[Jean-Pierre Tignol]], *Galois' Theory of Algebraic Equations*, World Scientific (2001) [[doi:10.1142/4628](https://doi.org/10.1142/4628)]

category: people


Jean-Pierre Wintenberger

* [Wikipedia entry](http://en.wikipedia.org/wiki/Jean-Pierre_Wintenberger)

## related $n$Lab entries

* [[function field analogy]]

* [[perfectoid space]]

category: people


Jean-Simon Lemay

* [Personal webpage](https://sites.google.com/view/jspl-personal-webpage/)

## Selected writings

On [[differential categories]]:

* [[Richard Blute]], [[Robin Cockett]], [[Jean-Simon Lemay]] and [[Robert Seely]], _Differential categories revisited,_ Appl. Categ. Struct. 28, 171-235 (2020). ([arXiv:1806.04804](https://arxiv.org/abs/1806.04804), [doi:10.1007/s10485-019-09572-y](https://doi.org/10.1007/s10485-019-09572-y))

category: people

[[!redirects Jean-Simon Pacaud Lemay]]
[[!redirects JS Pacaud Lemay]]


Jean-Yves Girard

* [webpage](http://girard.perso.math.cnrs.fr/Accueil.html)

## Selected writings
 {#SelectedWritings}

On [[System F]]:

* [[Jean-Yves Girard]], _Interprétation functionelle et élimination des coupures dans l'arithmétique d'ordre supérieure_, Ph.D. thesis, Université Paris VII (1972) [[pdf](http://www.cs.cmu.edu/afs/cs.cmu.edu/user/kw/www/scans/girard72thesis.pdf), [[Girard-InterpretationFunctionelle.pdf:file]]]

Introducing [[linear logic]]:

* {#Girard} [[Jean-Yves Girard]], _Linear logic_,   Theoretical Computer Science **50** 1 (1987)  [doi:10.1016/0304-3975(87)90045-4, [pdf](http://iml.univ-mrs.fr/~girard/linear.pdf)]

On [[formal logic|formal]] [[logic]] and [[formal proof|formal]] [[proof]] [[proof theory|theory]] ([[type theory|typed]] [[lambda-calculus|$\lambda$-calculus]], [[linear logic]],  [[coherence spaces]], ...)

* {#Girard89} [[Jean-Yves Girard]] (translated and with appendiced by [[Paul Taylor]] and [[Yves Lafont]]), *Proofs and Types*, Cambridge University Press (1989) [[ISBN:978-0-521-37181-0](), [webpage](http://www.paultaylor.eu/stable/Proofs+Types.html), [pdf](https://www.paultaylor.eu/stable/prot.pdf)]

On [[formal logic]] and its [[categorical semantics]] with an emphasis on [[linear logic]] and in fact on some kind of [[quantum logic]] (section 17), but emphatically not in the original sense of [Birkhoff & von Neumann (1936)(BirkhoffvonNeumann36):

* [[Jean-Yves Girard]], *[[Lectures on Logic|The Blind Spot: Lectures on Logic]]*, European Mathematical Society (2011) [[doi:10.4171/088](https://doi.org/10.4171/088)]

surveyed in:

* [[Jean-Yves Girard]], *The Blind Spot*, in Jocelyn Benoist, Jean-Yves Girard, Yoshinori Ogawa, Mitsuhiro Okada (eds.) *Towards New Logic and Semantics* (2006) [[ISBN:978-4-7664-1331-1 C3310](https://www.keio-up.co.jp/kup/eng/philo/13310.html), talk slides: [pdf](https://girard.perso.math.cnrs.fr/keio2006.pdf), [[Girard_Keio2006.pdf:file]]]

See also:

* _Transcendental syntax 2.0_, 2012 ([pdf](http://iml.univ-mrs.fr/~girard/TS2.pdf))

## Related entries

* [[linear logic]]

* [[Geometry of Interaction]]

* [[transcendental syntax]]

category: people

[[!redirects Girard]]


Jeff Cheeger

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

## Selected writings

On [[Cheeger-Simons differential characters]] and [[secondary invariants]]:

* {#CheegerSimons85} [[Jeff Cheeger]],  [[James Simons]], _Differential characters and geometric invariants_, pages 50–80 in: _Geometry and Topology_ Lecture Notes in Mathematics, vol 1167. Springer (1985)  ([pdf](http://numr.wdfiles.com/local--files/differential-cohomology/cheeger-simons.pdf), [doi:10.1007/BFb0075212](https://doi.org/10.1007/BFb0075212))

On [[special holonomy orbifolds]]:

* [[Jeff Cheeger]], Gang Tian, _Anti-Self-Duality of Curvature and Degeneration of Metrics with Special Holonomy_, Communications in Mathematical Physics volume 255, pages391–417 (2005) ([doi:10.1007/s00220-004-1279-0](https://doi.org/10.1007/s00220-004-1279-0))

category: people


Jeff Egger

* [webpage](http://www.mscs.dal.ca/~jegger/)

category: people


Jeff Giansiracusa

Jeff Giansiracusa is a professor at Swansea University in the Department of Mathematics. He has worked on [[homotopy theory|homotopy theoretic]] aspects of [[moduli space]]s, [[operad]]s, [[topological field theory]], and [[diffeomorphism group]]s, using [[topology|topological]] techniques from [[algebraic K-theory]] to study the [[homotopy theory]] of moduli spaces arising in [[algebraic geometry]] and now includes aspects of [[topological data analysis]], [[tropical geometry]], matroids, idempotent algebra, and non-archimedean geometry in his research interests.

* [personal homepage](https://sites.google.com/view/jeffreygiansiracusa/home)

* [homepage at Swansea](https://www.swansea.ac.uk/staff/science/maths/j.h.giansiracusa/)

## Selected writings

On the [[framed little 2-disk operad]]:

* {#GiansiracusaSalvatore09} [[Jeffrey Giansiracusa]], [[Paolo Salvatore]], _Formality of the framed little 2-discs operad and semidirect products_ , in: _Homotopy theory of function spaces and related topics_, Cont. Math. 519, AMS, pp. 115-121  ([arxiv 0911.4428](http://arxiv.org/PS_cache/arxiv/abs/0911/0911.4428))

category: people

[[!redirects Jeffrey Giansiracusa]]


Jeff Malpas

* [Webpage](http://jeffmalpas.com/)

category: people


Jeff Smith

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

* [Mathematics Genealogy page](https://mathgenealogy.org/id.php?id=63605)

## Selected writings

Introducing the [[nilpotence theorem]] in [[stable homotopy theory]]:

* {#DevinatzHopkinsSmith88} [[Ethan Devinatz]], [[Michael Hopkins]], [[Jeffrey Smith]], _Nilpotence and Stable Homotopy Theory I_, Annals of Mathematics Second Series, Vol. 128, No. 2 (Sep., 1988), pp. 207-241 ([jstor:1971440](https://www.jstor.org/stable/1971440))

* {#DevinatzHopkinsSmith98} [[Ethan Devinatz]], [[Michael Hopkins]], [[Jeffrey Smith]], _Nilpotence and Stable Homotopy Theory II_, Annals of Mathematics Second Series, Vol. 148, No. 1 (Jul., 1998), pp. 1-49 ([jstor:120991](https://www.jstor.org/stable/120991))

On [[homotopy commutative diagrams]]:

* [[William Dwyer]], [[Dan Kan]], [[Jeff Smith]], _Homotopy commutative diagrams and their realizations_, Journal of Pure and Applied Algebra 57 (1989) 5-24 (doi:10.1016/0022-4049(89)90023-6)

Introducing [[Delta-generated topological spaces]]:

* {#Smith} [[Jeff Smith]], _A really convenient category of topological spaces_ (unpublished and possibly non-existent, according to [Dugger 03, p. 4](Delta-generated+topological+space#Dugger03))

After Jeff Smith presented his recognition theorem for [[combinatorial model categories]] at a conference in Barcelona, its first appearance in a publication is apparently

* {#Beke} [[Tibor Beke]], Lemma 1.8 in: _Sheafifiable homotopy model categories_ , Math. Proc. Cambr. Phil. Soc. 129 (2000), 447–475 ([arXiv:math/0102087](http://arxiv.org/abs/math/0102087))

On [[generalized cup products]]:

* [[James E. McClure]], [[Jeffrey H. Smith]], _Multivariable cochain operations and little $n$-cubes_ ([arXiv:math/0106024v3](https://arxiv.org/abs/math/0106024v3))

On [[derived functors]] such as [[homotopy limit]]-functors on [[model categories]] and more general [[homotopical categories]]:

* [[William Dwyer]], [[Philip Hirschhorn]], [[Daniel Kan]], [[Jeff Smith]], **[[Homotopy Limit Functors on Model Categories and Homotopical Categories]]**, Mathematical Surveys and Monographs **113**, AMS 2004 ([ISBN: 978-1-4704-1340-8](https://bookstore.ams.org/surv-113-s), [pdf](http://dodo.pdmi.ras.ru/~topology/books/dhks.pdf))

## Related $n$Lab entries

Much of the theory of [[combinatorial model category|combinatorial model categories]] goes back to unpublished work by Jeff Smith: see for instance

* [[combinatorial model category]]

* [[Bousfield localization of model categories]]

Other contributions include:

* [[Delta-generated topological spaces]]

* [[symmetric spectra]]

* [[Hopkins-Smith nilpotence theorem]]

* [[left-determined model category]]

* theory of [[relative categories]], including [[homotopy limit]] and colimit functors

category: people

[[!redirects Jeffrey Smith]]
[[!redirects Jeffrey H. Smith]]
[[!redirects Jeffrey Henderson Smith]]


Jeffery Zucker

* [personal page](http://www.cas.mcmaster.ca/~zucker/)

## Selected writings

On the formalization of [[mathematical structures]] in [[Automath]] via [[type telescopes]]:

