database of categories

The idea here is to create an enormous list of well-known categories and their properties.  As the list gets large we'll have to figure out a good structure for it, but right now I'll just do a few entries in alphabetical order.  [[Andrew Stacey]] solicits input about making this a real database; see [the Forum](https://nforum.ncatlab.org/discussion/57/).

We can import new entries by looking at [category:category](http://ncatlab.org/nlab/list/category), which should have all articles dedicated to specific categories.

* [[Ab]]: [[abelian group|abelian groups]] as objects, homomorphisms as morphisms.  Since this category consists of models of a [[Lawvere theory]] it has all small [[limit|limits]] and [[colimit|colimits]].  It is the prototypical [[abelian category]] and also a [[closed symmetric monoidal category]] under the [[tensor product]] of abelian groups.

* [[Alg]]: [[algebra|algebras]] as objects, homomorphisms as morphisms.  This is actually many different categories, depending on a choice of ground [[field]] or more generally [[commutative ring]].  Since any one of these categories consists of models of a [[Lawvere theory]], it has all small [[limit|limits]] and [[colimit|colimits]].

* [[Bicat]]: [[bicategories]]($=$weak 2-categories) as objects, [[2-functors]] as its 1-cells, [[pseudonatural transformations]] between its 1-cells as its 2-cells, and [[modifications]] between its 2-cells as its 3-cells. BiCat is a [[tricategory]]. BiCat is sometimes denoted $Hom$.

* [[CartSp]]: spaces $\mathbb{R}^n$ as objects, smooth maps as morphisms.

* [[Cat]]: [[small category|small categories]] as objects, [[functor|functors]] as morphisms.  Since this category consists of models of a [[finite limits theory]], it has all small [[limit|limits]] and [[colimit|colimits]].  It is [[cartesian closed category|cartesian closed]], and its [[internal hom]]s make it into a [[2-category]].

* [[Diff]]: smooth [[manifold]]s as objects, smooth maps as morphisms.  This category has finite but not infinite [[products]], and all small [[coproducts]].  It does not have equalizers or coequalizers, and is not [[cartesian closed category|cartesian closed]].

* [[diffeological space|Diffeological spaces]] as objects, smooth maps as morphisms.  This category has all small limits and colimits, it is [[cartesian closed category|cartesian closed]], and it has a weak [[subobject classifier]].  So, it is a [[quasitopos]].

* [[Grp]]: [[group]]s as objects, homomorphisms as morphisms.  Since this category consists of models of a [[Lawvere theory]] it has all small [[limit|limits]] and [[colimit|colimits]].

* $Mod_R$: (right) $R$-[[modules]] as objects, $R$-module homomorphisms as morphisms.  There is one such category for any [[ring]] $R$ (or more generally, any small [[Ab-enriched category]].  This is also the category of models of a [[Lawvere theory]] and is thus complete and cocomplete.  It is an [[abelian category]] and even [[Grothendieck category]].  If $R$ is commutative, then $Mod_R$ is a [[closed symmetric monoidal category]] under the [[tensor product]] of $R$-modules.

* [[M-Set]]: Category of $M$-sets, a [[topos]].

* [[MultiSet]]: Category of [[multisets]].

* [[Rel]]: [[sets]] as objects, [[relation|relations]] as morphisms.  This is an [[allegory]] and therefore a [[dagger category]].   The empty set is an [[zero object]], and disjoint union plays the role of [[biproduct]].   This category does not have [[equalizer|equalizers]] or [[coequalizer|coequalizers]].

* [[Ring]]: [[ring|rings]] as objects, ring homomorphisms as morphisms.  Since this category consists of models of a [[Lawvere theory]] it has all small [[limit|limits]] and [[colimit|colimits]]. (maybe we should have unital rings $Ring_1$ separately; the difference is important sometimes).

* [[SimpSet]]: [[simplicial sets]] as objects, simplicial maps as morphisms.  This is a [[presheaf]] [[topos]].

* [[Set]]: [[sets]] as objects, [[functions]] as morphisms.
This has the following properties:

  * It is a [[topos]], and in particular it is [[locally cartesian closed category|locally cartesian closed]].
  * It is [[locally small category|locally small]].
  * It is [[complete category|complete]] and [[cocomplete category|cocomplete]], and therefore $\infty$-[[extensive category|extensive]] (as is any cocomplete topos).
  * It is [[well-pointed topos|well-pointed]].

  At least assuming [[classical logic]], these properties suffice to characterize $Set$ uniquely up to equivalence among all categories.  Note, however, that the definitions of "locally small" and "(co)complete" presuppose a notion of _small_ and therefore a knowledge of what a _set_ is.

  See also [[Understanding Set]].

* [[Top]]: [[topological space]]s as objects, continuous functions as morphisms.   This has all small limits and colimits, but is not cartesian closed --- a problem that may be addressed by introducing a [[convenient category of topological spaces]].

* $k$-[[Vect]]: [[vector space]]s as objects, linear maps as morphisms.  This is actually many different categories, depending on a choice of [[field]] $k$; in fact, it is a special case of $Mod_R$ when $R$ is a field.  Since any one of these categories consists of models of a [[Lawvere theory]], it has all small [[limit|limits]] and [[colimit|colimits]].

+-- {: .query}
Rafael Borowiecki: I could add something of the order 100 categories here, but i know very little of their properties. Should i add them anyway?

It would also be helpful to have a list of properties to fill in for each category to make it a real database. As a start i suggest: size, concrete, complete, enrichment, topos. This list could also get very large resulting in an even larger table (written as a list). For instance one could also add functoriality (is it a category of functors?, notice that the Yoneda lemma do not hold for any category), cartesian closedness, monoidality, model structure.

I don't know where to put this request but the logging of changes should be automated. Simply add a smaller box one might fill in if one wishes below the editing box and hope that not every edit will also edit this changes box. It could be limited to size.

_Toby_:  I also could add hundreds of categories.  At this stage, I\'m inclined to add only categories that we have pages for.  On the other hand, often people only create pages because there are links to them, so perhaps people should also add categories that they think are important and conspicuously missing?  As long as the page isn\'t flooded with a huge list, it will be manageable.  And maybe we could even manage a huge list?  I\'d like to hear what [[John Baez|John]] thinks.  (Sorry to be so indecisive!)

Automatic logging is not an option with Instiki, which is why we use [[latest changes]] instead.  You could request that it be added as a feature to [Instiki](http://www.instiki.org/show/HowToContribute), but (unless you can program it) don\'t hold your breath.  *However*, note that there is a page [Recently Revised](http://ncatlab.org/nlab/recently_revised); it\'s disabled now, but that should be temporary.  (Try [this one](http://ncatlab.org/tobybartels/recently_revised) to see how it\'s supposed to work.)  When it comes back, it will take care of much of the need for automatic logging, requiring people only to report major changes that others need to know about.

_Rafael_: I was wondering what happened to Recently Revised. Now i know it is not improved to Latest changes and will be back. Thx for the information.

_[[John Baez]]_: I don't see any use of listing categories here unless one includes information about their basic categorical properties: for starters, which sorts of limits and/or colimits they have:

* binary products
* binary coproducts
* terminal object
* initial object
* pullbacks
* pushouts
* equalizers
* coequalizers
* finite limits
* finite colimits
* small limits
* small colimits

whether they admit interesting monoidal structures, whether they are cartesian (or monoidal) closed, and whether they are topoi, quasitopoi or allegories.  In short: the basic properties one instantly wants to know about any category one meets.

My idea is that this article should be a quick place to look up basic categorical properties of categories, including categories that may not have their own entry yet.   The entries here should not become full-fledged articles on the categories involved, since we already have or can create those.

By the way: people have been talking to Rafael on [Recently Revised](http://ncatlab.org/nlab/recently_revised) for many weeks now, but he doesn't seem to reply to their comments there, which is making some people annoyed.

_Toby_:  I can see that a list of categories *with properties* could be useful.

John, you don\'t mean Recently Revised; you mean [[latest changes]].  (Your link will break when Recently Revised itself comes back.)

Rafael, I don\'t know if you\'ve been checking [[latest changes]], but I often log your edits there after I see them.  But I don\'t see why anyone would get upset that you don\'t read their commentary if they leave it on the wrong page.

_Rafael_: I am sorry to have missed the logging but i only recently by accident noticed that you also log at Latest Changes. I thought that all changes were in Recently Revised. Since Toby is logging for me, thanks Toby, i will try to remember to do it myself so others don't have to do it for me.

_John_: Sorry, I meant [[latest changes]].  It's a good way to discuss what's going on with various new entries.

_Andrew_: Actually, it's a very bad way to _discuss_ what's going on, but an okay way to _announce_ what's going on.  But that's another battle for another day.  What I'm really here for is to ponder the format of this page a little.  At the moment, we can't do a proper database-based page of all this stuff so we have to think of the next best thing.  Is the current format most useful?  Or would a table with loads of 'X's be more appropriate?  The categories would, of course, be linked to their pages where one could find out more.  For example, here we would merely record that, say, Rel didn't have all limits and colimits.  On the actual page there would be an example showing why not.  One would need a few "codes" for the entries along the lines of "Yes", "No", "Don't Know", "Sort of Yes", "Sort of No".  That sort of thing.  One could then search by name using the browser search.  What you wouldn't get, that you would get from a database, would be the ability to, say, only show complete categories.  But how likely is that to be a request?  I'd expect the main use to be "I don't remember if Frolicher spaces are locally cartesian closed or not.".  I would think that a table format would be more useful than this list format, but I may be in a minority here (I usually am) and I'd rather not go to the effort of putting it in that format only to find no-one else likes it.

[[Zoran Škoda]]: I agree with John that the main purpose is to list many properties of well known categories, rather than listijng definitions of exotic categories. Those categories which already have their page on the nlab could be expanded on those pages rather than here. For some not only existence of limits but also a construction of limits can be useful.

_Toby_:  I agree with Andrew about everything from 'Actually,' to 'it.'.  However, making a table with specific columns can be somewhat limiting, so we would need to make clear up top that adding new columns is fine.  Blank entries in the table should default to ‹Nobody has bothered to put the answer here yet.›, which should be distinguished from ‹This is an unsolved problem.›.  Other useful entries besides 'Yes' or 'No' might be 'if and only if $R$ is [[noetherian ring|noetherian]]', 'equivalent to the [[ultrafilter principle]]', and the like.  Some standard abbreviations might be useful here; tables can be hard to deal with when they get too wide.

=--

+-- {: .query}
_Rafael_: I have been thinking why the database is not growing. As for the existence of (co)limits, it must be because most existence results are hard to find, or at least hard enough to not search for them systematically. So, if some of you reading this could present _methods_ (even theorems that assert the existence under some conditions or characterization theorems) to prove such existences, one could check it oneself and include it in the database. The point is that i don't know any method except the one John Baez used (but i do know some useful but limited theorems such that toposes are finitely complete and finitely cocomplete). You can see where this is going? A lot of theorems (except for the methods) that imply properties of categories from other categories or other properties are needed. Then, we have to assume that the database will grow and a table would be much to cumbersome. I remember someone at nLab could write the database in Ruby, is this offer still on?

=--


database theory

# Contents
* table of contents
{: toc}

## Idea

_Database theory_ is a branch of [[computer science]] that treats [[database]] management and query languages.

## Related entries

* [[data]], [[data type]]

* [[database]]

* [[store comonad]]

## References

* Kristopher Brown, [[David I. Spivak]], Ryan Wisnesky, _Categorical Data Integration for Computational Science_, ([arXiv:1903.10579](https://arxiv.org/abs/1812.05765))

* Patrick Schultz, [[David I. Spivak]], Christina Vasilakopoulou, Ryan Wisnesky, _Algebraic Databases_, ([arXiv:1602.03501](https://arxiv.org/abs/1602.03501))


Dave Ripley

* Webpage: [http://davewripley.rocks](http://davewripley.rocks)

category: people


Davesh Maulik

* [webpage](https://math.mit.edu/directory/profile.php?pid=177)

## Selected writings

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

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

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

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

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

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

following the analogous non-elliptic discussion in:

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

category: people


David A. Cox


David A. Espinosa

* [personal page](https://groups.csail.mit.edu/mac/users/dae/)

* [github page](https://github.com/davidespinosa01/)

## Selected writings

On ([[denotational semantics]] of) [[functional programming]] with [[monadic effects]] and introducing the notion of [[monad transformers]]:

* {#Espinosa94} [[David A. Espinosa]], §3.2 in: *Building Interpreters by Transforming Stratified Monads* (1994) [[pdf](https://github.com/davidespinosa01/papers/blob/master/E/Espinosa%20David/espinosa-stratified-monads.pdf), [[Espinosa-StratifiedMonads.pdf:file]]]

* {#Espinosa95} [[David A. Espinosa]], *Semantic Lego*, PhD thesis, Columbia University (1995) [[pdf](https://github.com/davidespinosa01/papers/blob/master/E/Espinosa%20David/espinosa-stratified-monads.pdf), [[Espinosa-SemanticLego.pdf:file]], slides:[pdf](https://github.com/davidespinosa01/papers/blob/346c2ded6af78805701106d51daee8f7a756c948/E/Espinosa%20David/espinosa-thesis-slides.pdf), [[Espinosa-SemanticLego-slides.pdf:file]]]

category: people

[[!redirects David Espinosa]]


David A. Schmidt

* [personal page](https://people.cs.ksu.edu/~schmidt/)

## Selected writings

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

* [[David A. Schmidt]], *Denotational Semantics -- A methodology for language development*, Allyn and Bacon (1986)  [[pdf](https://people.cs.ksu.edu/~schmidt/text/DenSem-full-book.pdf), [webpage](https://people.cs.ksu.edu/~schmidt/text/densem.html)]

category: people

[[!redirects David Schmidt]]


David Albert

David Albert is a [[philosophy of physics|philosopher of physics]].

