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

#Contents#
* table of contents
{:toc}

## Statement

+-- {: .num_prop #MapsFromCompactSpacesToHausdorffSpacesAreClosed}
###### Proposition
**(maps from compact spaces to Hausdorff spaces are closed and proper)**

Let $f \colon (X, \tau_X) \longrightarrow (Y, \tau_Y)$ be a [[continuous function]] between [[topological spaces]] such that

1. $(X,\tau_X)$ is a [[compact topological space]];

1. $(Y,\tau_Y)$ is a [[Hausdorff topological space]].

Then $f$ is

1. a [[closed map]];

1. a [[proper map]].

=--

+-- {: .proof}
###### Proof

For the first statement, we need to show that if $C \subset X$ is a [[closed subset]] of $X$, then also $f(C) \subset Y$ is a closed subset of $Y$.

Now

1. since [[closed subsets of compact spaces are compact]] it follows that $C \subset X$ is also compact;

1. since [[continuous images of compact spaces are compact]] it then follows that $f(C) \subset Y$ is compact;

1. since [[compact subspaces of Hausdorff spaces are closed]] it finally follow that $f(C)$ is also closed in $Y$.

For the second statement we need to show that if $C \subset Y$ is a [[compact topological space|compact subset]], then also its [[pre-image]] $f^{-1}(C)$ is compact.

Now

1. since [[compact subspaces of Hausdorff spaces are closed]] it follows that $C \subset Y$ is closed;

1. since [[pre-images]] under continuous of closed subsets are closed, also $f^{-1}(C) \subset X$ is closed;

1. since [[closed subsets of compact spaces are compact]], it follows that $f^{-1}(C)$ is compact.

=--

## Consequences

+-- {: .num_cor #ContinuousBijectionsFromCompactSpacesToHausdorffSpacesAreHomeomorphisms}
###### Corollary ######
**(continuous bijections from compact spaces to Hausdorff spaces are homeomorphisms)**

Let $f \colon (X, \tau_X) \longrightarrow (Y, \tau_Y)$ be a [[continuous function]] between [[topological spaces]] such that

1. $(X,\tau_X)$ is a [[compact topological space]];

1. $(Y,\tau_Y)$ is a [[Hausdorff topological space]].

1. $f \;\colon\; X \longrightarrow Y$ is a [[bijection]] of [[sets]].

Then $f$ is a [[homeomorphism]], i. e. its [[inverse function]] $Y \to X$ is also a [[continuous function]].

In particular then both $(X,\tau_X)$ and $(Y, \tau_Y)$ are [[compact Hausdorff spaces]].

=--

+-- {: .proof}
###### Proof

Write $g \colon Y \to X$ for the [[inverse function]] of $f$.

We need to show that $g$ is continuous, hence that for $U \subset X$ an [[open subset]], then also its [[pre-image]] $g^{-1}(U) \subset Y$ is open in $Y$.
By passage to [[complements]], this is equivalent to the statement that for $C \subset X$ a [[closed subset]] then the [[pre-image]] $g^{-1}(C) \subset Y$ is also closed in $Y$.

But since $g$ is the [[inverse function]] to $f$, its [[pre-images]] are the [[images]] of $f$. Hence the last statement above equivalently says that $f$ sends closed subsets to closed subsets. This is true by prop. \ref{MapsFromCompactSpacesToHausdorffSpacesAreClosed}.

=--

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

The idea captured by corollary \ref{ContinuousBijectionsFromCompactSpacesToHausdorffSpacesAreHomeomorphisms} is that [[Hausdorff topological space|Hausdorffness]] is about having "enough" [[open sets]] whilst [[compact topological space|compactness]] is about having "not too many". Thus a [[compact Hausdorff space]] has both "enough" and "not too many". This theorem says that both conditions are at their limit: if we try to have more open sets, we lose compactness. If we try to have fewer open sets, we lose Hausdorffness.

=--

## Applications

### In Cohomotopy and Cobordism theory
  {#InCohomotopyAndCobordism}

[[Pontryagin's theorem]] establishes a [[bijection]]

$$
  \pi^n
  \big(
    X^d
  \big)
  \,=\,
  \pi_0 Maps
  \big(
    X^d, S^n
  \big)
  \overset
  {\simeq}{
    \;\;
    \longrightarrow
    \;\;
  }
  Cob^n_{Fr}
  \big(
    X^d
  \big)
$$

between

1. the $n$-[[Cohomotopy]] set of a _[[closed manifold|closed]]_ (hence: [[compact topological space|compact]]) [[smooth manifold]] $X^d$;