* [[Jeffery Zucker]], *Formalization of Classical Mathematics in Automath*, Colloques Internationaux du Centre National de la Recherche Scientifique **249** (1975) 135-145 [[web](https://www.win.tue.nl/automath/archive/webversion/aut042/aut042.html), [pdf](https://www.win.tue.nl/automath/archive/pdf/aut042.pdf)]

  also in: Studies in Logic and the Foundations of Mathematics **133** (1994) 127-139 [doi:10.1016/S0049-237X(08)70202-7]

category: people


Jeffrey Bub

* [webpage](http://www.philosophy.umd.edu/people/bub)

## Related pages

* [[philosophy of physics]]

* [[interpretation of quantum mechanics]]

category: people


Jeffrey C.Y. Teo

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

## Selected writings

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)$]$

category: people

[[!redirects Jeffrey C. Y. Teo]]
[[!redirects Jeffrey Teo]]


Jeffrey Ellis Mandula

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

## Selected writings

Introducing the [[Coleman-Mandula theorem]]:

* [[Sidney Coleman]], [[Jeffrey Ellis Mandula]], _All Possible Symmetries of the S Matrix_, Physical Review __159__ (5): 1251--1256 (1967) ([doi:10.1103/PhysRev.159.1251](https://doi.org/10.1103/PhysRev.159.1251))

On [[string diagram]]-calculus ([[Penrose notation]]) in [[representation theory]]:

* [[Jeffrey Ellis Mandula]], *Diagrammatic techniques in group theory*, Southampton Univ. Phys. Dept. (1981) ([cds:129911](https://cds.cern.ch/record/129911), [pdf](https://cds.cern.ch/record/129911/files/SHEP%2080-81-7.pdf))

category: people

[[!redirects Jeffrey Mandula]]
[[!redirects J. E. Mandula]]


Jeffrey Giansiracusa > history


Jeffrey Goldstone

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

## Selected writings

Early discussion of [[quantization]] of the [[string]] [[sigma-model]] in [[light-cone gauge]]:

* [[Peter Goddard]], [[Jeffrey Goldstone]], [[Claudio Rebbi]], [[Charles B. Thorn]], *Quantum dynamics of a massless relativistic string*, Nuclear Physics B **56** 1 (1973) 109-135 [doi:10.1016/0550-3213(73)90223-X]

On the [[baryon current]] as a [[WZW-term]]/[[Skyrmion]] current (in the [[exponentiated pion field]]):

* [[Jeffrey Goldstone]], [[Frank Wilczek]], _Fractional Quantum Numbers on Solitons_, Phys. Rev. Lett. 47, 986 (1981) ([doi:10.1103/PhysRevLett.47.986](https://doi.org/10.1103/PhysRevLett.47.986))

On [[adiabatic quantum computation]]:

* [[Edward Farhi]], [[Jeffrey Goldstone]], [[Sam Gutmann]], Michael Sipser, *Quantum Computation by Adiabatic Evolution* [[arXiv:quant-ph/0001106](https://arxiv.org/abs/quant-ph/0001106)]

* [[Edward Farhi]], [[Jeffrey Goldstone]], [[Sam Gutmann]], Joshua Lapan, Andrew Lundgren, Daniel Preda, *A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem*, Science  **292** 5516 (2001) 472-475 [[doi:10.1126/science.1057726](https://doi.org/10.1126/science.1057726)]

## Related entries

* [[Goldstone boson]]

category: people


Jeffrey Harvey

* [webpage](http://hamilton.uchicago.edu/~harvey/)

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

## Selected writings

Early argument that the [[RR-field]] [[flux]] [[differential form|density]]-expressions for [[D-brane charge]] are of the form of [[Chern characters]] on [[topological K-theory]], leading to the [[K-theory classification of D-brane charge]]:

* {#GreenHarveyMoore97} [[Michael Green]], [[Jeffrey A. Harvey]], [[Gregory Moore]], *I-Brane Inflow and Anomalous Couplings on D-Branes*, Class. Quant. Grav. **14** (1997) 47-52 [[arXiv:hep-th/9605033](https://arxiv.org/abs/hep-th/9605033), [doi:10.1088/0264-9381/14/1/008](https://doi.org/10.1088/0264-9381/14/1/008)]

Introducing [[heterotic string theory]]:

* [[David Gross]], [[Jeffrey Harvey]], [[Emil Martinec]], [[Ryan Rohm]]:

  _Heterotic string theory (I). The free heterotic string_  Nucl. Phys. B 256 (1985), 253 (doi:10.1016/0550-3213(85)90394-3)

  _Heterotic string theory (II). The interacting heterotic string_ , Nucl. Phys. B 267 (1986), 75 (doi:10.1016/0550-3213(86)90146-X)

On [[anomaly inflow]]:

* [[Curtis Callan]], [[Jeffrey Harvey]], _Anomalies and Fermion Zero Modes on Strings and Domain Walls_, Nucl. Phys. B250 (1985) 427-436 (doi:10.1016/0550-3213(85)90489-4, [spire:15691](http://inspirehep.net/record/15691))

The lift of [[Dp-D(p+2)-brane bound states]] in [[string theory]] to [[M2-M5-brane bound states]]/[[E-strings]] in  [[M-theory]], under [[duality between M-theory and type IIA string theory]]+[[T-duality]], via generalization of [[Nahm's equation]] (eventually motivating the [[BLG model]]/[[ABJM model]]):

* {#BasuHarvey05} [[Anirban Basu]], [[Jeffrey Harvey]], _The M2-M5 Brane System and a Generalized Nahm's Equation_, Nucl.Phys. B713 (2005) 136-150 ([arXiv:hep-th/0412310](https://arxiv.org/abs/hep-th/0412310))

On the [[Gross-Neveu model]] via [[intersecting D-brane models]]/[[AdS/QCD]]:

* E. Antonyan, [[Jeffrey Harvey]], [[David Kutasov]], _The Gross-Neveu Model from String Theory_, Nucl. Phys. B776:93-117, 2007 ([arxiv:hep-th/0608149](https://arxiv.org/abs/hep-th/0608149))

Discussion of the [[gauged WZW model|gauged]] [[WZW term]] for the [[chiral anomaly]] in [[chiral perturbation theory]] in view of the full [[standard model of particle physics]]:

* [[Jeffrey Harvey]], Christopher T. Hill, Richard J. Hill, _Standard Model Gauging of the WZW Term: Anomalies, Global Currents and pseudo-Chern-Simons Interactions_, Phys. Rev. D77:085017, 2008 ([arXiv:0712.1230](https://arxiv.org/abs/0712.1230))

On [[holographic QCD]] including [[h1-mesons]] and [[b1-mesons]]:

* {#DHR11} Sophia K. Domokos, [[Jeffrey Harvey]], Andrew B. Royston, _Completing the framework of AdS/QCD: $h_1$/$b_1$ mesons and excited $\omega$/$\rho$'s_, JHEP 05(2011)107 ([arXiv:1101.3315](https://arxiv.org/abs/1101.3315))

* {#DHR12}  Sophia K. Domokos, [[Jeffrey Harvey]], Andrew B. Royston, _Successes and Failures of a More Comprehensive Hard Wall AdS/QCD_, JHEP 04(2013)104 ([arXiv:1210.6351](https://arxiv.org/abs/1210.6351))

On relating the [[Monster vertex operator algebra]] and its cousins to [[quantum error correction]]:

* [[Jeffrey A. Harvey]], [[Gregory W. Moore]], *Moonshine, Superconformal Symmetry, and Quantum Error Correction*,  J. High Energ. Phys. **2020**, 146 (2020). ([arXiv:2003.13700](https://arxiv.org/abs/2003.13700))

category: people

[[!redirects Jeff Harvey]]

[[!redirects Jeffrey A. Harvey]]


Jeffrey Lagarias

* [webpage](http://www.math.lsa.umich.edu/~lagarias/)

## related $n$Lab entries

* [[zeta function]]

category: people


Jeffrey M. Lee

> Not to be confused with [[John Marshall Lee]], who also wrote a book on [[smooth manifolds]].

***

[Website](http://www.math.ttu.edu/~jlee/).

## Selected writings

On [[smooth manifolds]] and [[differential geometry]]:

* [[Jeffrey M. Lee]], _Manifolds and Differential Geometry_,
Graduate Studies in Mathematics 107 (2009), AMS ([doi:10.1090/gsm/107](https://doi.org/10.1090/gsm/107), [ISBN: 978-0-8218-4815-9](https://bookstore.ams.org/gsm-107)).

[[!redirects Jeffrey Lee]]
[[!redirects Jeffrey Marc Lee]]


Jeffrey Morton

[website](https://www.theoreticalatlas.net/index.html)

#related entries#

* [[multispan]]

* [[extended cobordism]]
* [[double bicategory]]
* [[groupoidification]]

category: people

[[!redirects Jeffrey C. Morton]]


Jeffrey Rabin

* [webpage](http://math.ucsd.edu/~jrabin/)

## Selected writings

On the [[moduli space of super Riemann surfaces]]:

* {#Rabin87} [[Jeffrey Rabin]], _Supermanifolds and Super Riemann Surfaces_,  In: H.C. Lee et. al (eds.) _Super Field Theories_, NATO Science Series (Series B: Physics), vol 160. Springer (1987) ([doi:10.1007/978-1-4613-0913-0_34](https://doi.org/10.1007/978-1-4613-0913-0_34), [pdf](https://www.osti.gov/servlets/purl/6687531))

## Related $n$Lab entries

* [[Green-Schwarz sigma model]]

category: people


Jeffrey Stopple

* [webpage](http://www.math.ucsb.edu/~stopple/)

## related $n$Lan entries

* [[theta function]]

category: people


Jeffrey Strom

* [webpage](https://wmich.edu/math/directory/strom)

## Selected writings

On [[homotopy theory]]:

* [[Jeffrey Strom]], *Modern classical homotopy theory*, Graduate Studies in Mathematics Vol. 127, American Mathematical Society, 2011 ([doi:10.1090/gsm/127](http://www.ams.org/books/gsm/127/)])

category: people


Jelena Grbić

* [Institute page](https://www.southampton.ac.uk/maths/about/staff/jg1u11.page)

## Selected writings

On [[Hopf algebras]] and [[homology of H-spaces]] (such as [[homology of loop spaces]]):