* [webpage](http://philosophy.columbia.edu/directories/faculty/david-z-albert)

* [Wikpedia entry](http://en.wikipedia.org/wiki/David_Albert)

* {#Albert12} _[On the origin of Everything](http://www.nytimes.com/2012/03/25/books/review/a-universe-from-nothing-by-lawrence-m-krauss.html?_r=1&adxnnl=1&adxnnlx=1415727315-pCXR9NUmWeBxo+FViR+NlA)_, 2012

## Related entries

* [[philosophy of physics]]

category: people


David Ayala

* [website](http://www.math.montana.edu/dayala/)

## related $n$Lab entries

* [[(infinity,n)-category with all adjoints]]

category: people


David B. Fairlie

* [InSpire page](https://inspirehep.net/authors/1010427)

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

## Selected writings

On [[Weyl quantization]]:

* [[Thomas L. Curtright]], [[David B. Fairlie]], [[Cosmas K. Zachos]], *A Concise Treatise on Quantum Mechanics in Phase Space*, World Scientific (2014) [[doi:10.1142/8870](https://doi.org/10.1142/8870)]

category: people

[[!redirects David Fairlie]]


David Bailey

* [personal page](https://www.davidhbailey.com/)

* Wikipedia entry

## Selected writings

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

* [[David Bailey]], [[Peter Borwein]], [[Simon Plouffe]]: *On the Rapid Computation of Various Polylogarithmic Constants*, Math. Comp. **66** (1997) 903-913 [[doi:1997-66-218/S0025-5718-97-00856-9](https://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9)]

category: people


David Baraglia

* [webpage](http://www.maths.adelaide.edu.au/david.baraglia/Homepage_of_David_Baraglia/David_Baraglia.html)

## related $n$Lab entries

* [[exceptional generalized geometry]]

* [[Bn-geometry]]

* [[Higgs bundle]]

category: people


David Barnes

* [webpage](http://www.qub.ac.uk/puremaths/Staff/David%20Barnes/)

## Selected writings

On [[stable homotopy theory]]:

* [[David Barnes]], [[Constanze Roitzheim]], _Foundations of Stable Homotopy Theory_ ([pdf](https://www.kent.ac.uk/smsas/personal/csrr/stablemodelcatsCUP.pdf))

On [[rational equivariant stable homotopy theory]]:

* [[David Barnes]], _Rational Equivariant Spectra_ ([arXiv:0802.0954](http://arxiv.org/abs/0802.0954))

* [[David Barnes]], _Classifying Rational $G$-Spectra for Finite $G$_ ([arXiv:0812.0317](http://arxiv.org/abs/0812.0317))

* [[David Barnes]], [[Magdalena Kedziorek]], _An introduction to algebraic models for rational G-spectra_ ([arXiv:2004.01566](https://arxiv.org/abs/2004.01566))

On [[Goodwillie calculus]]:

* [[David Barnes]], [[Rosona Eldred]], *Capturing Goodwillie's Derivative*, Journal of Pure and Applied Algebra
**220** 1 (2016) 197-222 [[arXiv:1406.0424](https://arxiv.org/abs/1406.0424), [doi:10.1016/j.jpaa.2015.06.006](https://doi.org/10.1016/j.jpaa.2015.06.006)]

On [[orthogonal calculus]]:

* [[David Barnes]], [[Rosona Eldred]], _Comparing the orthogonal and homotopy functor calculi_, Journal of Pure and Applied Algebra **220** 11 (2016) 3650-3675 [[arXiv:1505.05458](http://arxiv.org/abs/1505.05458), [doi:10.1016/j.jpaa.2016.05.005](https://doi.org/10.1016/j.jpaa.2016.05.005)]

## Related entries

* [[rational equivariant stable homotopy theory]]

* [[orthogonal calculus]]

category: people


David Ben-Zvi

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

## Selected writings

* D. Ben-Zvi, J. Francis, D. Nadler, _Integral transforms and Drinfeld centers in derived algebraic geometry_, [arXiv:0805.0157](http://arxiv.org/abs/0805.0157), Jour. Amer. Math. Soc. 2010, [doi](http://dx.doi.org/10.1090/S0894-0347-10-00669-7)

* David Ben-Zvi, David Nadler, _Loop spaces and Langlands parameters_ ([arXiv](http://arxiv.org/abs/0706.0322))

* D. Ben-Zvi, D. Nadler, _Loop spaces and connections_,
[arxiv/1002.3636](http://arxiv.org/abs/1002.3636)

* David Ben-Zvi kindly wrote an expositional piece on geometric function theory for the $n$-Category Café ([blog entry](http://golem.ph.utexas.edu/category/2009/01/benzvi_on_geometric_function_t.html))

* D. Ben-Zvi, [[BenZviGeometricFunctionTheory.pdf:file]] (Jan 2009).

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

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

On the [[relative Langlands program]]

* [[David Ben-Zvi]], [[Yiannis Sakellaridis]], [[Akshay Venkatesh]], _Relative Langlands duality_ ([pdf](https://www.math.ias.edu/~akshay/research/BZSVpaperV1.pdf)).

## Selected talks

* Talk at NorthWestern University, May 2009, [Gauge Theory and Representation Theory](http://math.utexas.edu/users/benzvi/GRASP/lectures/NWTFT/nwtft.pdf)

* Talk at Hamburg Center of mathematical physics, Febuary 2009, [[BenZviHamburg2009.pdf:file]]

* talk at _[ASPECTS of Topology](https://people.maths.ox.ac.uk/tillmann/ASPECTS.html)_ 2012, _[[Loop Groups, Characters and Elliptic Curves]]_ ([pdf slides](https://people.maths.ox.ac.uk/tillmann/ASPECTSbenzvi.pdf))

* D. Ben-Zvi has given many interesting answers to [http://mathoverflow.net](MathOverflow) questions, and a list can be found at [MO user page:David Ben-Zvi](http://mathoverflow.net/users/582/david-ben-zvi).

## Related $n$Lab entries

* [[geometric function theory]]

category: people

[[!redirects D. Ben-Zvi]]


David Berenstein

* [webpage](http://www.physics.ucsb.edu/people/academic/david-berenstein)

## Selected writings

On [[Penrose limit]] of [[anti de Sitter spacetimes]] to [[pp-wave spacetimes]], [[single trace operators]] in the [[AdS/CFT correspondence]], and introducing the [[BMN matrix model]]:

* {#BerensteinMaldacenaNastase02} [[David Berenstein]], [[Juan Maldacena]], [[Horatiu Nastase]], Section 2 of: _Strings in flat space and pp waves from $\mathcal{N} = 4$ Super Yang Mills_, JHEP 0204 (2002) 013 ([arXiv:hep-th/0202021](https://arxiv.org/abs/hep-th/0202021))

On [[flat space holography]]:

* [[David Berenstein]], *A toy model for the AdS/CFT correspondence*,  	JHEP 0407 (2004) 018 ([arXiv:hep-th/0403110](https://arxiv.org/abs/hep-th/0403110))

On [[thermodynamics]] of the [[BMN matrix model]]:

* Curtis T. Asplund, [[David Berenstein]], Diego Trancanelli, _Evidence for fast thermalization in the plane-wave matrix model_, 	Phys. Rev. Lett. 107, 171602 (2011) ([arXiv:1104.5469](https://arxiv.org/abs/1104.5469))

M-theory on ALE-spaces

* [[David Berenstein]], Richard Corrado, [[Jacques Distler]], _Aspects of ALE matrix models and twisted matrix strings_, Phys. Rev. D 58, 026005 (1998) ([arXiv:hep-th/9712049](https://arxiv.org/abs/hep-th/9712049))

category: people


David Berman

David Berman is professor in theoretical [[physics]] at Queen Mary University of London.

* [webpage](http://www.strings.ph.qmul.ac.uk/~dsb/)

## Selected writings

On [[boundary conditions]] for interacting [[M2-branes]] in regarding through the [[ABJM model]]:

* {#BPST09} [[David Berman]], [[Malcolm J. Perry]], [[Ergin Sezgin]], [[Daniel C. Thompson]], *Boundary Conditions for Interacting Membranes*, JHEP 1004:025, 2010 [[arXiv:0912.3504](https://arxiv.org/abs/0912.3504), doi:10.1007/JHEP04(2010)025]

On [[U-duality]] and [[diffeomorphisms]] in [[exceptional generalized geometry]]:

* [[David Berman]], [[Martin Cederwall]], [[Axel Kleinschmidt]], [[Daniel C. Thompson]], _The gauge structure of generalised diffeomorphisms_, High Energ. Phys. 2013, 64 (2013) [[arXiv:1208.5884](http://arxiv.org/abs/1208.5884)]

A review of [[exceptional field theory]]:

* [[David Berman]], [[Chris D. A. Blair]], _The Geometry, Branes and Applications of Exceptional Field Theory_,  International Journal of Modern Physics A **35** 30 (2020) 2030014  [[arXiv:2006.09777](http://arxiv.org/abs/2006.09777), [doi:10.1142/S0217751X20300148](https://doi.org/10.1142/S0217751X20300148)]

On the formulation of [[strings]] and [[black branes]] of [[supergravity]] (crucially including the [[exotic branes]]) respectively as [[pp-waves]] and [[monopoles]] in [[double field theory]]/[[exceptional field theory]]:

* [[David Berman]], Felix J. Rudolph, _Branes are Waves and Monopoles_ ([arXiv:1409.6314](https://arxiv.org/abs/1409.6314))

* {#BMO19} [[David Berman]], [[Edvard Musaev]], [[Ray Otsuki]], _Exotic Branes in M-Theory_, contribution to: *[Dualities and Generalized Geometries, Corfu Summer Institute 2018](http://www.physics.ntua.gr/corfu2018/dg.html)* ([arXiv:1903.10247](https://arxiv.org/abs/1903.10247))

About the formulation [[string theory]]/[[M-theory]] in terms of [[generalized geometry]]:

* [[David Berman]], [[Malcolm Perry]], _Generalized Geometry and M theory_ ([arXiv:1008.1763](https://arxiv.org/abs/1008.1763))

About the global geometry of [[double field theory]]/[[exceptional field theory]]:

* [[David Berman]], [[Martin Cederwall]], Axel Kleinschmidt, Daniel C. Thompson, _The gauge structure of generalised diffeomorphisms_ ([arXiv:1208.5884](https://arxiv.org/abs/1208.5884))

* [[David Berman]], [[Martin Cederwall]], [[Malcolm Perry]], _Global aspects of double geometry_ ([arXiv:1401.1311](https://arxiv.org/abs/1401.1311))

About [[Ehlers transformation]] being the double copy of [[S-duality]] in [[classical double copy]]:

* {#ABSP19} Rashid Alawadhi, [[David Berman]], Bill Spence, David Peinador Veiga, _S-duality and the Double Copy_ ([arXiv:1911.06797](https://arxiv.org/abs/1911.06797))

On the [[classical double copy]] for [[D=11 supergravity]]:

* [[David Berman]], Kwangeon Kim, Kanghoon Lee, _The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory_ ([arXiv:2010.08255](https://arxiv.org/abs/2010.08255))

## Related $n$Lab entries

* [[double field theory]], [[exceptional field theory]]

* [[exotic branes]], [[T-folds]], [[non-geometry]]

* [[generalized geometry]], [[exceptional generalized geometry]]

* [[confinement]] in [[AdS-CFT]] ([[string theory results applied elsewhere]])

* [[classical double copy]]

[[!redirects David S. Berman]]

category: people


David Blanc

David Abraham Blanc is an algebraic topologist at the Department of Mathematics, University of Haifa.

He got his PhD degree in 1988 from MIT, advised by [[Daniel M. Kan]].

His interests include homotopy operations and [[Pi-algebras]] and  higher-order homotopy operations.