* [[Victor Buchstaber]], [[Jelena Grbić]], *Hopf algebras and homology of loop suspension spaces* ([pdf](http://www.personal.soton.ac.uk/jg1u11/Papers/Buchstaber.Grbic.pdf), [[BuchstaberGrbicHopfAlgebrasAndHomology.pdf:file]]) in: V. Buchstaber et al. (eds.), *Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov’s Seminar 2012–2014*, American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences, 2014 ([ISBN:978-1-4704-1871-7](https://bookstore.ams.org/trans2-234))

category: people

[[!redirects Jelena Grbic]]


Jelle Herold

* [home page](http://www.cs.ru.nl/~jherold/)

category: people


Jennifer Balakrishnan

* [Website] (http://math.bu.edu/people/jbala/)

## Selected writings

On the [[Mordell conjecture]]:

* {#Balakrishnan19} [[Jennifer Balakrishnan]],  A. J. Best, F. Bianchi, [[Brian Lawrence]], J. S. Müller, N. Triantafillou, J. Vonk: *Two recent $p$-adic approaches to the (effective) Mordell conjecture*, in: *Arithmetic L-Functions and Differential Geometric Methods* Progress in Mathematics **338** Birkhäuser (2021) [[arxiv:1910.12755](https://arxiv.org/abs/1910.12755), [doi:10.1007/978-3-030-65203-6_2]( https://doi.org/10.1007/978-3-030-65203-6_2)]

category: people


Jennifer C. H. Wilson

* [personal page](http://www.math.lsa.umich.edu/~jchw/)

* [institute page](https://lsa.umich.edu/math/people/faculty/jchw.html)

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

## Selected writings

On [[braid groups]] and [[braid representations]]:

* [[Jennifer C. H. Wilson]], *The geometry and topology of braid groups*, lecture at *[2018 Summer School on Geometry and Topology](https://www.pims.math.ca/scientific-event/180611-ssgt)*, Chicago (2018) [[pdf](http://www.math.lsa.umich.edu/~jchw/RTG-Braids.pdf), [[Wilson-BraidGroups.pdf:file]]]

and specifically on the aspect of [[representation stability]]

* [[Jenny Wilson]], *A brief introduction to representation stability*, Oberwolfach Workshop (Jan 2018) [[pdf](https://dept.math.lsa.umich.edu/~jchw/OberwolfachTalk-IntroductionToRepStability.pdf), [[Wilson-RepresentationStability.pdf:file]], [[Wilson-CQTS-Apr-2023.pdf:file]]]

* [[Rita Jimenez Rolland]], [[Jennifer C. H. Wilson]], *Stability properties of moduli spaces*, Notices of the AMS [**69** 4](https://www.ams.org/notices/202204/202204FullIssue.pdf) (April 2022) [[arXiv:2201.04096](https://arxiv.org/abs/2201.04096), [pdf](https://www.ams.org/journals/notices/202204/rnoti-p522.pdf), [web](https://www.ams.org/journals/notices/202204/noti2452/noti2452.html)]

* [[Jennifer C. H. Wilson]], *Representation stability and the braid groups*, talk at *[ICERM -- Braids](https://icerm.brown.edu/programs/sp-s22/)* (Feb 2022) [[pdf](https://app.icerm.brown.edu/assets/362/3661/3661_3250_021720221430_Slides.pdf)]

* [[Jenny Wilson]], *Stability patterns for braid groups and configuration spaces*, [talk at](Center+for+Quantum+and+Topological+Systems#WilsonApr2023) [[CQTS]] (Apr 2023) [[web](Center+for+Quantum+and+Topological+Systems#WilsonApr2023), slides:[pdf](https://ncatlab.org/nlab/files/Wilson-CQTS-Apr-2023.pdf), video:[YT](https://www.youtube.com/watch?v=uO2CFY7h5lo)]

category: people

[[!redirects Jennifer Wilson]]
[[!redirects Jenny Wilson]]


Jennifer Paykin

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

## Selected writings

Introducing *[[QWIRE]]*, a [[quantum programming language]] based on [[linear type theory]] connected with [[intuitionistic type theory]] via the [[exponential modality]]:

* {#PaykinRandZdancewic17} [[Jennifer Paykin]], [[Robert Rand]], [[Steve Zdancewic]], *QWIRE: a core language for quantum circuits*, POPL 2017: Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming LanguagesJanuary 2017 Pages 846–858 ([doi:10.1145/3009837.3009894](https://doi.org/10.1145/3009837.3009894))

Theoretical background:

* [[Jennifer Paykin]], *Linear/non-Linear Types For Embedded Domain-Specific Languages*, 2018 ([upenn:2752](https://repository.upenn.edu/edissertations/2752))

Application to [[verified programming]] after implementation in [[Coq]]:

* [[Robert Rand]], [[Jennifer Paykin]], [[Steve Zdancewic]], *QWIRE Practice: Formal Verification of Quantum Circuits in Coq*, EPTCS 266, 2018, pp. 119-132 ([arXiv:1803.00699](https://arxiv.org/abs/1803.00699))

* [[Robert Rand]], [[Jennifer Paykin]], [[Dong-Ho Lee]], [[Steve Zdancewic]], *ReQWIRE: Reasoning about Reversible Quantum Circuits*, EPTCS **287** (2019) 299-312 [[arXiv:1901.10118](https://arxiv.org/abs/1901.10118), [doi:10.4204/EPTCS.287.17](https://doi.org/10.4204/EPTCS.287.17)]

Using ambient [[homotopy type theory]]:

* [[Jennifer Paykin]], [[Steve Zdancewic]], *A HoTT Quantum Equational Theory*, [talk at QPL2019](http://qpl2019.org/a-hott-quantum-equational-theory/) [[arXiv:1904.04371](https://arxiv.org/abs/1904.04371), [pdf](https://jpaykin.github.io/talks/HoTT-3-8-2019.pdf), [[PaykinZdancewic-HoTTQuantum.pdf:file]]]

category: people


Jens Eisert

* [institute webpage](https://www.physik.fu-berlin.de/en/einrichtungen/ag/ag-eisert/index.html)

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

## Selected writings

On [[quantum computing]]:

* [[Jens Eisert]], M. M. Wolf, _Quantum computing_, In: _Handbook of Nature-Inspired and Innovative Computing_, Springer 2006 ([arXiv:quant-ph/0401019](https://arxiv.org/abs/quant-ph/0401019))

On [[tensor networks]] and ([[holographic entanglement entropy|holographic]]) [[entanglement entropy]] in [[solid state physics]]:

* [[Jens Eisert]], M. Cramer, M.B. Plenio, _Area laws for the entanglement entropy - a review_, Rev. Mod. Phys. 82, 277 (2010) ([arXiv:0808.3773](https://arxiv.org/abs/0808.3773))

* [[Jens Eisert]], _Entanglement and tensor network states_, Modeling and Simulation 3, 520 (2013) ([arXiv:1308.3318](https://arxiv.org/abs/1308.3318))

* A. Kshetrimayum, C. Balz, B. Lake, [[Jens Eisert]], _Tensor network investigation of the double layer Kagome compound $Ca_{10} Cr_{7} O_{28}$_ ([arXiv:1904.00028](https://arxiv.org/abs/1904.00028))

On simulation of quantum [[spin chains]] on [[quantum computers]]:

* M. Gluza, M. Kliesch, [[Jens Eisert]], [[Leandro Aolita]], *Fidelity witnesses for fermionic quantum simulations*, Phys. Rev. Lett. **120** 190501 (2018) [[arXiv:1703.03152](https://arxiv.org/abs/1703.03152), [doi:10.1103/PhysRevLett.120.190501](https://doi.org/10.1103/PhysRevLett.120.190501)]

Introducing [[Majorana dimer codes]] ([[quantum error correcting codes]] induced by [[tensor networks]] exhibiting [[holographic entanglement entropy]]):

* [[Alexander Jahn]], [[Marek Gluza]], [[Fernando Pastawski]], [[Jens Eisert]], *Majorana dimers and holographic quantum error-correcting code*, Phys. Rev. Research 1, 033079 (2019) ([arXiv:1905.03268](https://arxiv.org/abs/1905.03268))

based on:

* [[Alexander Jahn]], [[Marek Gluza]], [[Fernando Pastawski]], [[Jens Eisert]], *Holography and criticality in matchgate tensor networks*, Science Advances 5, eaaw0092 (2019) ([arXiv:1711.03109](https://arxiv.org/abs/1711.03109), [doi:10.1126/sciadv.aaw0092](https://advances.sciencemag.org/content/5/8/eaaw0092))

Review:

* [[Alexander Jahn]], [[Jens Eisert]], _Holographic tensor network models and quantum error correction: A topical review_ ([arXiv:2102.02619](https://arxiv.org/abs/2102.02619))

On classification of ([[topological phases of matter|topological]]) [[phases of matter]] via [[tensor network states]]:

* C. Wille, O. Buerschaper, [[Jens Eisert]], _Fermionic topological quantum states as tensor networks_, Phys. Rev. B 95, 245127 (2017) ([arXiv:1609.02574](https://arxiv.org/abs/1609.02574))

* Andreas Bauer, [[Jens Eisert]], Carolin Wille, _Towards a mathematical formalism for classifying phases of matter_ ([arXiv:1903.05413](https://arxiv.org/abs/1903.05413))

Discussion of [[asymptotic boundaries]] of [[hyperbolic space|hyperbolic]] [[tensor networks]] as conformal [[quasicrystals]] (see also at [[AdS/CFT in solid state physics]]):

* [[Alexander Jahn]], [[Zoltán Zimborás]], [[Jens Eisert]], _Central charges of aperiodic holographic tensor network models_, Phys. Rev. A 102, 042407 ([arXiv:1911.03485](https://arxiv.org/abs/1911.03485))

* [[Alexander Jahn]], [[Zoltán Zimborás]], [[Jens Eisert]], _Tensor network models of AdS/qCFT_ ([arXiv:2004.04173](https://arxiv.org/abs/2004.04173))

category: people


Jens Fjelstad

* [linkedin page](http://cn.linkedin.com/pub/jens-fjelstad/3b/22b/6b7)

## Selected writings

The [[FRS-theorem on rational 2d CFT]]:

* [[Ingo Runkel]], [[Jens Fjelstad]], [[Jürgen Fuchs]], [[Christoph Schweigert]], *Topological and conformal field theory as Frobenius algebras*, in: *Categories in Algebra, Geometry and Mathematical Physics* Contemp. Math. **431** (2007) 225-248 $[$[doi:10.1090/conm/431](http://dx.doi.org/10.1090/conm/431), [arXiv:math/0512076](https://arxiv.org/abs/math/0512076)$]$

category: people


Jens Hoppe

* [website](http://www.e.kth.se/~hoppe/)

## Selected writings

Introducing the [[Poisson bracket]]-formulation of the [[classical mechanics|classical]] [[light-cone gauge]] [[Hamiltonian]] for the _[[bosonic modality|bosonic]]_ [[relativistic membrane]] and the corresponding matrix [[commutator]] regularization:

* [[Jens Hoppe]], _Quantum theory of a massless relativistic surface and a two-dimensional bound state problem_, MIT 1982 ([dspace:1721.1/15717](http://hdl.handle.net/1721.1/15717), [[HoppeMembrane82.pdf:file]])

On the regularized [[quantization]] of the [[supermembrane]] (the [[kappa-symmetry|kappa-symmetric]] [[Green-Schwarz sigma-model]] for the [[M2-brane]]) to the [[BFSS matrix model]]:

* {#deWitHoppeNicolai88} [[Bernard de Wit]], [[Jens Hoppe]], [[Hermann Nicolai]], _On the Quantum Mechanics of Supermembranes_, Nucl. Phys. B305 (1988) 545. ([pdf](http://pubman.mpdl.mpg.de/pubman/item/escidoc:153408:1/component/escidoc:153407/353961.pdf), [[deWitHoppeNicolai88.pdf:file]], [spire:261702](http://inspirehep.net/record/261702))

* [[Jens Hoppe]], _Membranes and Matrix Models_ ([arXiv:hep-th/0206192](https://arxiv.org/abs/hep-th/0206192))

On the [[BMN matrix model]]:

* [[Jens Hoppe]]. Ki-Myeong Lee, _New BPS Configurations of BMN Matrix Theory_, JHEP 0806:041, 2008 ([arXiv:0712.3616](https://arxiv.org/abs/0712.3616))

On exact solutions to the (regularized) bosonic [[membrane]]/[[M2-brane]] model:

* [[Jens Hoppe]], *Exact algebraic M(em)brane solutions* [[arXiv:2107.00569](https://arxiv.org/abs/2107.00569)]

* [[Jens Hoppe]], *The fast non-commutative sharp drop* [[arXiv:2302.13146](https://arxiv.org/abs/2302.13146)]

## Related entries

* [[brane]]

* [[sigma-model]]

category: people


Jens L. Petersen

* [InSpire page](https://inspirehep.net/authors/993633)

## Selected writings

On the [[AdS-CFT correspondence]]:

* [[Jens L. Petersen]], _Introduction to the Maldacena Conjecture on AdS/CFT_, Int. J. Mod. Phys. A **14** (1999) 3597-3672 [[hep-th/9902131](http://arxiv.org/abs/hep-th/9902131), [doi:10.1142/S0217751X99001676](http://dx.doi.org/10.1142/S0217751X99001676)]

category: people

[[!redirects Jens Lyng Petersen]]
[[!redirects Jens Petersen]]


Jeong-Hyuck Park

* [webpage](http://lab7616.sogang.ac.kr/lab7616/1093.html)

## Selected writings

On the [[BMN matrix model]]:

* [[Nakwoo Kim]], [[Jeong-Hyuck Park]], _Superalgebra for M-theory on a pp-wave_, Phys.Rev. D66 (2002) 106007 ([arXiv:hep-th/0207061](https://arxiv.org/abs/hep-th/0207061))

On [[topological twists]]:

* [[Jeong-Hyuck Park]], [[Dimitrios Tsimpis]], _Topological twisting of conformal supercharges_, Nucl. Phys. B776:405-430, 2007 ([arXiv:hep-th/0610159](http://arxiv.org/abs/hep-th/0610159))

category: people


Jeremiah Ostriker

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

## related $n$Lab entries

* [[fuzzy dark matter]]

* [[axion]]

category: people


Jeremy Avigad

* [webpage](http://www.andrew.cmu.edu/user/avigad/)

## related $n$Lab entries

* [[Lean]]

category: people


Jeremy Butterfield

Jeremy Butterfield is a Senior Research Fellow at Trinity College, Cambridge and a member of the Faculty of Philosophy.

* [website](http://www.trin.cam.ac.uk/butterfield/)

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

## Selected writings

Proposal that the [[Kochen-Specker theorem]] suggests to understand [[quantum physics]] via the [[internal logic]] of
(what later would be called) a *[[Bohr topos]]*:

* {#ButterfieldHamiltonIsham} [[Jeremy Butterfield]],  John Hamilton, [[Chris Isham]], _A topos perspective on the Kochen-Specker theorem_, _I. quantum states as generalized valuations_, Internat. J. Theoret. Phys. **37** 11 (1998) 2669-2733 [[MR2000c:81027](http://www.ams.org/mathscinet-getitem?mr=1669557), [doi:10.1023/A:1026680806775](http://dx.doi.org/10.1023/A:1026680806775)]

  _II. conceptual aspects and classical analogues_ Int. J. of Theor. Phys. **38**  3 (1999) 827-859 [[MR2000f:81012](http://www.ams.org/mathscinet-getitem?mr=1697983), [doi:10.1023/A:1026652817988](http://dx.doi.org/10.1023/A:1026652817988)]

  _III. Von Neumann algebras as the base category_, Int. J. of Theor. Phys. **39** 6 (2000) 1413-1436 [[arXiv:quant-ph/9911020](http://arxiv.org/abs/quant-ph/9911020), [MR2001k:81016](http://www.ams.org/mathscinet-getitem?mr=1788498),[doi:10.1023/A:1003667607842](http://dx.doi.org/10.1023/A:1003667607842)]

  _IV. Interval valuations_, Internat. J. Theoret. Phys. __41__ 4 (2002) 613-639 [[MR2003g:81009](http://www.ams.org/mathscinet-getitem?mr=1902067), [doi](http://dx.doi.org/10.1023/A:1015276209768)]

with some review and outlook in

* [[Chris Isham]], [[Jeremy Butterfield]], *Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity*, Found. Phys. **30** (2000) 1707-1735 [[arXiv:gr-qc/9910005](https://arxiv.org/abs/gr-qc/9910005), [doi:10.1023/A:1026406502316](https://doi.org/10.1023/A:1026406502316)]

On the [[AdS/CFT correspondence]]:

* Sebastian De Haro, Daniel R. Mayerson, [[Jeremy Butterfield]], _Conceptual Aspects of Gauge/Gravity Duality_, Foundations of Physics (2016), 46 (11), pp. 1381-1425 ([arXiv:1509.09231](https://arxiv.org/abs/1509.09231))

On [[black holes in string theory]] and [[black hole entropy]]:

* Sebastian De Haro, Jeroen van Dongen, Manus Visser, [[Jeremy Butterfield]], _Conceptual Analysis of Black Hole Entropy in String Theory_ ([arXiv:1904.03232](https://arxiv.org/abs/1904.03232))

* Jeroen van Dongen, Sebastian De Haro, Manus Visser, [[Jeremy Butterfield]], _Emergence and Correspondence for String Theory Black Holes_ ([arXiv:1904.03234](https://arxiv.org/abs/1904.03234))

## Related $n$Lab entries

* [[BV-BRST formalism]]

* [[Kochen-Specker theorem]]

* [[Timeline of category theory and related mathematics]]

* [[reconstruction theorem]]

category: people


Jeremy Gibbons

Jeremy Gibbons is a Professor of Computing at the University of Oxford.

* [webpage](https://www.cs.ox.ac.uk/people/jeremy.gibbons/)

* [wikipedia](https://en.wikipedia.org/wiki/Jeremy_Gibbons)

## Selected writings

On well-behaved [[lenses (in computer science)]] as the [[coalgebra over a comonad|coalgebras]] over the [[costate comonad]]:

* {#GibbonsJohnson12} [[Jeremy Gibbons]], [[Michael Johnson]], *Relating Algebraic and Coalgebraic Descriptions of Lenses*, Electronic Communications of the EASST **49** (2012) [[doi:10.14279/tuj.eceasst.49.726](http://dx.doi.org/10.14279/tuj.eceasst.49.726), [pdf](http://www.cs.ox.ac.uk/jeremy.gibbons/publications/colens.pdf)]

On [[optics (in computer science)]]:

* [[Bryce Clarke]], Derek Elkins, [[Jeremy Gibbons]], [[Fosco Loregian]], [[Bartosz Milewski]], Emily Pillmore, [[Mario Román]], _Profunctor optics, a categorical update_, 2020. ([arXiv:2001.07488](https://arxiv.org/abs/2001.07488))

category: people


Jeremy Hahn

* [personal page](https://web.mit.edu/~jhahn01/www/)

## Selected writings

On the [[Morava E-theory]] of [[configuration spaces of points]]:

* [[Lukas Brantner]], [[Jeremy Hahn]], [[Ben Knudsen]], *The Lubin-Tate Theory of Configuration Spaces: I* ([arXiv:1908.11321](https://arxiv.org/abs/1908.11321))

category: people


jerk

+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
###Context###
#### Differential geometry
+--{: .hide}
[[!include synthetic differential geometry - contents]]
=--
#### Physics
+-- {: .hide}
[[!include physicscontents]]
=--
=--
=--

# Contents
* table of contents
{: toc}

## Definition

Given a [[Cartesian space]] $V$ and a [[smooth curve]] $r:\mathbb{R} \to V$, the **jerk** of $r$ is given by the [[third derivative]] of $r$: $j \coloneqq \partial_t^3 r$.

## See also

* [[curve]]
* [[velocity]]
* [[acceleration]]

## References

See the references at *[[differential geometry of curves and surfaces]]*

See also

* Wikipedia, *Jerk (physics)*

[[!redirects jerks]]


Jeroen Hekking

* [personal page](https://www.jeroenhekking.nl/)

## Selected writings

On [[complete Segal spaces]] [[internalization|internal]] to [[homotopical categories]]:

* {#Hekking17} [[Jeroen Hekking]], *Segal Objects in Homotopical Categories & K-theory of Proto-exact Categories*, Leiden (2017) [[pdf](https://www.universiteitleiden.nl/binaries/content/assets/science/mi/scripties/master/hekking_master.pdf)]

On [[derived blow-ups]]:

* [[Jeroen Hekking]], _Graded algebras, projective spectra and blow-ups in derived algebraic geometry_ [[arXiv:2106.01270](https://arxiv.org/abs/2106.01270)]

* [[Oren Ben-Bassat]], [[Jeroen Hekking]], _Blow-ups and normal bundles in connective and nonconnective derived geometries_ [[arXiv:2303.11990](https://arxiv.org/abs/2303.11990)]

category: people


Jeroen van der Meer

* [webpage](https://www.math.ku.dk/english/about/news/new-names/jeroen-van-der-meer-phd-student/)

## Selected writings

On [[KU-local stable homotopy theory]]:

* [[Jeroen van der Meer]], _A Stack-Theoretic Perspective on $\mathrm{KU}$-Local Stable Homotopy Theory_, 2019 ([pdf](https://www.universiteitleiden.nl/binaries/content/assets/science/mi/scripties/master/2018-2019/jvd-meer-thesisroot.pdf))

[[!redirects Jeroen W. van der Meer]]

category: people


Jerome Gauntlett

Jerome Gauntlett is professor for theoretical [[physics]] at Imperial College London.

* [webpage](http://www3.imperial.ac.uk/people/j.gauntlett)

## Selected writings

On [[black holes]] in [[D=5 supergravity]]:

* {#GauntlettMyersTownsend98} [[Jerome Gauntlett]], [[Robert C. Myers]], [[Paul Townsend]], *Black Holes of $D=5$ Supergravity*, Class.Quant.Grav. **16** (1999) 1-21 [[arXiv:hep-th/9810204](http://arxiv.org/abs/hep-th/9810204), [doi:10.1088/0264-9381/16/1/001](https://doi.org/10.1088/0264-9381/16/1/001)]

On [[D=11 N=1 supergravity]] solutions for the [[near horizon geometry]] of [[black brane|black]] [[M5-branes]] [[wrapped brane|wrapped]] on [[supersymmetric cycles]]:

* [[Jerome Gauntlett]], [[Nakwoo Kim]], [[Daniel Waldram]], _M-Fivebranes Wrapped on Supersymmetric Cycles_, Phys. Rev. D63 (2001) 126001 ([arXiv:hep-th/0012195](https://arxiv.org/abs/hep-th/0012195))

On [[D=5 supergravity]]:

* {#GGHPR02} [[Jerome Gauntlett]], [[Jan Gutowski]], [[Christopher Hull]], Stathis Pakis, [[Harvey Reall]], _All supersymmetric solutions of minimal supergravity in five dimensions_, Class. Quant. Grav. 20 (2003) 4587-4634 [[arXiv:hep-th/0209114](http://arxiv.org/abs/hep-th/0209114), [doi:10.1088/0264-9381/20/21/005](https://doi.org/10.1088/0264-9381/20/21/005)]

Specifically on [[D=11 N=1 supergravity]] solutions for the [[near horizon geometry]] of [[black brane|black]] [[M5-branes]] [[wrapped brane|wrapped]] on [[hyperbolic 3-manifolds]] $\Sigma^3 = H^3/\Gamma$:

* Aristomenis Donos, [[Jerome Gauntlett]], [[Nakwoo Kim]], Oscar Varelam, _Wrapped M5-branes, consistent truncations and AdS/CMT_, JHEP 1012:003, 2010 ([arXiv:1009.3805](https://arxiv.org/abs/1009.3805))

On [[flux compactifications]] in terms of [[G-structure]]:

* [[Jerome Gauntlett]], Dario Martelli, Stathis Pakis, [[Daniel Waldram]], _G-Structures and Wrapped NS5-branes_, Commun.Math.Phys. 247 (2004) 421-445 ([arxiv:hep-th/0205050](https://arxiv.org/abs/hep-th/0205050))

## Related entries

* [[supermembrane in 4d]]

* [[associative submanifold]]

* [[Green-Schwarz action functional]], [[BPS charges]]

category: people


Jerome Jenquin

* [Math Genealogy Page](http://www.genealogy.math.ndsu.nodak.edu/id.php?id=143079)

## related $n$Lab entries

* [[Spin Chern-Simons theory]]

category: people


Jerome Kaminker

**Jerome Kaminker** is doing research in [[algebraic topology]], K-theory of [[operator algebras]] and [[noncommutative geometry]]. He is
a professor emeritus at Indianpolis (IUPUI).

* J. Kaminker, I. Putnam, _K-theoretic duality for shifts of
finite type_, Comm. Math. Phys. __187__, 509--522; [arXiv:funct-an/9612010](http://arxiv.org/abs/funct-an/9612010)

category: people

[[!redirects Jerry Kaminker]]


Jerome Keisler

* [website](https://www.math.wisc.edu/~keisler/)

## Selected writings

On [[nonstandard analysis]] (with [[infinitesimals]]):

* {#Keisler76} [[Jerome Keisler]], *Foundations of Infinitesimal Calculus*, Prindle Weber & Schmidt (1976, 2022) [[pdf](https://people.math.wisc.edu/~hkeisler/foundations.pdf)]

* [[Jerome Keisler]], _Elementary calculus: an infinitesimal approach_, [online](http://www.math.wisc.edu/~keisler/calc.html) undergraduate textbook.

On [[continuous logic]]

* [[Jerome Keisler]], _Model Theory for Real-valued Structures_, ([arXiv:2005.11851](https://arxiv.org/abs/2005.11851))

On [[model theory]]

* Chen Chung Chang, [[H. Jerome Keisler]], _Model Theory. Studies in Logic and the Foundations of Mathematics_. 1973, 1990, Elsevier.

[[!redirects H. Jerome Keisler]]
[[!redirects Howard Jerome Keisler]]


Jerome Scherer

* [webpage](http://gr-he.epfl.ch/Scherer)

## Selected writings

On [[homotopy pullbacks]]:

* {#CPS05} [[Wojciech Chacholski]], Wolfgang Pitsch, and [[Jerome Scherer]], _Homotopy pullback squares up to localization_, in [[Dominique Arlettaz]], [[Kathryn Hess]] (eds.) _An Alpine Anthology of Homotopy Theory_ ([arXiv:math/0501250](http://arxiv.org/abs/math/0501250), [pdf](http://sma.epfl.ch/~jscherer/articles/hopullbacks2.pdf), [doi:10.1090/conm/399](http://dx.doi.org/10.1090/conm/399))

On [[Goodwillie calculus]], [[n-excisive functors]] and [[Whitehead products]]:

* {#SchererChorny11} [[Jerome Scherer]], [[Boris Chorny]], _Goodwillie calculus and Whitehead products_, Forum Math. 27 (2015), no. 1, 119 - 130 ([arXiv:1109.2691](https://arxiv.org/abs/1109.2691))

## related $n$Lab entries

* [[homotopy theory]]

* [[homotopy pullback]]

category:people

[[!redirects Jérôme Scherer]]


Jerrold Marsden

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

## Related entries

* [[Marsden-Weinstein reduction]] ([[symplectic reduction]])
* [[symplectic integrator]]

category: people
[[!redirects Jerrold E. Marsden]]
[[!redirects J. E. Marsden]]


Jerry Shurman

* [personal page](https://people.reed.edu/~jerry/)

* [MathematicsGenealogy page](https://people.reed.edu/~jerry/)

## Selected writings

On [[modular forms]] (and the [[modularity theorem]]):

* [[Fred Diamond]], [[Jerry Shurman]], *A First Course in Modular Forms*, GTM **228**, Springer (2005) $[$[doi:10.1007/978-0-387-27226-9](https://doi.org/10.1007/978-0-387-27226-9), ISBN-13: 978-0387232294$]$

category: people


Jerzy Dydak

* [website](http://www.math.utk.edu/people/bio/Jerzy/Dydak)

## Selected writings

On [[shape theory]]:

* [[Karol Borsuk]], [[Jerzy Dydak]], _What is the theory of shape?_, Bulletin of the Australian Mathematical Society, 1980, 22(2), 161-198, ([doi:10.1017/S000497270000647X](https://doi.org/10.1017/S000497270000647X))

* {#DydakSegal78} [[Jerzy Dydak]], [[Jack Segal]], _Shape Theory_, Lecture Notes in Mathematics, Springer 1978 ([doi:10.1007/BFb0067572](https://link.springer.com/book/10.1007/BFb0067572))

category: people


Jerzy Karczmarczuk

* [personal page](https://karczmarczuk.users.greyc.fr/)

## Selected writings

On efficient representations in [[exact real computer arithmetic]] of [[pi]] and related [[irrational numbers]] ([[Bailey-Borwein-Plouffe algorithm]])

* [[Jerzy Karczmarczuk]], *Infinite precision real fractions, and lazy carry propagation* or: *The Most Unreliable Technique in the World to Compute $\pi$*, A Braga School (1998) [[pdf](https://karczmarczuk.users.greyc.fr/arpap/lazypi.pdf), [[Karczmarczuk-Pi.pdf:file]], [web](https://karczmarczuk.users.greyc.fr/arpap/)]

category: people


Jerzy Kijowski

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

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

## Selected writings

On [[symplectic manifold|symplectic]] [[phase spaces]] of [[classical field theories]]:

* J. Kijowski, _Symplectic geometry and second quatization_, [pdf](http://www.cft.edu.pl/~kijowski/Odbitki-prac/128.pdf)

* J. Kijowski, W. Szczyrba, _A canonical structure for classical field theories_, Commun. Math. Phys. __46__, 1976, 183–206.