[Webpage](http://math.haifa.ac.il/blanc/).

category:people

[[!redirects D. Blanc]]
[[!redirects David A. Blanc]]
[[!redirects David Abraham Blanc]]


David Bohm

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

## Selected writings

Introducing the [[hidden variable theory]] of [[quantum mechanics]] that came to be known as *[[Bohmian mechanics]]*:

* [[David Bohm]], *A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I*, Phys. Rev. **85** (1952) 166 [[doi:10.1103/PhysRev.85.166](https://doi.org/10.1103/PhysRev.85.166)]

* [[David Bohm]], *A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II*, Phys. Rev. **85** (1952) 180 [[doi:10.1103/PhysRev.85.180](https://doi.org/10.1103/PhysRev.85.180)]

Discussion of what came to be known as the [[Aharonov-Bohm effect]]:

* [[Yakir Aharonov]], [[David Bohm]], *Significance of Electromagnetic Potentials in the Quantum Theory*, Phys. Rev. **115** (1959) 485 [[doi:10.1103/PhysRev.115.485](https://doi.org/10.1103/PhysRev.115.485), [pdf](https://journals.aps.org/pr/pdf/10.1103/PhysRev.115.485)]

category: people


David Borthwick

* [webpage](http://www.mathcs.emory.edu/~davidb/)

## related $n$Lab entries

* [[almost Kähler geometric quantization]]

category: people


David Brook

## Selected

On [[higher twisted K-theory]]:

* [[David Brook]], *Computations in higher twisted K-theory*,  ([arXiv:2007.08964A](https://arxiv.org/abs/2007.08964A))

* [[David Brook]], *Higher twisted K-theory*, ([dspace:2440/125740)](https://digital.library.adelaide.edu.au/dspace/handle/2440/125740))

category: people


David Buchsbaum

__David Alvin Buchsbaum__ was an American algebraist, working mainly in commutative algebra and homological algebra. He was a student of Eilenberg with a Ph. D. thesis about [[Abelian category|Abelian categories]].

* wikipedia: [David Buchsbaum](https://en.wikipedia.org/wiki/David_Buchsbaum), [Auslander-Buchsbaum theorem](https://en.wikipedia.org/wiki/Auslander%E2%80%93Buchsbaum_theorem), [Auslander-Buchsbaum formula](https://en.wikipedia.org/wiki/Auslander%E2%80%93Buchsbaum_formula)
* mathematical [obituary](https://www.commalg.org/2021/01/11/david-buchsbaum-1929-2021)

## Selected works

Work with a notion close to the notion of [[Quillen exact category]]

* D. A. Buchsbaum, _A note on homology in categories_, Ann. of Math. (2) 69 (1959) 66-74 [MR140556](https://mathscinet.ams.org/mathscinet-getitem?mr=140556)

In a 1957 article with [[Maurice Auslander]] they proved the [[Auslander-Buchsbaum formula]] on projective dimension of projective modules over commutative Noetherian local rings.

* [[Maurice Auslander]], David A. Buchsbaum, _Homological dimension in local rings_, Trans. Amer. Math. Soc. __85__ (2): 390--405 (1957) [doi](https://doi.org/10.2307/1992937) [MR0086822](https://mathscinet.ams.org/mathscinet-getitem?mr=86822)

In a 1959 article with Buchsbaum they proved the [[Auslander-Buchsbaum theorem]] that every commutative Noetherian regular local ring is a [[unique factorization domain]].

* [[Maurice Auslander]], David A. Buchsbaum, _Unique factorization in regular local rings,_ Proc. Nat. Acad. Sci. __45__ (5): 733-734 (1959) [doi](https://doi.org/10.1073/pnas.45.5.733) [MR0103906](https://mathscinet.ams.org/mathscinet-getitem?mr=0103906)

category: people

[[!redirects David Alvin Buchsbaum]]


David Calderbank

* [webpage](http://people.bath.ac.uk/dmjc20/)

## related $n$Lab entries

* [[BGG resolution]]

* [[parabolic geometry]]

category: people


David Carchedi

* [website](http://math.gmu.edu/~dcarched/)

## Selected writings

On [[topological stacks]] and [[differentiable stacks]]:

* {#Carchedi11} [[David Carchedi]], _Categorical Properties of Topological and Diffentiable Stacks_, PhD thesis, Universiteit Utrecht, 2011 ([dspace:1874/208971](https://dspace.library.uu.nl/handle/1874/208971), [pdf](http://math.gmu.edu/~dcarched/Thesis_David_Carchedi.pdf), [[CarchediDifferentiableStacks.pdf:file]])

On [[smooth superalgebras]]:

* [[David Carchedi]], [[Dmitry Roytenberg]], *On Theories of Superalgebras of Differentiable Functions* [[arXiv:1211.6134](http://arxiv.org/abs/1211.6134)]

On [[étale infinity-groupoids]]:

* [[David Carchedi]], _Étale Stacks as Prolongations_, Advances in Mathematics Volume 352, 20 August 2019, Pages 56-132 ([arXiv:1212.2282](http://arxiv.org/abs/1212.2282))

* [[David Carchedi]], _Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi_, Memoirs of the American Mathematical Society 2020; 120 ([arXiv:1312.2204](https://arxiv.org/abs/1312.2204),[ISBN:978-1-4704-5810-2](https://bookstore.ams.org/memo-264-1282))

* {#Carchedi15} [[David Carchedi]], _On The Homotopy Type of Higher Orbifolds and Haefliger Classifying Spaces_, Advances of Mathematics, Volume 294, 2016, Pages 756-818 ([arXiv:1504.02394](http://arxiv.org/abs/1504.02394))

* [[David Carchedi]], _On the étale homotopy type of higher stacks_ ([arXiv:1511.07830](https://arxiv.org/abs/1511.07830))

{#DerivedFieldTheory} On [[derived geometry]] for [[Lagrangian field theory]] in terms of [[smooth stacks]]:

* [[David Carchedi]], *Derived differential geometry and quantum field theory*, talk in the *[Prague Mathematical Physics Seminar](https://www.youtube.com/@praguemathematicalphysicss9088)* (Dec 2020) [video:[YT](https://www.youtube.com/watch?v=VdMSnlf7qK0)]

* [[David Carchedi]], *Derived differential geometry and the quantization of gauge field theories*, talk at *[Workshop on Supergeometry and Bracket Structures in Mathematics and Physics](http://www.fields.utoronto.ca/activities/21-22/supergeometry)*, Fields Institute (Mar 2022) [video:[YT](https://www.youtube.com/watch?v=C8fEZPPsg_M)]

On [[derived smooth manifolds]]:

* [[David Carchedi]], [[Pelle Steffens]], _On the universal property of derived manifolds_ [[arXiv:1905.06195](https://arxiv.org/abs/1905.06195)]

* [[David Carchedi]], *Derived Manifolds as Differential Graded Manifolds* [[arXiv:2303.11140](https://arxiv.org/abs/2303.11140)]

On higher [[orbifolds]] and [[Deligne-Mumford stacks]] as [[(∞,1)-toposes]]:

* [[David Carchedi]], *Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi*, Memoirs of the American Mathematical Society **264** 1282 (2020) [[doi:10.1090/memo/1282](https://doi.org/10.1090/memo/1282), [arXiv:1312.2204](https://arxiv.org/abs/1312.2204)]

## Related $n$Lab entries

* [[geometric stack]]

  * [[topological stack]]

  * [[differentiable stacks]]

category: people

[[!redirects David Carchedi]]

[[!redirects Dave Carchedi]]


David Carlson

* [webpage](http://www.cardozo.yu.edu/directory/david-g-carlson)

## related $n$Lab entries

* [[Science of Logic]]

category: people


David Chataur

* [personal page](http://math.univ-lille1.fr/~chataur/)

## Selected writings

On [[string topology]] and [[cyclic loop spaces]] ("[[string spaces]]")

* {#Chataur05} [[David Chataur]], *A bordism approach to string topology*, International Mathematics Research Notices **2005** 46, (2005)  ([arXiv:math/0306080](https://arxiv.org/abs/math/0306080), [doi:10.1155/IMRN.2005.2829](https://doi.org/10.1155/IMRN.2005.2829))

On [[free loop spaces]]:

* [[David Chataur]], Alexandru Oancea, *Basics on free loop spaces*, Chapter I in: Janko Latchev, Alexandru Oancea (eds.): *Free Loop Spaces in Geometry and Topology*, IRMA Lectures in Mathematics and Theoretical Physics **24**, EMS 2015 [[ISBN:978-3-03719-153-8](https://bookstore.ams.org/emsilmtp-24/)]

category: people


David Chatterjee

* [maths genealogy page](http://www.genealogy.ams.org/id.php?id=49514)

## Publications

* _On Gerbs_, 1998 ([pdf](http://people.maths.ox.ac.uk/hitchin/hitchinstudents/chatterjee.pdf))

on [[bundle gerbes]]

## Related entries

* [[twistor space]]

category: people


David Chester

* [webpage](https://quantumgravityresearch.org/david-chester)

## Selected writings

On [[D=14 supersymmetry]]:

* [[Michael Rios]], [[Alessio Marrani]], [[David Chester]], _The Geometry of Exceptional Super Yang-Mills Theories_, Phys. Rev. D 99, 046004 (2019) ([arXiv:1811.06101](https://arxiv.org/abs/1811.06101))

On [[12-dimensional supergravity]], [[D=14 supersymmetry]] et al. and further indications that [[M-theory]] in 10+1 dimensions may be understood as the [[KK-compactification]] on Cayley-plane [[fibers]] of some kind of [[bosonic M-theory]] in 26+1 dimensions:

* [[Michael Rios]], [[Alessio Marrani]], [[David Chester]], _The Geometry of Exceptional Super Yang-Mills Theories_, Phys. Rev. D **99** (2019) 046004  [[arXiv:1811.06101](https://arxiv.org/abs/1811.06101), [doi:10.1103/PhysRevD.99.046004](https://doi.org/10.1103/PhysRevD.99.046004)]

* [[Michael Rios]], [[Alessio Marrani]], [[David Chester]], *Exceptional Super Yang-Mills in $D=27+3$ and Worldvolume M-Theory*, Phys. Lett. B **808** (2020) 135674 [[arXiv:1906.10709](https://arxiv.org/abs/1906.10709), [doi:10.1016/j.physletb.2020.135674](https://doi.org/10.1016/j.physletb.2020.135674)]

Relation to the [[Monster group]], [[Moonshine]] and the [[Monster vertex operator algebra]]:

* [[Alessio Marrani]], [[Michael Rios]], [[David Chester]], *Monstrous M-theory*, Symmetry **15** 2 (2023) 490; [[doi:10.3390/sym15020490](https://doi.org/10.3390/sym15020490), [arXiv:2008.06742](https://arxiv.org/abs/2008.06742)]

On [[quasicrystals]] as a substrate for [[topological quantum computation]] with [[Fibonacci anyons]]:

* Marcelo Amaral, [[David Chester]], Fang Fang, Klee Irwin, *Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing*, Symmetry **14** 9 (2022) 1780 [[arXiv:2207.08928](https://arxiv.org/abs/2207.08928), [doi:10.3390/sym14091780](https://doi.org/10.3390/sym14091780)]

category: people


David Cohen-Steiner

* [personal page](https://www-sop.inria.fr/members/David.Cohen-Steiner/)

## Selected writings

Introducing [[stability of persistence diagrams]]:

* {#CohenSteinerEdelsbrunnerHarer07} [[David Cohen-Steiner]], [[Herbert Edelsbrunner]], [[John Harer]], *Stability of Persistence Diagrams*, Discrete & Computational Geometry **37** (2007) 103–120 $[$[doi:10.1007/s00454-006-1276-5](https://doi.org/10.1007/s00454-006-1276-5)$]$

* [[Frédéric Chazal]], [[David Cohen-Steiner]], [[Marc Glisse]], [[Leonidas J. Guibas]], [[Steve Y. Oudot]], *Proximity of persistence modules and their diagrams*, SCG '09: Proceedings of the twenty-fifth annual symposium on Computational geometry (2009) 237–246 $[$[doi:10.1145/1542362.1542407](https://doi.org/10.1145/1542362.1542407)$]$

category: people


David Copeland Johnson

* [Mathematics Genealogy page](https://www.mathgenealogy.org/id.php?id=16286)

## Selected writings

Introducing the [[Johnson-Wilson spectrum]] ([[Morava K-theory]])

* [[David Copeland Johnson]], [[W. Stephen Wilson]], _BP operations and Morava's extraordinary K-theories_, Math. Z. 144 (1): 55−75 (1975) ([pdf](https://people.math.rochester.edu/faculty/doug/otherpapers/jw-morava.pdf))

On unstable [[cohomology operations]] (hence: in [[non-abelian cohomology]]):

* [[John Michael Boardman]], [[David Copeland Johnson]], [[W. Stephen Wilson]], _Unstable Operations in Generalized Cohomology_ ([pdf](https://hopf.math.purdue.edu/Boardman-Johnson-Wilson/bjw.pdf)), in: [[Ioan Mackenzie James]] (ed.) _[[Handbook of Algebraic Topology]]_ Oxford 1995 ([doi:10.1016/B978-0-444-81779-2.X5000-7](https://doi.org/10.1016/B978-0-444-81779-2.X5000-7))

category: people


David Corfield

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I'm a [senior lecturer](http://www.kent.ac.uk/secl/philosophy/staff/corfield.html) in [[philosophy|philosophy]] in the School of European Culture of Languages at the University of Kent.