* [[Jerzy Kijowski]], [[Wlodzimierz M. Tulczyjew]], *A Symplectic Framework for Field Theories*, Lecture Notes in Physics **107** (1979, 2005) [[doi:10.1007/3-540-09538-1](https://doi.org/10.1007/3-540-09538-1)]

[[!redirects J. Kijowski]]


Jerzy Król

## Publications

Król has been speculating about applications of [[category theory]], [[topos theory]] and [[higher category theory]] to fundamental [[physics]], notably in the study of [[gravity]], [[gauge theory]] [[quantum gravity]] and [[string theory]] (see also: [[n-categorical physics]]).

* [[Jerzy Król]] _Background independence in quantum gravity and forcing constructions_ Found. of Physics, 34, (2004), 361--403

* [[Jerzy Król]] _Exotic smoothness and non-commutative spaces.the model-theoretic approach_ Found. of Physics, 34, (2004), 843--869

* [[Jerzy Król]] _Model theory and the AdS/CFT correspondence_ presented at the IPM String School and Workshop, Queshm Island, Iran, 05--14. 01. 2005, [arXiv](http://arxiv.org/abs/hep-th/0506003)

* [[Jerzy Król]] _A model for spacetime: The role of interpretation in some grothendieck topoi_ Found. Phys., 36, (2006), 1070--∞

* [[Jerzy Król]] _A model for spacetime ii. the emergence of higher dimensions and field theory/strings dualities_ Found. Phys., 36 (2006), 1778--∞

* [[Jerzy Król]] _Structure of spacetime and topos theory_ talk presented at 42 nd Karpacz Winter School of Theoretical Physics, Lądek Zdrój, 5--11. 02. 2006, Int. J. Geom. Meth. Mod. Phys. 4 No3, 1--7 (2007)

* [[Jerzy Król]] _Higher YM theories and the compactification in string theory_  Acta Phys. Polon. B38 (2007) 3641--3646

* [[Jerzy Król]] _Higher symmetry of gravity and the cosmological constant problem_ PASCOS2008, Waterloo, Kanada, pirsa.org/08060091 (2008).

* [[Jerzy Król]] _$2$-Groups and gravity_ talk presented at The Jubilee 40th Symposium on Mathematical Physics "Geometry & Quanta" Toruń, June 25--28, 2008

[[!redirects Jerzy Krol]]

category: people


Jesper Cockx

* [website](https://jesper.sikanda.be/)

## Selected publications

* [[Gaëtan Gilbert]], [[Jesper Cockx]], [[Matthieu Sozeau]], [[Nicolas Tabareau]], *Definitional Proof-Irrelevance without K*. Proceedings of the ACM on Programming Languages, Volume 3, Issue POPL, Article 3, pp 1–28, January 2019. ([doi:10.1145/3290316](https://doi.org/10.1145/3290316))

category: people


Jesper Grodal

* [webpage](http://web.math.ku.dk/~jg/)

## Selected writings

On [[p-compact groups]]/[[homotopy Lie groups]]:

* {#AndersenGrodal06} Kasper Andersen, [[Jesper Grodal]], _The classification of 2-compact groups_, J. Amer. Math. Soc. 22 (2009), 387-436 ([arXiv:math/0611437](https://arxiv.org/abs/math/0611437))

* {#Grodal10} [[Jesper Grodal]], _The Classification of $p$–Compact Groups and Homotopical Group Theory_, Proceedings of the International Congress of Mathematicians, Hyderabad 2010 ([arXiv:1003.4010](https://arxiv.org/abs/1003.4010), [pdf](http://web.math.ku.dk/~jg/papers/icm.pdf), [[GrodalpCompactGroups2010.pdf:file]])

category: people


Jesper Michael Møller

* [webpage](http://web.math.ku.dk/~moller/)

## Selected writings

On [[homotopy Lie groups]]:

* {#Moller95} [[Jesper M. Møller]], _Homotopy Lie groups_, Bull. Amer. Math. Soc. (N.S.) 32 (1995) 413-428 ([arXiv:math/9510218](https://arxiv.org/abs/math/9510218))

* With [[Kasper K. Andersen]], [[Jesper Grodal]], and [[Antonio Viruel]], _The classification of $p$-compact groups for $p$ odd_. Ann. of Math. (2) 167 (2008), no. 1, 95-210. ([pdf](http://www.math.ku.dk/~moller/reprints/poddclass.pdf))

On [[fundamental groupoids]] and [[covering spaces]] in [[general topology]] (the [[fundamental theorem of covering spaces]]):

* {#Moller11} [[Jesper Møller]], _The fundamental group and covering spaces_ (2011) [[arXiv:1106.5650](https://arxiv.org/abs/1106.5650), [pdf](http://www.math.ku.dk/~moller/f03/algtop/notes/covering.pdf), [[Moller-FundamentalGroup.pdf:file]]]

On [[homotopy theory]]:

* [[Jesper Michael Møller]], _Homotopy theory for beginners_, 2015 ([pdf](http://www.math.ku.dk/~moller/e01/algtopI/comments.pdf), [[Moller_HomotopyTheory.pdf:file]])

## Related entries

* [[fundamental group]], [[covering space]]

* [[homotopy Lie group]]

* [[p-compact group]]

category: people

[[!redirects Jesper Moller]]
[[!redirects Jesper Møller]]
[[!redirects Jesper M. Moller]]
[[!redirects Jesper M. Møller]]
[[!redirects Jesper Michael Moller]]


Jesse Han

[[!redirects jesse]]

I'm currently a second-year master's student at McMaster University. I'm interested in [[model theory]], especially from the perspective of [[categorical logic]].

Here is my [homepage](http://ms.mcmaster.ca/~hanj18).

* {#Han18} _Flypitch project -- Formal proof of the independence of CH_ ([github:flypitch](https://github.com/flypitch), [pdf](https://github.com/flypitch/flypitch-notes/blob/master/forcing-notes.pdf))

  ([[formal proof]] of independence of the [[continuum hypothesis]])

[//]: # (This syntax works like a comment, and won't appear in any output.)

category: people


Jesse Wolfson

* [webpage](https://jpwolfson.wordpress.com/)

## Selected writings

On [[arithmetic topology]]:

* Claudio Gómez-Gonzáles, [[Jesse Wolfson]], _Problems in Arithmetic Topology_ ([arXiv:2012.15434](https://arxiv.org/abs/2012.15434))

category: people


Jesús Francisco Espinoza Fierro

* [institute page](https://investigadores.unison.mx/en/persons/jesus-f-espinoza)

* [Mathematics Genealogy page](https://www.mathgenealogy.org/id.php?id=175944)

## Selected writings

On the [[topology]] of the infinite [[unitary group]] [[U(ℋ)]] on a [[separable Hilbert space]] ([[operator topology]] and [[compact-open topology]]):

* {#EspinozaUribe} [[Jesus Espinoza]], [[Bernardo Uribe]], _Topological properties of the unitary group_, JP Journal of Geometry and Topology **16** (2014) Issue 1, pp 45-55 ([arXiv:1407.1869](https://arxiv.org/abs/1407.1869), [journal](http://www.pphmj.com/abstract/8730.htm))

and of the corresponding [[projective unitary group]] [[PU(ℋ)]]:

* [[Jesus Espinoza]], [[Bernardo Uribe]], *Topological properties of spaces of projective unitary representations*, Rev. Acad. Colombiana Cienc. Exact. Fís. Natur. 40 (2016), no. 155, 337-352 ([arXiv:1511.06785](https://arxiv.org/abs/1511.06785), [scielo:S0370-39082016000200013](http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0370-39082016000200013), [doi:10.18257/raccefyn.317](https://doi.org/10.18257/raccefyn.317))

On 3-[[twisted equivariant K-theory]] via the [[universal equivariant PU(H)-bundle|universal equivariant $PU(\mathcal{H})$-bundle]]:

* {#BEJU14} [[Noé Bárcenas Torres|Noé Bárcenas]], [[Jesús Francisco Espinoza Fierro|Jesús Espinoza]], [[Michael Joachim]], [[Bernardo Uribe]], _Universal twist in Equivariant K-theory for proper and discrete actions_, Proceedings of the London Mathematical Society, Volume 108, Issue 5 (2014) ([arXiv:1202.1880](https://arxiv.org/abs/1202.1880), [doi:10.1112/plms/pdt061](https://doi.org/10.1112/plms/pdt061))

* [[Noé Bárcenas Torres|Noé Bárcenas]], [[Jesús Francisco Espinoza Fierro|Jesús Espinoza]], [[Bernardo Uribe]], [[Mario Velasquez]], Section 3.2 of: _Segal's spectral sequence in twisted equivariant K-theory for proper and discrete actions_, Proceedings of the Edinburgh Mathematical Society **61** 1 (2018) ([arXiv:1307.1003](https://arxiv.org/abs/1307.1003), [doi:10.1017/S0013091517000281](https://doi.org/10.1017/S0013091517000281))

[[!redirects Jesús Espinoza]]
[[!redirects Jesus Espinoza]]

category: people


jet (infinity,1)-category

+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
###Context###
#### Goodwillie calculus
+--{: .hide}
[[!include Goodwillie calculus - contents]]
=--
=--
=--

#Contents#
* table of contents
{:toc}

## Idea

Given a [[differentiable (∞,1)-category]] $\mathcal{C}$, then the [[(∞,1)-category]] of [[n-excisive functors]] from the [[finite homotopy type|finite]] [[pointed objects]] in [[∞Grpd]] to $\mathcal{C}$ behaves like the [[bundles]] of order-$n$ [[Goodwillie calculus|Goodwillie derivatives]] over all [[objects]] of $\mathcal{C}$. Hence this is like an analog in [[Goodwillie calculus]] of the $n$th order [[jet bundle]] in [[differential geometry]].

In particular for $n = 1$ the "1-jet $\infty$-category" of $\mathcal{C}$ is the [[tangent (∞,1)-category]] of $\mathcal{C}$.

## Properties

### Jet toposes
 {#JetToposes}

By the discussion at _[n-excisive functor -- Properties -- n-Excisive approximation](n-excisive+%28∞,1%29-functor#nExcisiveApproximation)_, for $\mathbf{H}$ an [[(∞,1)-topos]] also its $n$th jet $(\infty,1)$-category

$$
  J^n \mathbf{H} \coloneqq Exc^n(\infty Grpd_{fin}^{\ast/}, \mathbf{H})
$$

is an $(\infty,1)$-topos, for all $n \in \mathbb{N}$. For $n = 1$ this is the [[tangent (∞,1)-topos]] $J^1 \mathbf{H} = T \mathbf{H}$ (see also at _[[tangent cohesion]]_). If $\mathbf{H}$ is [[cohesive (infinity,1)-topos|cohesive]], so too is $J^n \mathbf{H}$.

##Related entries

* [[twisted cohomology]]

## References

* [[Jacob Lurie]], section 6.1 of _[[Higher Algebra]]_

[[!redirects jet (infinity,1)-categories]]

[[!redirects jet (∞,1)-category]]
[[!redirects jet (∞,1)-categories]]

[[!redirects Goodwillie jet (∞,1)-category]]
[[!redirects Goodwillie jet (∞,1)-categories]]
[[!redirects Goodwillie jet (infinity,1)-category]]
[[!redirects Goodwillie jet (infinity,1)-categories]]

[[!redirects Goodwillie jet (∞,1)-topos]]
[[!redirects Goodwillie jet (∞,1)-toposes]]
[[!redirects Goodwillie jet (infinity,1)-topos]]
[[!redirects Goodwillie jet (infinity,1)-toposes]]

[[!redirects Goodwillie n-jet (∞,1)-topos]]
[[!redirects Goodwillie n-jet (∞,1)-toposes]]
[[!redirects Goodwillie n-jet (infinity,1)-topos]]
[[!redirects Goodwillie n-jet (infinity,1)-toposes]]

[[!redirects jet category]]
[[!redirects jet categories]]


jet bundle

+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
###Context###
#### Differential geometry
+--{: .hide}
[[!include synthetic differential geometry - contents]]
=--
=--
=--

#Contents#
* table of contents
{:toc}

## Idea

A jet can be thought of as the [[infinitesimal]] [[germ]] of a [[section]] of some [[bundle]] or of a map between spaces. Jets are a coordinate free version of Taylor-polynomials and Taylor series.

## Definition

### Concrete

For

$$
  p \coloneqq E \to X
$$

a [[surjective submersion]] of [[smooth manifolds]] and $k \in \mathbb{N}$, the bundle

$$
  J^k P \to X
$$

of **order-$k$ jets of sections of $p$** is the bundle whose [[fiber]] over a point $x \in X$ is the space of equivalence classes of [[germ|germs]] of [[section|sections]] of $p$, where two germs are considered equivalent if their first $k$ partial [[derivative|derivatives]] at $x$ coincide.

In the case when $p$ is a trivial bundle $p:X\times Y \to X$ its sections are canonically in bijection with maps from $X$ to $Y$ and two sections have the same partial derivatives iff the partial derivatives of the corresponding maps from $X$ to $Y$ agree. So in this case the [[jet space]] $J^k P$ is called the space of jets of maps from $X$ to $Y$ and commonly denoted with $J^k(X,Y)$.

In order to pass to $k \to \infty$ to form the _infinite jet bundle_ $J^\infty P$ one forms the [[projective limit]] over the finite-order jet bundles,

$$
  J^\infty E \coloneqq \underset{\longleftarrow}{\lim}_k J^k E
  =
  \underset{\longleftarrow}{\lim}
  \left(
    \cdots J^3 E \to J^2 E \to J^1 E \to E
  \right)
$$

but one has to decide in which category of [[infinite-dimensional manifolds]] to take this limit:

1. one may form the limit formally, i.e. in [[pro-manifolds]]. This is what is implicit for instance in [Anderson, p.3-5](#Anderson);

1. one may form the limit in [[Fréchet manifolds]], this is farily explicit in ([Saunders 89, chapter 7](#Saunders89)). See at _[Fréchet manifold -- Projective limits of finite-dimensional manifolds](Frechet+manifold#ProjectiveLimitsOfSmoothFiniteDimensionalManifolds)_. Beware that this is not equivalent to the pro-manifold structure (see the remark [here](Frechet+manifold#DifferenceBetweenProManifoldAndFrecherManifoldStructure)). It makes sense to speak of _[[locally pro-manifolds]]_.

### The Atiyah exact sequence

When $(X,\mathcal{O}_X)$ is a complex-analytic manifold with the structure sheaf of holomorphic functions, and $E$ a locally free sheaf of $\mathcal{O}_X$-modules, we can be even more explicit.
The first jet bundle $J^1(E)$ fits into a short exact sequence, called the Atiyah exact sequence:

$$
  0\to
  E\otimes_{\mathcal{O}_X}\Omega_X^1\to
  J^1(E)\to
  E\to
  0
$$

where $J^1(E) = (E\otimes\Omega_X^1)\oplus E$ as a $\mathbb{C}$-module, but with an $\mathcal{O}_X$-action given by

$$
  f(s\otimes\omega,t)
  =
  (f s\otimes\omega+t\otimes\mathrm{d}f, f t).
$$

The extension class $[J^1(E)]\in\mathrm{Ext}_{\mathcal{O}_X}^1(E,E\otimes\Omega_X^1)$ of this exact sequence is called the Atiyah class of $E$, and is somewhat equivalent to the first Chern class of $E$.
Note that the Atiyah class is exactly the obstruction to the Atiyah exact sequence admitting a splitting, and a (holomorphic) splitting of the Atiyah exact sequence is exactly a Koszul connection.

### General abstract
 {#GeneralAbstractDefinition}

We discuss a [[general abstract]] definition of jet bundles.

Let  $\mathbf{H}$ be an [[(∞,1)-topos]] equipped with [[differential cohesion]] with [[infinitesimal shape modality]] $\Im$ (or rather a tower $\Im_k$ of such, for each infinitesimal order $k \in \mathbb{N} \cup \{\infty\}$ ).

For $X \in \mathbf{H}$, write $\Im(X)$ for the corresponding [[de Rham space]] object.

Notice that we have the canonical morphism, the $X$-component of the [[unit of a monad|unit]] of the $\Im$-[[monad]]

$$
  i \colon X \to \Im(X)
$$

("inclusion of constant paths into all infinitesimal paths").

The corresponding [[base change]] [[geometric morphism]] is

$$
  (i^\ast \dashv i_\ast)
  \;\colon\;
  \mathbf{H}_{/X}
   \stackrel{\overset{i^*}{\longleftarrow}}{\underset{Jet := i_*}{\longrightarrow}}
  \mathbf{H}_{/\Im(X)}
$$

+-- {: .num_defn #GeneralAbstractDefinition}
###### Definition

The _[[jet comonad]]_ is the [[(∞,1)-comonad]]

$$
  i^\ast i_\ast
  \;\colon\;
  \mathbf{H}_{/X}
  \longrightarrow
  \mathbf{H}_{/X}
$$

=--

+-- {: .num_remark}
###### Remark

Since [[base change]] gives even an [[adjoint triple]] $(i_! \dashv i^\ast \dashv i_\ast)$, there is a [[left adjoint]] $T_{inf} X \times_X (-)$ to the [[jet comonad]] of def. \ref{GeneralAbstractDefinition},

$$
  T_{inf}X \times_X (-) \;\dashv\; Jet
$$

where $T_{inf} X$ is the [[infinitesimal disk bundle]] of $X$, see at _[differential cohesion -- infinitesimal disk bundle -- relation to jet bundles](differential+cohesion#RelationOfInfinitesimalDiskBundleToJetBundle)_

=--

+-- {: .num_remark #LiteratureOnGeneralAbstractCharacterization}
###### Remark

In the context of [[differential geometry]] the fact that the jet bundle construction is a comonad was explicitly observed in ([Marvan 86](#Marvan86), see also [Marvan 93, section 1.1](#Marvan93), [Marvan 89](#Marvan89)). It is almost implicit in ([Krasil'shchik-Verbovetsky 98, p. 13, p. 17](#KrasilshchikVerbovetsky98), [Krasilshchik 99, p. 25](#Krasilshchik99)).

In the context of [[synthetic differential geometry]] the fact that the jet bundle construction is [[right adjoint]] to the [[infinitesimal disk bundle]] construction is ([Kock 80, prop. 2.2](#Kock80)).

{#InTheContextOf} In the context of [[algebraic geometry]] and of [[D-schemes]] as in ([BeilinsonDrinfeld, 2.3.2](#BeilinsonDrinfeld), reviewed in [Paugam, section 2.3](#Paugam)), the base change comonad formulation inf def. \ref{GeneralAbstractDefinition} was noticed in ([Lurie, prop. 0.9](#Lurie)).

=--

In as in ([BeilinsonDrinfeld, 2.3.2](#BeilinsonDrinfeld), reviewed in [Paugam, section 2.3](#Paugam)) jet bundles are expressed dually in terms of algebras in [[D-modules]]. We now indicate how the translation works.

+-- {: .num_remark}
###### Remark

In terms of [[differential homotopy type theory]] this means that
forming "jet types" of [[dependent types]] over $X$ is the
[[dependent product]] operation along the unit of the [[infinitesimal shape modality]]

$$
  jet(E) \coloneqq \underset{X \to \Im X}{\prod} E
  \,.
$$

=--

+-- {: .num_defn}
###### Definition

A [[quasicoherent (∞,1)-sheaf]] on $X$ is a morphism of [[(∞,2)-sheaves]]

$$
  X \to Mod
  \,.
$$

We write

$$
  QC(X) := Hom(X, Mod)
$$

for the [[stable (∞,1)-category]] of [[quasicoherent (∞,1)-sheaves]].

A _[[D-module]]_ on $X$ is a morphism of [[(∞,2)-sheaves]]

$$
  \Im (X) \to Mod
  \,.
$$

We write

$$
  DQC(X) := Hom(\Im (X), Mod)
$$

for the [[stable (∞,1)-category]] of D-modules.

=--

The **Jet algebra** functor is the [[left adjoint]] to the [[forgetful functor]] from [[associative algebra|commutative algebras]] over $\mathcal{D}(X)$ to those over the [[structure sheaf]] $\mathcal{O}(X)$

$$
  (Jet \dashv F)
   :
   Alg_{\mathcal{D}(X)}
    \stackrel{\overset{Jet}{\leftarrow}}{\underset{F}{\to}}
   Alg_{\mathcal{O}(X)}
  \,.
$$

## Application

Typical [[Lagrangian|Lagrangians]] in [[quantum field theory]] are defined on jet bundles. Their [[variational calculus]] is governed by [[Euler-Lagrange equation|Euler-Lagrange equations]].