I have published three books:

1. [Towards a Philosophy of Real Mathematics](http://www.amazon.com/Towards-Philosophy-Mathematics-David-Corfield/dp/0521817226) Chapter 10 treats some aspects of higher-dimensional category theory.

1. [Why Do People Get Ill?](https://www.amazon.com/Why-Do-People-Get-Ill/dp/0241143160)

1. [Modal Homotopy Type Theory](https://www.amazon.com/Modal-Homotopy-Type-Theory-Philosophy/dp/0198853408)

On my old blog I began a discussion on [[Klein 2-geometry]], which I continued at the $n$-Category Café.

My [personal area](http://ncatlab.org/davidcorfield/show/HomePage) on nLab.

category: people


David D. Awschalom

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

* [Awschalom group](https://pme.uchicago.edu/group/awschalom-group)

## Selected writings

On [[quantum sensing]] and [[quantum information theory|quantum information processing]] via [[spin resonance qbits]] realized on a [[nitrogen-vacancy center in diamond]]:

* {#AHWZ18} [[David D. Awschalom]], Ronald Hanson, Jörg Wrachtrup & Brian B. Zhou, *Quantum technologies with optically interfaced solid-state spins*, Nature Photonics **12** (2018) 516–527 [[doi:10.1038/s41566-018-0232-2](https://doi.org/10.1038/s41566-018-0232-2)]

* [Awschalom group](https://pme.uchicago.edu/group/awschalom-group), *The Nitrogen-Vacancy Center in Diamond* [[web](https://pme.uchicago.edu/awschalom-group/nitrogen-vacancy-center-diamond)]

category: people

[[!redirects David Awschalom]]


David Deutsch

* [personal page](http://www.daviddeutsch.org.uk/)

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

## Selected writings

Introducing the model of [[quantum computation]] based on [[quantum Turing machines]]:

* [[David Deutsch]], *Quantum theory, the Church–Turing principle and the universal quantum computer*, Proceedings of the Royal Society of London A **400** 1818 (1985) 97-117 [[doi:10.1098/rspa.1985.0070](https://doi.org/10.1098/rspa.1985.0070), [pdf](https://www.daviddeutsch.org.uk/wp-content/deutsch85.pdf)]

and based on [[quantum circuits]] of [[quantum gates]]:

* [[David E. Deutsch]], *Quantum computational networks*, Proceedings of the Royal Society A, **425** 1868 (1989) 73-90 [[doi:10.1098/rspa.1989.0099](https://doi.org/10.1098/rspa.1989.0099), [jstor:2398494](https://www.jstor.org/stable/2398494)]

On [[algorithms]] for which [[quantum computation]] is expected to exhibit [[quantum supremacy]] (specifically what is now called the *[[Deutsch-Jozsa algorithm]]*):

* [[David Deutsch]], [[Richard Jozsa]], *Rapid solution of problems by quantum computation*. Proc. R. Soc. Lond. A **439** 1907 (1992) 553-558 [[pdf](https://www.isical.ac.in/~rcbose/internship/lectures2016/rt08deutschjozsa.pdf), [doi:10.1098/rspa.1992.0167](https://doi.org/10.1098/rspa.1992.0167)]

[[!redirects David E. Deutsch]]

category: people


David E. Evans

* [personal page](https://davidemrysevans.wordpress.com/)

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

## Selected writings

On [[completely positive maps]] ([[quantum channels]]):

* [[David E. Evans]], [[John T. Lewis]],  *Dilations of irreversible evolutions in algebraic quantum theory*, Communications of the Dublin Institute for Advanced Studies, Series A: Theoretical Physics **24** (1977) [[eprint:34031](https://orca.cardiff.ac.uk/id/eprint/34031), [pdf](https://orca.cardiff.ac.uk/id/eprint/34031/1/Evans_Lewis_DIAS.pdf)]

On [[higher twisted K-theory]] via [[C-star algebras|$C^\ast$-algebras]]:

* [[David E. Evans]], [[Ulrich Pennig]], *Spectral Sequence Computation of Higher Twisted K-Groups of $SU(n)$* [[arXiv:2307.00423](https://arxiv.org/abs/2307.00423)]

[[!redirects David Evans]]


David Edwards

David Edwards is an American mathematician working at the University of Georgia, who has made significant contributions to [[strong shape]] theory and [[proper homotopy theory]]. He has also written on philosophy of science.

* [webpage](http://www.math.uga.edu/~davide)

[[!redirects D.A. Edwards]]
[[!redirects D. A. Edwards]]


David Eisenbud

* [homepage](https://www.msri.org/~de)
* [wikipedia](https://en.wikipedia.org/wiki/David_Eisenbud)

A comprehensive monograph on commutative algebra

* David Eisenbud, _Commutative algebra with a view toward algebraic geometry_, Graduate Texts in Mathematics __150__
[MR1322960](https://mathscinet.ams.org/mathscinet-getitem?mr=1322960)

Introducing [[matrix factorization]]s:

* [[David Eisenbud]], _Homological algebra on a complete intersection, with an application to group representations_, Trans. Amer. Math. Soc. __260__:35-64 (1980) [doi](https://doi.org/10.1090/S0002-9947-1980-0570778-7)

[[!redirects D.Eisenbud]]

[[!redirects D. Eisenbud]]

category:people


David Elkouss

* [personal page](https://qutech.nl/person/david-elkouss/)

## Selected writings

On [[quantum networks]]:

* [[Koji Azuma]], Stefan Bäuml, Tim Coopmans, [[David Elkouss]], Boxi Li, *Tools for quantum network design* [[arXiv:2012.06764](https://arxiv.org/abs/2012.06764)]

On [[quantum repeaters]] for [[quantum networks]]:

* [[Koji Azuma]], [[Sophia E. Economou]], [[David Elkouss]], Paul Hilaire, Liang Jiang, Hoi-Kwong Lo, Ilan Tzitrin, *Quantum repeaters: From quantum networks to the quantum internet* [[arXiv:2212.10820](https://arxiv.org/abs/2212.10820)]

category: people


David Ellerman

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

## Selected writings

On [[heteromorphisms]]:

* {#Ellerman06} [[David Ellerman]], _A Theory of Adjoint Functors --- with Some Thoughts on Their Philosophical Significance_, in: G. Sica (e.) _What Is Category Theory?_, 12783. Milan: Polimetrica. (2006)

* {#Ellerman07} [[David Ellerman]], _Adjoint Functors and Heteromorphisms_ [[arXiv:0704.2207](http://arxiv.org/abs/0704.2207)]

* [[David Ellerman]], *Mac Lane, Bourbaki, and Adjoints: A Heteromorphic Retrospective* (2015) [[pdf](http://www.ellerman.org/wp-content/uploads/2015/06/Maclane-Bourbaki-Redux.pdf), [doi:10.2139/ssrn.2620333](https://dx.doi.org/10.2139/ssrn.2620333)]

## Related entries

* [[heteromorphism]]

* [[partition logic]]

category: people


David Epstein

* [Wikipedia entry](http://en.wikipedia.org/wiki/David_B._A._Epstein)

## related $n$Lab entries

* [[Steenrod operations]]

category: people


David Fernández

__David Fernández__ is a mathematician whose research interests are quantum groups, infinite dimensional Lie algebras, cluster algebras, representation theory and its interactions with algebraic geometry and mathematical physics.

* [webpage](https://webusers.imj-prg.fr/~david.hernandez/index2.html)
* Maxime Fairon, David Fernández, _On the noncommutative Poisson geometry of certain wild character varieties_, [arXiv:2103.10117](https://arxiv.org/abs/2103.10117); _Euler continuants in noncommutative quasi-Poisson geometry_, [arXiv:2105.04858](https://arxiv.org/abs/2105.04858)
* Luis Álvarez-Cónsul, David Fernández, Reimundo Heluani, _Noncommutative Poisson vertex algebras and Courant-Dorfman algebras_, [arXiv:2106.00270](https://arxiv.org/abs/2106.00270)
* David Fernández, Estanislao Herscovich, _Cyclic $A_\infty$-algebras and double Poisson algebras_, [arXiv:1902.00787](https://arxiv.org/abs/1902.00787); _Double quasi-Poisson algebras are pre-Calabi-Yau_, [arXiv:2002.10495](https://arxiv.org/abs/2002.10495)

category: people


David Fried

* [webpage](http://www.bu.edu/math/people/faculty/dynamical-systems/fried/)

## related $n$Lab entries

* [[Selberg zeta function]]

* [[Ruelle zeta function]]

category: people


David Gale

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

* [MacTutor biography](https://mathshistory.st-andrews.ac.uk/Biographies/Gale/)

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=10282)

## Selected writings

On the [[compact-open topology]] and introducing the notion of [[compactly generated topological spaces]] ([following](compactly+generated+topological+space#fn:2) unpublished lectures by [[Witold Hurewicz]]):

* {#Gale50} [[David Gale]], _Compact Sets of Functions and Function Rings_, Proc. AMS **1** (1950) pp.303-308. ([pdf](http://www.ams.org/journals/proc/1950-001-03/S0002-9939-1950-0036503-X/S0002-9939-1950-0036503-X.pdf), [doi:10.2307/2032373](https://doi.org/10.2307/2032373), [jstor:2032373](https://www.jstor.org/stable/2032373))

category: people


David Gepner

* [website](https://www.math.purdue.edu/~dgepner/),
[new website](http://math.soimeme.org/~davidgepner/)

## Selected writings

On [[equivariant elliptic cohomology]] in [[(infinity,1)-topos]] theory.

*  [[David Gepner]], _[[Homotopy topoi and equivariant elliptic cohomology]]_
PhD thesis, University of Illinois at Urbana-Champaign, 2005. ([[GepnerElliptic05.pdf:file]])

* [[David Gepner]], [[Lennart Meier]], _On equivariant topological modular forms_, ([arXiv:2004.10254](https://arxiv.org/abs/2004.10254))

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

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

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

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

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

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

On [[Becker-Gottlieb transfer]] and [[differential algebraic K-theory]]:

* [[Ulrich Bunke]], [[David Gepner]], _Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory_, Memoirs of the American Mathematical Society 2021 ([arXiv:1306.0247](http://arxiv.org/abs/1306.0247), [ISBN:978-1-4704-4685-7](https://bookstore.ams.org/cdn-1608276327798/memo-269-1316/))

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

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

## Related entries

* [[noncommutative motive]], [[algebraic K-theory]]

* [[(infinity,1)-module bundle]], [[twisted Umkehr map]]

category: people


David Goss

* [webpage](https://people.math.osu.edu/goss.3/)

## Selected writings

On [[shtukas]]:

* [[David Goss]], *What is ... a Shtuka?*, Notices of the AMS **50** 1 (2003) 36-37 [[pdf](http://www.ams.org/notices/200301/what-is.pdf), full issue:[pdf](http://www.ams.org/notices/200301/200301FullIssue.pdf)]

## Related entries

* [[arithmetic geometry]]

* [[Mellin transform]]

category: people


David Gross

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

## Selected writings

Introducing [[Kaluza-Klein monopoles]]:

* {#GrossPerry83} [[David Gross]], [[Malcolm Perry]], _Magnetic Monopoles in Kaluza-Klein Theories_  Nucl. Phys. B226 (1983) 29 (doi:10.1016/0550-3213(83)90462-5)

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 [[2d QCD]]:

* [[David Gross]], [[Washington Taylor]], _Two Dimensional QCD is a String Theory_, Nucl.Phys.B400:181-210, 1993

## Related $n$Lab entries

* [[instanton in QCD]]

* [[higher spin gauge theory]]

* [[causal locality]]

* [[heterotic string theory]]

* [[S-matrix]]

* [[Kaluza-Klein monopole]]

* [[current algebra]]

* [[Chan-Paton bundle]]

* [[string scattering amplitude]]

category: people


David H. Delphenich

* [personal page](http://www.neo-classical-physics.info/index.html)

* [InSpire page](https://inspirehep.net/authors/1012091)

## Selected writings

On [[pre-metric electromagnetism]]:

* {#Delphenich05a} [[David H. Delphenich]], *On the Axioms of Topological Electromagnetism*, Annalen Phys. **14** (2005) 347-377 [[arXiv:hep-th/0311256](https://arxiv.org/abs/hep-th/0311256), [doi:10.1002/andp.20055170601](https://doi.org/10.1002/andp.20055170601)]

* {#Delphenich05b} [[David H. Delphenich]], *Symmetries and pre-metric electromagnetism*, Ann. Phys. **14** (2005) 663-704 [[arXiv:gr-qc/0508035](https://arxiv.org/abs/gr-qc/0508035), [doi:10.1002/andp.200510159](https://doi.org/10.1002/andp.200510159)]