## Related concepts

* [[jet prolongation]]

* [[jet space]]

* [[jet group]], [[jet groupoid]]

* [[differential equation]]

* [[evolutionary vector field]]

* [[variational bicomplex]]

  * [[local Lagrangian]]

  * [[source form]], [[Lepage form]]

* [[metric jet]]

* [[h-principle]]

* [[arithmetic jet space]]

[[!include infinitesimal and local - table]]

* in [[homotopy theory]]/[[Goodwillie calculus]]: [[jet (∞,1)-category]]

## References

Exposition of [[variational calculus]] in terms of jet bundles and [[Lepage forms]] and aimed at examples from [[physics]] is in

* {#MusilovaHronek16} [[Jana Musilová]],  [[Stanislav Hronek]], _The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories_, Communications in Mathematics, Volume 24, Issue 2 (Dec 2016) ([doi.org/10.1515/cm-2016-0012]( https://doi.org/10.1515/cm-2016-0012))

Lecture notes and textbook accounts:

* {#Michor80} [[Peter Michor]], _Manifolds of differentiable mappings_, Shiva Publishing (1980) [pdf](http://www.mat.univie.ac.at/~michor/manifolds_of_differentiable_mappings.pdf)

* {#Saunders89} [[David Saunders]], _The geometry of jet bundles_, London Mathematical Society Lecture Note Series __142__, Cambridge Univ. Press 1989.

* [[Demeter Krupka]], [[Josef Janyška]], Part 1 of: _Lectures on differential invariants_, Univerzita J. E. Purkyně, Brno (1990) [ISBN:80-210-165-8, [researchgate](https://www.researchgate.net/publication/36792711_Lectures_on_Differential_Invariants)]

* [[Jean-François Pommaret]], Chapter II in: *Partial Differential Equations and Group Theory*, Springer (1994) [[doi:10.1007/978-94-017-2539-2](https://doi.org/10.1007/978-94-017-2539-2)]

* {#Krasilshchik99} [[Joseph Krasil'shchik]] in collaboration with Barbara Prinari, _Lectures on Linear Differential Operators over Commutative Algebras_, 1998 ([pdf](http://diffiety.ac.ru/preprint/99/01_99.pdf))

* Shihoko Ishii, _Jet schemes, arc spaces and the Nash problem_, [arXiv:math.AG/0704.3327](http://arXiv.org/abs/0704.3327)

* G. Sardanashvily, _Fibre bundles, jet manifolds and Lagrangian theory_,  Lectures for theoreticians, [arXiv:0908.1886](http://xxx.lanl.gov/abs/0908.1886)

* [[Peter Olver]], _Lectures on Lie groups and differential equation_,  chapter 3, _Jets and differential invariants_, 2012 ([pdf](http://www.math.umn.edu/~olver/sm_/j.pdf))

Early accounts include

* Hubert Goldschmidt, _Integrability criteria for systems of nonlinear partial differential equations_, J. Differential Geom. Volume 1, Number 3-4 (1967), 269-307 ([Euclid](http://projecteuclid.org/euclid.jdg/1214428094))

The algebra of smooth functions of just _locally_ finite order on the jet bundle ("[[locally pro-manifold]]") was maybe first considered in

* {#Takens79} [[Floris Takens]], _A global version of the inverse problem of the calculus of variations_, J. Differential Geom. Volume 14, Number 4 (1979), 543-562. ([Euclid](https://projecteuclid.org/euclid.jdg/1214435235))

{#DiscussionOfFrechetManifoldStructure} Discussion of the [[Fréchet manifold]] structure on infinite jet bundles includes

* {#Saunders89} [[David Saunders]], chapter 7 _Infinite jet bundles_ of _The geometry of jet bundles_, London Mathematical Society Lecture Note Series __142__, Cambridge Univ. Press 1989.

* M. Bauderon, _Differential geometry and Lagrangian formalism in the calculus of variations_, in _Differential Geometry, Calculus of Variations, and their Applications_, Lecture Notes in Pure and Applied Mathematics, 100, Marcel Dekker, Inc., N.Y., 1985, pp. 67-82.

* {#DodsonGalanisVassiliou15}[[C. T. J. Dodson]], George Galanis, Efstathios Vassiliou,, p. 109 and section 6.3 of _Geometry in a Fréchet Context: A Projective Limit Approach_, Cambridge University Press (2015)

* [[Andrew Lewis]], _The bundle of infinite jets_ (2006) ([pdf](http://www.mast.queensu.ca/~andrew/notes/pdf/2006a.pdf))

Discussion of finite-order jet bundles in tems of [[synthetic differential geometry]] is in

* {#Kock80} [[Anders Kock]], _Formal manifolds and synthetic theory of jet bundles_, Cahiers de Topologie et Géométrie Différentielle Catégoriques (1980) Volume: 21, Issue: 3 ([Numdam](http://www.numdam.org/item?id=CTGDC_1980__21_3_227_0))

* {#Kock10} [[Anders Kock]], section 2.7 of _Synthetic geometry of manifolds_, Cambridge Tracts in Mathematics 180 (2010). ([pdf](http://home.imf.au.dk/kock/SGM-final.pdf))

The [[jet comonad]] structure on the jet operation in the context of differential geometry is made explicit in

* {#Marvan86} [[Michal Marvan]], _A note on the category of partial differential equations_, in _Differential geometry and its applications_, Proceedings of the Conference August 24-30, 1986, Brno ([[MarvanJetComonad.pdf:file]])

  (notice that prop. 1.3 there is wrong, the correct version is in the thesis of the author)

with further developments in

* {#Marvan89} [[Michal Marvan]] _On the horizontal cohomology with general coefficients_, 1989 ([web announcement](http://old.math.slu.cz/People/MichalMarvan/Annotations/horizontal.php), [web archive](http://dml.cz/dmlcz/701469))

  **Abstract:** In the present paper the horizontal cohomology theory is interpreted as a special case of the Van Osdol bicohomology theory applied to what we call a "jet comonad". It follows that differential equations have well-defined cohomology groups with coefficients in linear differential equations.

* {#Marvan93} [[Michal Marvan]], section 1.1 of _On Zero-Curvature Representations of Partial Differential Equations_,  (1993) ([web](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.5631))

* [[Igor Khavkine]], [[Urs Schreiber]], _[[schreiber:Synthetic variational calculus|Synthetic geometry of differential equations: I. Jets and comonad structure]]_ ([arXiv:1701.06238](https://arxiv.org/abs/1701.06238))

In the context of algebraic geometry, the abstract characterization of jet bundles as the direct images of base change along the de Rham space projection is noticed in

* {#Lurie} [[Jacob Lurie]], p. 6 of: *Notes on crystals and algebraic $\mathcal{D}$-modules* (2010) [[[Lurie-NotesOnCrystals.pdf:file]]]

The explicit description in terms of formal duals of [[commutative monoids]] in [[D-module|D-modules]] is in

* {#BeilinsonDrinfeld} [[Alexander Beilinson]], [[Vladimir Drinfeld]], _[[Chiral Algebras]]_

Exposition:

* {#Paugam} [[Frédéric Paugam]], Section 2.3 of: _Homotopical Poisson Reduction of gauge theories_ ([pdf](http://people.math.jussieu.fr/~fpaugam/documents/homotopical-poisson-reduction-of-gauge-theories.pdf))

A discussion of jet bundles with an eye towards discussion of the [[variational bicomplex]] on them :

* {#Anderson} [[Ian Anderson]], chapter 1, section A of: _The variational bicomplex_ [[[AndersonVariationalBicomplex.pdf:file]]]

The [[de Rham complex]] and [[variational bicomplex]] of jet bundles is discussed in

* G. Giachetta, L. Mangiarotti, [[Gennadi Sardanashvily]], _Cohomology of the variational bicomplex on the infinite order jet space_, Journal of
Mathematical Physics 42, 4272-4282 (2001) ([arXiv:math/0006074](http://arxiv.org/abs/math/0006074))

where both versions (smooth functions being globally or locally of finite order) are discussed and compared.

Discussion of all this in the convenient context of [[smooth sets]]:

* {#GiotopoulosSati23} [[Grigorios Giotopoulos]], [[Hisham Sati]], §4 in: *Field Theory via Higher Geometry I: [[schreiber:Smooth Sets of Fields]]* [[arXiv:2312.16301](https://arxiv.org/abs/2312.16301)]

Discussion of jet-restriction of the [[Haefliger groupoid]] is in

* Arne Lorenz, _Jet Groupoids, Natural Bundles
and the Vessiot Equivalence Method_, Thesis ([pdf](http://wwwb.math.rwth-aachen.de/~arne/Dissertation_Lorenz_Arne.pdf))

Discussion of jet bundles in [[supergeometry]] includes

* Arthemy V. Kiselev, Andrey O. Krutov, appendix of _On the (non)removability of spectral parameters in $\mathbb{Z}_2$-graded zero-curvature representations and its applications_ ([arXiv:1301.7143](http://arxiv.org/abs/1301.7143))

* [[Gennadi Sardanashvily]], _Graded infinite order jet manifolds_, _Int. J. Geom. Methods Mod. Phys. v.4 (2007) 1335-1362_ ([arXiv:0708.2434](https://arxiv.org/abs/0708.2434))

See also

* {#KrasilshchikVerbovetsky98} [[Joseph Krasil'shchik]], [[Alexander Verbovetsky]], _Homological Methods in Equations of Mathematical Physics_ ([arXiv:math/9808130](http://arxiv.org/abs/math/9808130))

On jet bundles of $\mathbb{Z}$-[[graded manifold|graded manifolds]] and their [[vector bundle|vector bundles]]:

* [[Jan Vysoky]]. *Graded Jet Geometry*. (2023). ([arXiv:2311.15754](https://arxiv.org/abs/2311.15754))

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