* {#Delphenich07} [[David H. Delphenich]], *On linear electromagnetic constitutive laws that define almost-complex structures*, Annalen Phys. **16** (2007) 207-217 [[doi:gr-qc/0610031](https://arxiv.org/abs/gr-qc/0610031), [doi:10.1002/andp.200610227](https://doi.org/10.1002/andp.200610227)]

* {#Delphenich08} [[David H. Delphenich]], *Spinors and Pre-Metric Electromagnetism*, Advances in Applied Clifford Algebras **18** (2008) 567–578 [[doi:10.1007/s00006-008-0115-6](https://doi.org/10.1007/s00006-008-0115-6)]

* {#Delphenich15} [[David H. Delphenich]], *Pre-metric electromagnetism as a path to unification*, in: *Unified Field Mechanics*, World Scientific (2015) 215-220 [[arXiv:1512.05183](https://arxiv.org/abs/1512.05183), [doi:10.1142/9789814719063_0023](https://doi.org/10.1142/9789814719063_0023)]

* {#DelphenichBook} [[David H. Delphenich]], *Pre-Metric Electromagnetism* [part I:[pdf](http://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/intro-chap_vi.pdf), part II:[pdf](http://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/chapter_vii-xii.pdf), full:[[Delphenich-PreMetricElectromagnetism.pdf:file]]]

English translation of original articles:

* {#Kottler22a} [[Friedrich Kottler]], *Newtonsches Gesetz und Metrik*, Sitzungsber. Akad. Wiss. Wien, Math.-Naturw. Klasse, Abt. IIa, **131** (1922) 1-14 [Engl. transl. by [[David H. Delphenich|Delphenich]]: [pdf](http://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/kottler_-_newtons_law_and_metrics.pdf), [[Kottler-NewtonsLawAndMetric.pdf:file]]]

* {#Kottler22b} [[Friedrich Kottler]], *Maxwell'sche Gleichungen und Metrik*, Sitz. Akad. Wien IIa **131** (1922) 119-146 [Engl. transl. by [[David H. Delphenich|Delphenich]]: [pdf](http://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/kottler_-_maxwells_equation.pdf), [[Kottler-MaxwellEquationsAndMetric.pdf:file]]]

category: people

[[!redirects David Delphenich]]


David H. Fremlin

David H. Fremlin is Professor Emeritus at the University of Essex.

[Website](https://www1.essex.ac.uk/maths/people/fremlin/index.htm).

## Selected works

* [Measure Theory](https://www1.essex.ac.uk/maths/people/fremlin/mt.htm),
a comprehensive treatment of [[measure theory]] in 6 volumes.

On [[singular homology]] and [[Čech homology]]:

* [[David H. Fremlin]], *Singular homology for amateurs* (2016) $[$[pdf](https://www1.essex.ac.uk/maths/people/fremlin/n16703.pdf), [[FremlinSIngularHomology.pdf:file]]$]$

category: people

[[!redirects David Fremlin]]


David Hernandez

* [webpage](https://webusers.imj-prg.fr/~david.hernandez)
* fr.wikipedia: David Hernandez (mathématicien)

## Selected writing

* David Hernandez, [[Bernard Leclerc]], _Quantum Grothendieck rings and derived Hall algebras_, J. Reine Angew. Math. 701 (2015) 77--126 [doi](https://doi.org/10.1515/crelle-2013-0020) [arXiv/1109.0862](https://arxiv.org/abs/1109.0862)
* David Hernandez, _An introduction to affine Kac-Moody algebras_, 2006 [pdf](http://www.ctqm.au.dk/events/2006/October/Week42/Masterclassnotes.pdf)

category: people


David Hestenes

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

## related $n$Lab entries

* [[geometric algebra]]

category: people


David Hilbert

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

## Selected writings

On the mathematical foundations of [[quantum mechanics]]:

* {#HilbertvonNeumannNordheim} [[David Hilbert]], [[John von Neumann]], [[Lothar W. Nordheim]], *Über die Grundlagen der Quantenmechanik*,  Math. Ann. **98** (1928) 1–30 [[doi:10.1007/BF01451579](https://doi.org/10.1007/BF01451579)]

## Further resources

* the (English translation) of the lecture of David Hilbert at the International Congress of Mathematicians at Paris in 1900 (with the list of  "Hilbert's problems") is [here](http://aleph0.clarku.edu/~djoyce/hilbert/problems.html)

* Felix E. Browder. Mathematical Developments Arising from Hilbert Problems. Proceedings of Symposia in Pure Mathematics. XXVIII.2. American Mathematical Society.

Lectures by Hilbert on [[physics]] and especially on [[general relativity]] are collected here:

* {#SauerMajer} [[Tilman Sauer]], [[Ulrich Majer]] with  Arne Schirrmacher, Heinz-Jürgen Schmidt (eds.): *David Hilbert's Lectures on the foundations of physics 1915-1927 --- Relativity, Quantum Theory and Epistemology*, Springer (2009) [[doi:10.1007/b12915](https://doi.org/10.1007/b12915)]

  > Around pages 417, 423 there is discussion of "Weltgesetze", roughly what today in  fundamental physical might be called [[theories of everything]], with some remarks comparing to the perspective of [[Hegel]] in the _[[Science of Logic]]_.

* _[[Naturerkennen und Logik]]_, Lecture at the _Kongress der Gesellschaft Deutscher Naturforscher und Ärtze_, 1930  ([pdf](http://math.sfsu.edu/smith/Documents/HilbertRadio/HilbertRadio.pdf), [audio](http://math.sfsu.edu/smith/Documents/HilbertRadio/HilbertRadio.mp3)),

  see also [[Eugene Wigner]], _[[The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]_

## Stories
 {#Stories}

> Cassirer liked to tell the following story: once he met the great mathematician Hilbert, the "Euclid of our time," and asked him about one of the latter's disciples. Hilbert answered: "He is all right. You know, for a mathematician he did not have enough imagination. But he has become a poet and now he is doing fine.

(from [archive.org/details/philosophyoferns033109mbp](https://archive.org/details/philosophyoferns033109mbp))

## Related pages

* [[Hilbert's problems]]

* [[Hilbert's program]]

* [[Einstein-Hilbert action]]

* [[Hilbert's theorem 90]]

* [[Hilbert space]]

* [[Naturerkennen und Logik]]

category: people

[[!redirects Hilbert]]


David J. Pym

* [personal page](http://www0.cs.ucl.ac.uk/staff/D.Pym/)

## Selected writings

On [[bunched logic]]:

* [[Peter O'Hearn]], [[David J. Pym]], *The Logic of Bunched Implications*, The Bulletin of Symbolic Logic **5** 2 (1999) 215-244  [[pdf](http://www.lsv.ens-cachan.fr/~demri/OHearnPym99.pdf), [doi:10.2307/421090](https://doi.org/10.2307/421090)]

* {#Pym2002} [[David Pym]], *The Semantics and Proof Theory of the Logic of Bunched Implications*, Applied Logic Series **26**, Springer (2002) [[doi:10.1007/978-94-017-0091-7](https://doi.org/10.1007/978-94-017-0091-7), [GoogleBooks](https://books.google.com/books/about/The_Semantics_and_Proof_Theory_of_the_Lo.html?id=0bAfqhzDuOcC&redir_esc=y)]

category: people

[[!redirects David Pym]]


David Jackson

* [webpage](http://www.math.uwaterloo.ca/~dmjackso/)

## Selected writings

On [[Vassiliev invariants|Vassiliev]] [[knot invariants]]:

* [[David Jackson]], [[Iain Moffat]], _An Introduction to Quantum and Vassiliev Knot Invariants_, Springer 2019 ([doi:10.1007/978-3-030-05213-3](https://link.springer.com/book/10.1007/978-3-030-05213-3))

category: people


David Jaz Myers

[[!redirects David Myers]]

David Jaz Myers is postdoctoral researcher at [[CQTS]] @ NYU Abu Dhabi.

* [personal webpage](http://davidjaz.com/)

* [institute page](https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts/david-myers.html) at NYU Abu Dhabi

* [old institute page](https://mathematics.jhu.edu/directory/david-myers/) at Johns Hopkins

## Selected writings

On a [[string diagram]]-calculus for ([[virtual double category|virtual]]) [[double categories]] with ([[virtual equipment|virtual]]) [[2-category equipped with proarrows|pro-arrow equipments]]:

* {#Myers16} [[David Jaz Myers]], _String Diagrams For Double Categories and (Virtual) Equipments_ [[arXiv:1612.02762](https://arxiv.org/abs/1612.02762)]

* [[David Jaz Myers]], *String Diagrams for (Virtual) Proarrow Equipments* (2017) [slides: [pdf](http://www.mat.uc.pt/~ct2017/slides/myers_d.pdf), [[Myers-StringDiagrams2017.pdf:file]]]

On [[dynamical systems]] and their [[categorical systems theory]]:

* [[David Jaz Myers]], *Double Categories of Open Dynamical Systems*, EPTCS **333** (2021) 154-167 [[arXiv:2005.05956](https://arxiv.org/abs/2005.05956), [doi:10.4204/EPTCS.333.11](https://doi.org/10.4204/EPTCS.333.11)]

* {#Myers} [[David Jaz Myers]], *Categorical systems theory*, book project [[github](https://github.com/DavidJaz/DynamicalSystemsBook/tree/master/book), [pdf](http://davidjaz.com/Papers/DynamicalBook.pdf)]

* [[David Jaz Myers]], *[Categorical systems theory](https://topos.site/blog/2021/11/categorical-systems-theory/)*, [Topos Institute Blog](https://topos.site/blog/) (Nov 2021)

* [[David Jaz Myers]], *Double Categories of Dynamical Systems* (2020) [[pdf](http://davidjaz.com/Talks/DJM_Dyn2020.pdf)]

* [[David Jaz Myers]], *A general definition of open dynamical systems*, talk at *MIT Category Theory Seminar* (2020) [video:[YT](https://youtu.be/8T-Km3taNko)]

On [[logical topology]] in the context of [[cohesive toposes]], [[modal type theory]] and [[cohesive homotopy type theory]]:

* [[David Jaz Myers]], _Logical Topology and Axiomatic Cohesion_, talk at _[Geometry in Modal Homotopy Type Theory](http://felix-cherubini.de/modal-workshop.html)_ 2019 ([pdf slides](http://felix-cherubini.de/myers-slides.pdf))

On [[modal type theory]] and [[cohesive homotopy type theory]]

* [[David Jaz Myers]], _Good Fibrations through the Modal Prism_ ([arXiv:1908.08034v2](https://arxiv.org/abs/1908.08034v2))

Formalization of the [[shape modality|shape]]/[[flat modality|flat]]-[[fracture square]] ([[differential cohomology hexagon]]) in [[cohesive homotopy type theory|cohesive]] [[modal homotopy type theory|modal homotopy type theory]] [[homotopy type theory]]:

* [[David Jaz Myers]], _Modal Fracture of Higher Groups_ ([arXiv:2106.15390](https://arxiv.org/abs/2106.15390)), related talk at *[CMU-HoTT Seminar](https://www.cmu.edu/dietrich/philosophy/hott/seminars/index.html)*, 2021 ([pdf](http://davidjaz.com/Talks/CMU_March_2021.pdf), [[MyersModalFracture2021.pdf:file]])

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On [[twisted cohomology]] towards [hypergeometric integral KZ-solutions](Knizhnik-Zamolodchikov+equation#BraidRepresentationsViaTwisteddRCohomologyOfConfigurationSpaces) in [[homotopy type theory]]:

* [[David Jaz Myers]], *Objective Cohomology -- Towards topological quantum computation*, talk at *Geometry, Topology and Physics*-Seminar at [[CQTS]] ([Sep 2022](Center+for+Quantum+and+Topological+Systems#DavidJMyers22)) [[[DavidJazMyers-ObjectiveCohomology-220928.pdf:file]]]

On [[orbifolds]] in [[differential cohesive (infinity,1)-topos|differential]] [[cohesive homotopy type theory]]:

* [[David Jaz Myers]], *Orbifolds as microlinear types in synthetic differential cohesive homotopy type theory* [[arXiv:2205.15887](https://arxiv.org/abs/2205.15887)]

On [[cohesive homotopy type theory]] with a pair of commuting cohesive structures (such as for [[differential cohomology|differential]] [[orbifold cohomology]]):

* [[David Jaz Myers]], [[Mitchell Riley]], *Commuting Cohesions* [[arXiv:2301.13780](https://arxiv.org/abs/2301.13780)]

with exposition in:

* [[David Jaz Myers]], *Simplicial, Differential, and Equivariant Homotopy Type Theory*, talk at [[CQTS]] (Jan 2023) [video: [rec](https://nyu.zoom.us/rec/play/uk0LXy5ub2YUpJPhYq5p7GvpZ2I8_CZaWHSpWvZgwuUyHeWjXgUj2AQd21K1WSJo90V5DrE0BVhl7NuB.QbyHhtPHaJVQUj2A?continueMode=true&_x_zm_rtaid=Xyx9WZFLQzyRzu0Oh-2mNQ.1675318497581.13147cc7929a947e978b29124a207f98&_x_zm_rhtaid=938)]

Exposition of [[homotopy type theory]]:

* [[David Jaz Myers]], *How do you identify one thing with another? -- an intro to Homotopy Type Theory*, talk in Prof. [[Sadok Kallel]]'s seminar at American University of Sharjah (10 Apr 2023) [slides: [[Myers-IntroHoTT-Apr2023.pdf:file]]]

## Related $n$Lab entries

* [[logical topology]]

* [[synthetic differential topology]]

* [[modal type theory]]

category: people

[[!redirects David J. Myers]]


David John Simms

David Simms was an Irish Mathematician based at Trinity College Dublin.

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

* [Mathematics Genealogy page](https://www.mathgenealogy.org/id.php?id=85350)

## Selected writings

On the [[topological space|topoloy]] of [[PU(ℋ)]] (the [[projective unitary group]] on a [[separable Hilbert space]]):

* [[David John Simms]], *Topological aspects of the projective unitary group*, Math. Proc. Camb. Phil. Soc. **68** 1 (1970) 57-60  ([doi:10.1017/S0305004100001043](https://doi.org/10.1017/S0305004100001043))

category: people

[[!redirects David J. Simms]]
[[!redirects D. J. Simms]]


David Jordan

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

## Selected writings

On [[4d TQFTs]] from [[fully dualizable object|fully dualizable]] [[braided monoidal category|braided]] [[tensor categories]], via the [[cobordism hypothesis]]:

* [[Adrien Brochier]], [[David Jordan]], [[Pavel Safronov]], [[Noah Snyder]], _Invertible braided tensor categories_ ([arXiv:2003.13812](https://arxiv.org/abs/2003.13812))

## Related $n$Lab entries

* [[double affine Hecke algebra]]

* [[factorization homology]]

* [[4d TQFT]]

category: people


David Joyce

* [personal page](https://mathcs.clarku.edu/~djoyce/)

## Selected writings

On the [[Dedekind-Peano axioms]] for the [[natural numbers]]:

* [[David E. Joyce]], *The Dedekind/Peano Axioms* (2005) [[pdf](http://aleph0.clarku.edu/~djoyce/numbers/peano.pdf)]

On [[hyperbolic tesselations]]:

* [[David Joyce]], *[Hyperbolic Tesselations](https://mathcs.clarku.edu/~djoyce/poincare/index.html)*

category: people

[[!redirects David E. Joyce]]


David K. Harrison

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

## Selected writings

On [[categorical algebra]]:

* [[Samuel Eilenberg|S. Eilenberg]], [[D. K. Harrison]], [[S. MacLane]], [[H. Röhrl]] (eds.): *[[Proceedings of the Conference on Categorical Algebra - La Jolla 1965]]*, Springer (1966) [[doi:10.1007/978-3-642-99902-4](https://doi.org/10.1007/978-3-642-99902-4)]

category: people

[[!redirects D. K. Harrison]]
[[!redirects David Kent Harrison]]


David Kastor

* [personal webpage](https://blogs.umass.edu/kastor/)

* [institute page](https://www.physics.umass.edu/people/david-kastor)

## Selected writings

On [[black strings]] in [[D=5 gravity]]/[[D=5 supergravity]] from [[M5-branes]] [[wrapped brane|wrapped]] on [[4-manifolds]]:

* [[David Kastor]], Section 3 of: _From wrapped M-branes to Calabi-Yau black holes and strings_, JHEP 0307 (2003) 040 ([arXiv:hep-th/0305261](https://arxiv.org/abs/hep-th/0305261))

category: people


David Kazhdan

__David Kazhdan__ (or Každan) is an Israeli mathematician educated in Moscow, professor at Hebrew University (homepage [kazhdan](http://www.ma.huji.ac.il/~kazhdan/)) emeritus of Harvard University ([homepage](http://www.math.harvard.edu/people/KazhdanDavid.html)); while he is a rennesaince mathematician with wide knowledge from model theory to mathematical physics, he has made especially deep contributions to representation theory. Kazhdan, Lusztig and Deodhar discovered the famous [[Kazhdan-Lusztig theory]].

* [wikipedia](http://en.wikipedia.org/wiki/David_Kazhdan)

## Selected writings

Introducing [[Kazhdan's property (T)]]:

* [[David Kazhdan]], _Connection of the dual space of a group with the structure of its close subgroups_, Funct Anal Its Appl (1967) 1: 63 ([doi:10.1007/BF01075866](https://doi.org/10.1007/BF01075866))

## Quotes
 {#Quotes}

> Physics is very interesting: There are many, many interesting theorems. Unfortunately,there are no definitions.

Quoted this way in:

* [[James Milne]]'s "[Mathematics Site](https://www.jmilne.org/math/)"

* [[Greg Moore]], p. 27 of: _[[Physical Mathematics and the Future]]_, 2014 ([pdf](http://www.physics.rutgers.edu/~gmoore/PhysicalMathematicsAndFuture.pdf), [[MooreVisionTalk2014.pdf:file]])

category: people

[[!redirects David Každan]]
[[!redirects D. Kazhdan]]


David Kosower

* [preprints](http://arxiv.org/find/hep-ph/1/au:+Kosower_D/0/1/0/all/0/1)

## related $n$Lab entries

* [[worldline formalism]]

category: people


David Kraines

* [webpage](https://math.duke.edu/people/david-p-kraines)

## related $n$Lab entries

* [[Massey product]]

category: people


David Kutasov

* [webpage](https://physics.uchicago.edu/page/david-kutasov)

## Selected writings

On [[geometric engineering of QFT]] in [[intersecting D-brane models]] subject to the [[s-rule]]:

* [[Amit Giveon]], [[David Kutasov]], _Brane Dynamics and Gauge Theory_, Rev. Mod. Phys. 71:983-1084, 1999 ([arXiv:hep-th/9802067](https://arxiv.org/abs/hep-th/9802067))

On [[NS5-brane]]-[[brane intersections|intersections]] with [[D-branes]]:

* {#EGKRS00} [[Shmuel Elitzur]], [[Amit Giveon]], [[David Kutasov]], [[Eliezer Rabinovici]], [[Gor Sarkissian]], *D-Branes in the Background of NS Fivebranes*, JHEP 0008 (2000) 046 [[arXiv:hep-th/0005052](https://arxiv.org/abs/hep-th/0005052), [doi:10.1088/1126-6708/2000/08/046](https://doi.org/10.1088/1126-6708/2000/08/046)]

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))

## Related $n$Lab entries

* [[little string theory]]

category: people


David L. Rector

David Lee Rector is a mathematician at UC Irvine.

* [Institute page](https://www.math.uci.edu/people/david-rector)

* [MathematicsGenealogy page](https://www.mathgenealogy.org/id.php?id=51114)

He got his PhD degree in 1966 from MIT, advised by [[Daniel M. Kan]].

## Selected writings

On the [[Rector completion theorem]]:

* {#Rector74} [[David L. Rector]], _Modular characters and K-theory with coefficients in a finite field_, Journal of Pure and Applied Algebra **4** 2 (1974) 137-158 $[$doi:10.1016/0022-4049(74)90019-X$]$

## Related entries

* [[Rector completion theorem]]

category: people


David Lawrence Johnson

* [MathematicsGenealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=85600)

## Selected writings

On [[group presentations]] ([[combinatorial group theory]]):

* [[David Lawrence Johnson]], *Topics in Theory of Group Presentations*, London Mathematical Society Lecture notes series **42**, Cambridge Univ. Press (1980) [[doi:10.1017/CBO9780511629303](https://doi.org/10.1017/CBO9780511629303)]

* [[David Lawrence Johnson]], *Presentations of Groups*, London Mathematical Society Student Texts **15**, Cambridge Univ. Press (1990) [[doi:10.1017/CBO9781139168410](https://doi.org/10.1017/CBO9781139168410)]

category: people

[[!redirects D. L. Johnson]]


David Li-Bland

* [webpage](https://math.berkeley.edu/~libland/)

category: people


David Lubicz

* [webpage](http://perso.univ-rennes1.fr/david.lubicz/)

category: people


David Marzocca

* [personal page](https://people.sissa.it/~dmarzocc/)

## Selected writings

On the [[flavour anomalies]]:

In relation to a [[composite Higgs boson]]:

* {#Marzocca18} [[David Marzocca]], _Addressing the B-physics anomalies in a fundamental Composite Higgs Model_, JHEP07(2018)121 ([arXiv:1803.10972](https://arxiv.org/abs/1803.10972))

In relation to [[leptoquarks]]:

* {#GMV20} Valerio Gherardi, [[David Marzocca]], Elena Venturini, _Low-energy phenomenology of scalar leptoquarks at one-loop accuracy_ ([arXiv:2008.09548](https://arxiv.org/abs/2008.09548))

On a joint explanation of the [[flavour anomalies]], the [[Cabibbo anomaly]] and the [[(g-2)-anomaly]] via [[leptoquarks]]:

* {#MarzoccaTrifinopoulos21} [[David Marzocca]], Sokratis Trifinopoulos, *A Minimal Explanation of Flavour Anomalies: B-Meson Decays, Muon Magnetic Moment, and the Cabbibo Angle* ([arXiv:2104.05730](https://arxiv.org/abs/2104.05730))

category: people


David Mateos

* [webpage](https://www.icrea.cat/Web/ScientificStaff/David-Mateos-465)

## Selected writings

On the [[3-brane in 6d]]:

* [[Joaquim Gomis]], [[David Mateos]], [[Joan Simón]], [[Paul Townsend]], _Brane-Intersection Dynamics from Branes in Brane Backgrounds_, Phys. Lett. B430 (1998) 231-236 ([arXiv:hep-th/9803040](http://arxiv.org/abs/hep-th/9803040))

On [[D-brane polarization]] into [[supertubes]]:

* [[David Mateos]], [[Paul Townsend]], _Supertubes_, Phys. Rev. Lett. 87 (2001) 011602 ([arXiv:hep-th/0103030](https://arxiv.org/abs/hep-th/0103030))

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

* [[Henriette Elvang]], [[Roberto Emparan]], [[David Mateos]], [[Harvey Reall]], _Supersymmetric 4D Rotating Black Holes from 5D Black Rings_, JHEP0508:042,2005 ([arXiv:hep-th/0504125](http://arxiv.org/abs/hep-th/0504125))

On reducing these to [[black holes]]:

* {#ElvangEmparanMateosReall05} [[Henriette Elvang]], [[Roberto Emparan]], [[David Mateos]], [[Harvey Reall]], _Supersymmetric 4D Rotating Black Holes from 5D Black Rings_, JHEP0508:042,2005 ([arXiv:hep-th/0504125](http://arxiv.org/abs/hep-th/0504125))

On the [[quark-gluon plasma]] via [[holographic QCD]]:

* Jorge Casalderrey-Solana, Hong Liu, [[David Mateos]], Krishna Rajagopal, Urs Achim Wiedemann, _Gauge/string duality, hot QCD and heavy ion collisions_, Cambridge University Press, 2014 ([arXiv:1101.0618](https://arxiv.org/abs/1101.0618))

category: people


David McAllester

* [personal page](https://home.ttic.edu/~dmcallester/)

## Selected writings

On [[mathematical structures]] and their [[isomorphism]] via [[dependent type theory]]:

* [[David McAllester]], *Dependent Type Theory as Related to the Bourbaki Notions of Structure and Isomorphism* [[arXiv:2104.08958](https://arxiv.org/abs/2104.08958)]

category: people


David Mehrle

* [personal page](http://pi.math.cornell.edu/~dmehrle/)

## Selected writings

On [[chromatic homotopy theory]]:

* {#Mehrle18} [[David Mehrle]], _Chromatic homotopy theory: Journey to the frontier_, Graduate workshop notes, Boulder 16-17 May 2018, ([pdf](http://pi.math.cornell.edu/~dmehrle/notes/conferences/cht/cht-notes.pdf), [[Mehrle_ChromaticHomotopyTheory.pdf:file]])

category: people


David Mermin

* [institute page](https://physics.cornell.edu/n-david-mermin)

* [Wikipedia entri](https://en.wikipedia.org/wiki/N._David_Mermin)

## Selected writings

On [[solid state physics]]:

* [[Neil Ashcroft]], [[N. David Mermin]], *Solid State Physics*, Saunders College Publishing (1973) [[archive](https://archive.org/details/AshcroftSolidState), [Wikipedia entry](https://en.wikipedia.org/wiki/Ashcroft_and_Mermin)]

On [[defect]]$\;$[[anyons]]:

* [[N. David Mermin]], *The topological theory of defects in ordered media*, Rev. Mod. Phys. **51** (1979) 591 $[$[doi:10.1103/RevModPhys.51.591](https://doi.org/10.1103/RevModPhys.51.591)$]$

  > (including a review of [basic homotopy theory](Introduction+to+Topology+--+2))

On [[interpretations of quantum mechanics]] and introducing the catch-phrase "shut up and calculate":

* [[N. David Mermin]], *What's Wrong with this Pillow?*, Physics Today **42** 4 (1989) 9–11 [[doi:10.1063/1.2810963](https://doi.org/10.1063/1.2810963)]

and its mis-attribution to [[Richard Feynman]]:

* [[N. David Mermin]], *Could Feynman Have Said This?*, Physics Today **57** 5 (2004) 10–11 [[doi:10.1063/1.1768652](https://doi.org/10.1063/1.1768652)]

On [[quantum Bayesianism]]/[[QBism]]:

* {#FMS2014} [[Christopher Fuchs]], [[David Mermin]], [[Ruediger Schack]], *An Introduction to QBism with an Application to the Locality of Quantum Mechanics*, American Journal of Physics **82**  8 (2014) 749--754 [[arXiv:1311.5253](https://arxiv.org/abs/1311.5253)]

## Related entries

* [[solid state physics]]

* [[Bayesian interpretation of quantum mechanics]]

* [[philosophy of physics]]

category: people

[[!redirects N. David Mermin]]


David Merritt

* Wikipedia, [David Merritt](https://en.wikipedia.org/wiki/David_Merritt)

## Selected publications

On [[galaxy|galactic]] nuclei:

* {#Merritt13} [[David Merritt]], *Dynamics and Evolution of Galactic Nuclei*. Princeton University Press, 2013. ISBN:978-0691158600

On [[MOND]]:

* {#Merritt20} [[David Merritt]], *A Philosophical Approach to MOND: Assessing the Milgromian Research Program in Cosmology*. Cambridge University Press, 2020. ISBN:978-1108492690

category: people


David Metzler

* [webpage](http://dspace.mit.edu/bitstream/handle/1721.1/43933/37923964.pdf?sequence=1)

category: people


David Michael Roberts

[[!redirects David Roberts]]

* table of contents
{:toc}

## About me

I work on [[bundle gerbes]], [[principal 2-bundles|2-bundles]], [[geometric stacks]] and [[internal category|internal groupoids and categories]], and [[category theory]] more generally with a side interest in [[foundations]]. I have a particular interest in constructing examples in (low-dimensional) [[higher geometry]].

From May 2022 I am a Visiting Associate Lecturer at the University of Adelaide, in the School of Computer and Mathematical Sciences, and I teach in the Maths Learning Centre (NB this is an independent part of the university, not attached to the School of Maths!).
For August–December 2022 I am also a casual lecturer for two pure mathematics subjects at Flinders University.

For March 2018–December 2021 I was a Research Associate (that is, a postdoc) at the [Institute for Geometry and its Applications](http://www.iga.adelaide.edu.au/) in the [School of Mathematical Sciences](http://maths.adelaide.edu.au/) at U Adelaide.

Previous to this, for July-2017 to February 2018 I was a 'Level B' Lecturer (=Assistant Professor in the US system) in the School of Mathematical Sciences.
I was also a Research Associate at U Adelaide from October 2012 to April 2015.

I have also worked as an applied statistician/survey analyst/data analyst/consultant in the public sector, with 3+ years experience of daily work in the software [SAS](https://en.wikipedia.org/wiki/SAS_%28software%29).

You may also find me on: [MathSciNet](https://www.ams.org/mathscinet/search/author.html?mrauthid=788905), [Google Scholar](https://scholar.google.com.au/citations?user=KGianq8AAAAJ&hl=en), [MathOverflow](https://mathoverflow.net/users/4177/david-roberts), [arXiv](https://arxiv.org/a/roberts_d_1.html), [ORCiD](http://orcid.org/0000-0002-3478-0522), [Publons](https://publons.com/a/430214/), or my blog, [theHigherGeometer](https://thehighergeometer.wordpress.com/).

If you need it, here is my email:  droberts.(fifth and largest-known [[Fermat prime]])@gmail.[etc] or [first].[last]@adelaide.edu.au

## Writing

### Preprints

* _Classifying bi-invariant 2-forms on infinite-dimensional Lie groups_ (2023) arXiv:[2311.03913](https://arxiv.org/abs/2311.03913). (submitted for publication)

* _Rigid models for 2-gerbes I: Chern-Simons geometry_ (2022) arXiv:[2209.05521](https://arxiv.org/abs/2209.05521). Joint with [[nLab:Raymond Vozzo|Raymond Vozzo]]. (submitted for publication)

* _Homotopy types of topological stacks of categories_ (2009/2022) arXiv:[2204.02778](https://arxiv.org/abs/2204.02778) (this paper was written when I was a PhD student, in 2008/09, but only polished and released on the arXiv in 2022). (submitted for publication)

### Papers

* _Substructural fixed-point theorems and the diagonal argument: theme and variations_, [Compositionality](https://compositionality-journal.org/) **5**, 8 (2023), doi:[10.32408/compositionality-5-8](https://doi.org/10.32408/compositionality-5-8), arXiv:[2110.00239](https://arxiv.org/abs/2110.00239).

* _Many finite-dimensional lifting bundle gerbes are torsion_, Bulletin of the Australian Mathematical Society **105** Issue 2 (2022) 323–338, doi:[10.1017/S000497272100071X](https://doi.org/10.1017/S000497272100071X), arXiv:[2104.07936](https://arxiv.org/abs/2104.07936).

* _Extending Whitney's extension theorem: nonlinear function spaces_, Annales de l’Institut Fourier **71** no. 3 (2021) 1241–1286, doi:[10.5802/aif.3424](https://doi.org/10.5802/aif.3424), [arXiv:1801.04126](https://arxiv.org/abs/1801.04126). Joint with [[Alexander Schmeding]].

* _The elementary construction of formal anafunctors_, Categories and General Algebraic Structures with Applications vol **15** issue 1 (2021) 183–229, doi:[10.52547/cgasa.15.1.183](https://doi.org/10.52547/cgasa.15.1.183), arXiv:[1808.04552](https://arxiv.org/abs/1808.04552). (Note that this was cited in _Internal Categories, Anafunctors and Localisations_ with the title _Strict 2-sites, J-spans and Localisations_, and some paper containing these notes may yet have that title).

* _(Re)constructing code loops_, American Mathematical Monthly **128** Issue 2 (2021) 151–161, doi:[10.1080/00029890.2021.1852047](https://doi.org/10.1080/00029890.2021.1852047), [arXiv:1903.02748](https://arxiv.org/abs/1903.02748). Joint with Ben Nagy.

* _Topological sectors for heterotic M5-brane charges under Hypothesis H_  J. High Energ. Phys. **2020** no. 52 (2020) doi:[10.1007/JHEP06(2020)052](https://doi.org/10.1007/JHEP06%282020%29052) (2020), arXiv:[2003.09832](https://arxiv.org/abs/2003.09832).

* _Smooth loop stacks of differentiable stacks and gerbes_, [[Cahiers de Topologie et Géométrie Différentielle Catégoriques]], Vol LIX no 2 (2018) pp 95-141 [journal version](http://cahierstgdc.com/index.php/volume-lix-2018/), [arXiv:1602.07973](https://arxiv.org/abs/1602.07973). Joint with [[nLab:Raymond Vozzo|Raymond Vozzo]].

* _The smooth Hom-stack of an orbifold_, In: Wood D., de Gier J., Praeger C., Tao T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1 (2018) doi:[10.1007/978-3-319-72299-3_3](https://doi.org/10.1007/978-3-319-72299-3_3), [arXiv:1610.05904](https://arxiv.org/abs/1610.05904), [MATRIX hosted version](https://www.matrix-inst.org.au/2016-matrix-annals/). Joint with [[nLab:Raymond Vozzo|Raymond Vozzo]]

* _Equivariant bundle gerbes_, [Advances in Theoretical and Mathematical Physics](https://intlpress.com/site/pub/pages/journals/items/atmp/_home/_main/)
 21 (2017) no. 4 pp 921-975, doi:[10.4310/ATMP.2017.v21.n4.a3
](https://doi.org/10.4310/ATMP.2017.v21.n4.a3
), [arXiv:1506.07931](https://arxiv.org/abs/1506.07931).
Joint with [[nLab:Michael Murray|Michael Murray]], [[nLab:Danny Stevenson|Danny Stevenson]] and [[nLab:Raymond Vozzo|Raymond Vozzo]].

* _Quasi-periodic paths and a string 2-group model from the free loop group_, [Journal of Lie Theory](https://www.heldermann.de/JLT/jltcover.htm), 27 (2017), No. 4, 1151-1177. [journal version](https://www.heldermann.de/JLT/JLT27/JLT274/jlt27058.htm) (paywall), [arXiv:1702.01514](https://arxiv.org/abs/1702.01514). Joint with [[Michael Murray]] and [[Christoph Wockel]].

* _A bigroupoid's topology (or, Topologising the homotopy bigroupoid of a space)_, [Journal of Homotopy and Related Structures](https://link.springer.com/journal/40062) Volume 11, Issue 4 (2016) pp 923-942, doi:[10.1007/s40062-016-0160-0](https://doi.org/10.1007/s40062-016-0160-0), [ReadCube](http://rdcu.be/l2yl), [arXiv:1302.7019](https://arxiv.org/abs/1302.7019).

* _On certain 2-categories admitting localisation by bicategories of
  fractions_, [Applied Categorical Structures](https://link.springer.com/journal/10485) Volume 24, Issue 4 (2016) pp 373-384, doi:[10.1007/s10485-015-9400-4](http://dx.doi.org/10.1007/s10485-015-9400-4), [ReadCube](https://rdcu.be/5uvT), [arXiv:1402.7108](http://arxiv.org/abs/1402.7108).

* _Simplicial principal bundles in parametrized spaces_, [New York Journal of Mathematics](https://nyjm.albany.edu/) Volume 22 (2016) 405-440, [journal version](http://nyjm.albany.edu/j/2016/22-19.html), [arXiv:1203.2460](https://arxiv.org/abs/1203.2460), joint with [[nLab:Danny Stevenson|Danny Stevenson]].

* _A topological fibrewise fundamental groupoid_, [Homology, Homotopy and Applications](https://intlpress.com/site/pub/pages/journals/items/hha/_home/_main/index.html), Volume 17, Number 2 (2015) 37-51, doi:[10.4310/HHA.2015.v17.n2.a4](https://doi.org/10.4310/HHA.2015.v17.n2.a4), [arXiv:1411.5779](https://arxiv.org/abs/1411.5779).

* _The weak choice principle WISC may fail in the category of sets_, [Studia Logica](https://link.springer.com/journal/11225) Volume 103, Issue 5 (2015) pp 1005-1017, doi:[10.1007/s11225-015-9603-6](https://doi.org/10.1007/s11225-015-9603-6) [arXiv:1311.3074](https://arxiv.org/abs/1311.3074).

* _The universal simplicial bundle is a simplicial group_, [New York Journal of Mathematics](https://nyjm.albany.edu/), Volume 19 (2013) 51-60, [journal version](http://nyjm.albany.edu/j/2013/19-5.html), [arXiv:1204.4886](https://arxiv.org/abs/1204.4886).

* _On the existence of bibundles_, [Proc. London Math. Soc.](https://www.lms.ac.uk/publication/plms) (2012) 105 (6): 1290-1314, doi:[10.1112/plms/pds028](https://doi.org/10.1112/plms/pds028), [arXiv:1102.4388](https://arxiv.org/abs/1102.4388). Joint with [[nLab:Michael Murray|Michael Murray]] and [[nLab:Danny Stevenson|Danny Stevenson]]

* _Internal categories, anafunctors and localisations_, [[Theory and Applications of Categories]], Vol. 26, 2012, No. 29, pp 788-829, [journal version](http://www.tac.mta.ca/tac/volumes/26/29/26-29abs.html), [arXiv:1101.2363](https://arxiv.org/abs/1101.2363)

*  _Fundamental bigroupoids and 2-covering spaces_, PhD thesis, University of Adelaide (2010). [DSpace@Adelaide](https://digital.library.adelaide.edu.au/dspace/handle/2440/62680)

* _The inner automorphism 3-group of a strict 2-group_, [Journal of Homotopy and Related Structures](https://tcms.org.ge/Journals/JHRS/), vol. 3(1), 2008, pp.193–245, [journal version](https://tcms.org.ge/Journals/JHRS/volumes/2008/volume3-1.htm), [arXiv:0708.1741](https://arxiv.org/abs/0708.1741). Joint with [[nLab:Urs Schreiber|Urs Schreiber]].

* _Yang-Mills theory for bundle gerbes_, [Journal of Physics A: Mathematical and Theoretical](https://iopscience.iop.org/1751-8121) 39:6039-6044, 2006, doi:[10.1088/0305-4470/39/20/027](https://doi.org/10.1088/0305-4470/39/20/027), [arXiv:hep-th/0509037](https://arxiv.org/abs/hep-th/0509037). Joint with [[nLab:Mathai Varghese|Mathai Varghese]]. **Sadly, this paper [had to be retracted](https://doi.org/10.1088/1751-8121/ad1d59).** See also [this blog post](https://thehighergeometer.wordpress.com/2024/01/25/ctrl-z-18-years-later-yang-mills-theory-for-bundle-gerbes-is-now-retracted/).

### Notes/Other

* _Explicit String bundles_ (2014/2022) arXiv:[2203.04544](https://arxiv.org/abs/2203.04544). (Notes from a talk delivered at Herriot-Watt University on 26 June 2014 at the Workshop on Higher Gauge Theory and Higher Quantization)

* _A Crisis of Identification_, Inference: International Review of Science **4** Issue 3 (2019), doi:[10.37282/991819.19.2](https://doi.org/10.37282/991819.19.2). This article was subsequently reprinted for the special collection "A Christmas [Chrestomathy](https://en.wiktionary.org/wiki/chrestomathy), 2014–2020", in vol **5** Issue 4.

* _Class forcing and topos theory_ (2018) notes from my 2015 talk at IHES, doi:[10.4225/55/5b2252e3092af](https://doi.org/10.4225/55/5b2252e3092af)

* _Comments on Mochizuki’s 2018 Report_ (2018) doi:[10.25909/5c5ce1fda4b7c](https://doi.org/10.25909/5c5ce1fda4b7c), ([blog post](https://thehighergeometer.wordpress.com/2018/09/28/on-mochiukis-report-on-discussions/))

* _No Ancient Scottish Evidence of Fifth Platonic Solid_, Letter to the Editor, Notices of the American Mathematical Society **65** no 6 (2018) p 677 ([link](https://www.ams.org/journals/notices/201806/rnoti-p676.pdf))

* _What do mathematicians think about their journals? Peer review quality tops list of stated issues_, LSE Impact Blog, June 22 2016 [Blog post](http://blogs.lse.ac.uk/impactofsocialsciences/2016/06/22/what-do-mathematicians-think-about-their-journals-peer-review-quality-tops-list-of-stated-issues/) (joint with Cameron Neylon and Mark C. Wilson)

* Review of _Mathematics without apologies: Portrait of a problematic vocation_ by Michael Harris. ([publisher's page](http://press.princeton.edu/titles/10317.html)) Appears in: Gazette of the Australian Mathematical Society, Vol. 43 (2016) No. 2 ([journal pdf](http://www.austms.org.au/Publ/Gazette/2016/May16/BkRev.pdf))

* Contribution to _The "Bounded Gaps between Primes" Polymath Project: A Retrospective Analysis_, Newsletter of the European Mathematical Society, No. 94, December 2014. (page 19 of [this pdf](http://www.ems-ph.org/journals/newsletter/pdf/2014-12-94.pdf))

* Review of _Lectures on real analysis_ by [[Finnur Larusson]], Australian Mathematical Society Lecture Series, No. 21. ([publisher's page](https://www.cambridge.org/us/academic/subjects/mathematics/real-and-complex-analysis/lectures-real-analysis))
Appears in: Gazette of the Australian Mathematical Society, Vol. 41 (2014) No. 5 ([journal pdf](http://www.austms.org.au/Publ/Gazette/2014/Nov14/BkRev.pdf))

## Talks

See [[davidroberts:talks|here]] for a comprehensive list.

## Supervision and teaching

See [[davidroberts:teaching/students|here]] for a list of student projects I have supervised and courses I have taught.

## Copyright statement ##

My contributions to the [[HomePage|nLab]] are released under a [CC0](http://creativecommons.org/publicdomain/zero/1.0/) license. This is essentially public domain, but works in jurisdictions where such matters are difficult. Normal academic standards do apply, so attribution of ideas where they are clearly mine would be nice.

category: people


David Morrison

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

## Selected writings

On [[F-theory]] [[KK-compactification|KK-compactified]] on [[Calabi-Yau manifolds]] and [[duality between F-theory and heterotic string theory]]:

* {#MorrisonVafa96a} [[David Morrison]], [[Cumrun Vafa]], _Compactifications of F-Theory on Calabi--Yau Threefolds -- I_, Nucl. Phys. B473 (1996) 74-92 ([arXiv:hep-th/9602114](http://arxiv.org/abs/hep-th/9602114))

* {#MorrisonVafa96b} [[David Morrison]], [[Cumrun Vafa]], _Compactifications of F-Theory on Calabi--Yau Threefolds -- II_, Nucl. Phys. B476:437-469, 1996 ([arXiv:hep-th/9603161](http://arxiv.org/abs/hep-th/9603161))

and in relation to the [[duality between M-theory and heterotic string theory]]:

* [[Bobby Acharya]], Alex Kinsella, [[David Morrison]], *Non-Perturbative Heterotic Duals of M-Theory on $G_2$ Orbifolds* ([arXiv:2106.03886](https://arxiv.org/abs/2106.03886))

On the [[D=6 N=(1,0) SCFT]] on [[heterotic M5-branes]] and their [[KK-compactifications]]:

* [[Ori Ganor]], [[David Morrison]], [[Nathan Seiberg]], _Branes, Calabi-Yau Spaces, and Toroidal Compactification of the $N=1$ Six-Dimensional $E_8$ Theory_, Nucl. Phys. B487:93-127, 1997 ([arXiv:hep-th/9610251](https://arxiv.org/abs/hep-th/9610251))

On [[small instantons]] under [[duality between F-theory and heterotic string theory]]:

* {#AspinwallGross96} [[Paul Aspinwall]], [[Mark Gross]], _The $SO(32)$ Heterotic String on a K3 Surface_, Phys. Lett. B387 (1996) 735-742 ([arXiv:hep-th/9605131](https://arxiv.org/abs/hep-th/9605131))

* {#AspinwallMorrison97} [[Paul Aspinwall]], [[David Morrison]], _Point-like Instantons on K3 Orbifolds_, Nucl. Phys. B503 (1997) 533-564 ([arXiv:hep-th/9705104](https://arxiv.org/abs/hep-th/9705104))

On [[string theory]] [[perturbative string theory vacuum|vacua]] [[KK-compactification|compactified]] on [[orbifolds]] and [[orientifolds]]:

* {#BDHKMMS01} [[Jan de Boer]], [[Robbert Dijkgraaf]], [[Kentaro Hori]], [[Arjan Keurentjes]], [[John Morgan]], [[David Morrison]], [[Savdeep Sethi]], section 3 of _Triples, Fluxes, and Strings_, Adv.Theor.Math.Phys. 4 (2002) 995-1186 ([arXiv:hep-th/0103170](https://arxiv.org/abs/hep-th/0103170))

On [[ADE-singularities]] in [[string theory]]:

* [[Paul Aspinwall]], [[David Morrison]], _Point-like Instantons on K3 Orbifolds_,  Nucl. Phys. B503 (1997) 533-564 ([arXiv:hep-th/9705104](https://arxiv.org/abs/hep-th/9705104))

Also:

* {#MorrisonPlesser99} [[David Morrison]], [[M. Ronen Plesser]], _Non-Spherical Horizons, I_, Adv. Theor. Math. Phys.3:1-81, 1999 ([arXiv:hep-th/9810201](https://arxiv.org/abs/hep-th/9810201))

* Lectures on [[K3]]-singularities in [[string theory]] ([here](https://sites.duke.edu/scshgap/dave-morrison-lectures/#09sep18))

One of the editors and organizers of

* [[Pierre Deligne]], [[Pavel Etingof]], [[Dan Freed]], [[Lisa Jeffrey]], [[David Kazhdan]], [[John Morgan]], [[David R. Morrison]], [[Edward Witten]], (eds.), _[[Quantum Fields and Strings]]_

## Related $n$Lab entries

* [[K3 surface]]

* [[conifold transition]]

* [[discrete torsion]]

* [[moduli space of Calabi-Yau spaces]]

* [[F/M-theory on elliptically fibered Calabi-Yau 3-folds]]

* [[geometric engineering of quantum field theory]]

* [[duality between F-theory and heterotic string theory]]

* [[superdeterminant]]

* [[chiral algebra]]

* [[ADE classification]]

* [[associative submanifold]]

* [[mirror symmetry]]

* [[supergeometry]]

* [[little string theory]]

* [[spin geometry]]

* [[fractional D-brane]]

* [[6d (2,0)-superconformal QFT]]

* [[M-theory on 8-manifolds]]

  [[8-manifold]], [[exotic 7-sphere]]

category: people

[[!redirects D. R. Morrison]]
[[!redirects David R. Morrison]]


David Mumford

**David Mumford** is an [[algebraic geometry|algebraic geometer]], who sharply switched at some point in his career to study pattern recognition. His contributions include the creation of modern [[geometric invariant theory]] (as a method of building [[moduli spaces]]), the introduction of [[Deligne-Mumford stacks]] and especially of the [[Deligne-Mumford compactification]] of the moduli space of curves, the Mumford-Tate curve, Mumford cohomological classes on the moduli space of curves, [[Mumford conjecture]] (recently proved by Madsen and Weiss), the classification of algebraic surfaces in positive characteristics and solutions to a number of difficult problems in mainstream algebraic geometry. He is also well known for clear exposition, and wrote several books on algebraic geometry (Tata lectures on theta, Geometric invariant theory, "Red book"...).

Scans of most, if not all, his papers are available at his

* [website](http://www.dam.brown.edu/people/mumford/index.php)

## Selected writings

On [[geometric invariant theory]]:

*  {#MumfordFogartyKirwan65} [[David Mumford]], [[John Fogarty]], [[Frances Clare Kirwan]], _Geometric invariant theory_, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) __34__, Springer-Verlag (1965/1982) ([ISBN:978-3-540-56963-3](https://www.springer.com/gp/book/9783540569633), [pdf](https://altexploit.files.wordpress.com/2017/08/mumford-d-fogarty-j-geometric-invariant-theory-springer-1982.pdf))

Introducing the notion of [[algebraic stacks]] and (what came to be called) [[Deligne-Mumford stacks]], and on the example of the [[moduli space of curves]]:

* {#DeligneMumford69} [[Pierre Deligne]], [[David Mumford]], *The irreducibility of the space of curves of given genus*, Publications Mathématiques de l'IHÉS (Paris) **36**   (1969) 75-109 [[doi:10.1007/BF02684599](https://doi.org/10.1007/BF02684599), [numdam:PMIHES_1969__36__75_0](http://www.numdam.org/item?id=PMIHES_1969__36__75_0)]

category:people


David Nadler

* [website](http://www.math.northwestern.edu/~nadler/)

## Selected writings

On a [[stable (infinity,1)-category|stable $(\infty,1)$-category]] of [[Lagrangian cobordisms]]:

* {#NadlerTannaka11} [[David Nadler]], [[Hiro Tannaka]], _A stable infinity-category of Lagrangian cobordisms_, Adv. Math. __366__ 3 (2020) 107026 [[arXiv:1109.4835](https://arxiv.org/abs/1109.4835), [doi:10.1016/j.aim.2020.107026](https://doi.org/10.1016/j.aim.2020.107026)]

## Related entries

* [[loop space object]]

* [[Hochschild cohomology]]

* [[geometric ∞-function theory]]

category: people


David Nowak

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

## Selected writings

On [[monads in computer science]] (as [[strong monads]] and [[commutative monad|commutative]] [[monoidal monads]]):

* {#GLLN08} [[Jean Goubault-Larrecq]], [[Slawomir Lasota]], [[David Nowak]], *Logical Relations for Monadic Types*, Mathematical Structures in Computer Science, **18** 6 (2008) 1169-1217 [[arXiv:cs/0511006](https://arxiv.org/abs/cs/0511006), [doi:10.1017/S0960129508007172](https://doi.org/10.1017/S0960129508007172)]

category: people


David Olive

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

## Selected writings

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

* [[Claus Montonen]], [[David Olive]], _Magnetic Monopoles As Gauge Particles?_ Phys. Lett. B72 (1977) 117-120 ([spire:121372](https://inspirehep.net/literature/121372), doi:10.1016/0370-2693(77)90076-4)

* {#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)]

On the [[Wess-Zumino-Witten model]] [[2d CFT]] (via [[Kac-Moody algebra]] and [[Virasoro algebra]]):

* [[Peter Goddard]], [[David Olive]], *Kac-Moody and Virasoro algebras in relation to quantum physics*,  International Journal of Modern Physics A **01** 02 (1986) 303-414 [[doi:10.1142/S0217751X86000149](https://doi.org/10.1142/S0217751X86000149), [spire:18583](https://inspirehep.net/literature/18583)]

## Related $n$Lab entries

* [[S-matrix]]

* [[Montonen-Olive duality]] ([[S-duality]])

* [[BPS state]]

category: people