1. the [[cobordism classes]] of its [[normally framed submanifolds]] of [[codimension]] $n$;

by taking the [[homotopy class]] of any [[map]] $[X \overset{c}{\to}S^n]$ into the [[n-sphere]] to the [[preimage]] of any [[regular point]] (say $\{0\} \subset S^n$, for definiteness) of a [[smooth function|smooth]] representative $c$:

$$
  \Sigma_c \;\coloneqq\; c^{-1}\big( \{0\} \big)
  \,.
$$

To show that this construction is indeed [[injection|injective]], one needs that, similarly, the [[pre-image]] of any regular point of a [[smooth homotopy]]

$$
  X^d \times [0,1]
  \overset{\eta}{\longrightarrow}
  S^d
$$

between two such smooth representatives $c_0, c_1$ is a [[cobordism]] between $\Sigma_{c_0}$ and $\Sigma_{c_1}$. But for a subspace of $X^d \times [0,1]$ to constitute a [[cobordism]] between submanifolds of $X^d$ it is necessary that its [[projection]] onto the $[0,1]$-factor is compact.

That this is implied here is guaranteed by the assumption that $X^d$ is [[closed manifold|closed]], hence [[compact topological space|compact]], [so that](compact+topological+space#ProductOfCompactSpacesIsCompact) also the [[product topological space|product space]] $X^d \times [0,1]$ is compact:

With this and since the [[n-sphere]] is, of course, [[Hausdorff space|Hausdorff]], Prop. \ref{MapsFromCompactSpacesToHausdorffSpacesAreClosed} implies that the maps $c_i$ and $\eta$ above are all [[proper maps|proper]], hence that the corresponding pre-images (of [[singleton]], hence compact, subspaces) are indeed compact, so that in particular the projection of the pre-image of $\eta$ to $[0,1]$ is compact (since [[continuous images of compact spaces are compact]]).

## Related statements

* [[continuous metric space valued function on compact metric space is uniformly continuous]]

* [[proper maps to locally compact spaces are closed]]

* [[CW-complexes are paracompact Hausdorff spaces]]

* [[Hausdorff implies sober]]

* [[continuous image of a compact space is compact]]

* [[closed subsets of compact spaces are compact]]

* [[compact subspaces of Hausdorff spaces are closed]]

* [[closed subspaces of compact Hausdorff spaces are equivalently compact subspaces]]

* [[quotient projections out of compact Hausdorff spaces are closed precisely if the codomain is Hausdorff]]

* [[paracompact Hausdorff spaces are normal]]

* [[paracompact Hausdorff spaces equivalently admit subordinate partitions of unity]]

[[!redirects map from compact space to Hausdorff space]]
[[!redirects map from compact space to Hausdorff space]]
[[!redirects map from a compact space to a Hausdorff space]]
[[!redirects maps from a compact space to a Hausdorff space]]
[[!redirects maps from compact spaces to Hausdorff spaces]]

[[!redirects continuous bijections from compact spaces to Hausdorff spaces are homeomorphisms]]


Marc Bezem

* [webpage](https://www.ii.uib.no/~bezem/)

## Selected writings

On [[symmetry]] and introducing the language of [[homotopy type theory]] for [[univalent foundations of mathematics]]:

* [[Marc Bezem]], [[Ulrik Buchholtz]], [[Pierre Cagne]], [[Bjørn Ian Dundas]], [[Daniel R. Grayson]]: *[[Symmetry]]* (2021) $[$[pdf](https://unimath.github.io/SymmetryBook/book.pdf)$]$

## Related entries

* [[univalence]]

* [[cubical type theory]]

category: people


Marc Glisse

* [institute page](https://geometrica.saclay.inria.fr/team/Marc.Glisse/)

## Selected writings

On [[persistence modules]] and [[stability of persistence diagrams]]:

* [[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)$]$

* [[Frédéric Chazal]], [[Vin de Silva]], [[Marc Glisse]], [[Steve Oudot]],  *The structure and stability of persistence modules*, SpringerBriefs in Mathematics, Springer (2016) $[$[arXiv:1207.3674](https://arxiv.org/abs/1207.3674), [doi:10.1007/978-3-319-42545-0](https://doi.org/10.1007/978-3-319-42545-0)$]$

category: people


Marc Henneaux

* [website](http://www.ulb.ac.be/sciences/ptm/pmif/membres/henneaux.html)

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

## Selected writings

On [[3d gravity]] as a [[Chern-Simons theory]] and its [[holography|holographic]] relation to a [[2d CFT]] [[boundary field theory]] (well before [[AdS/CFT]] was conceived from [[string theory]]):

* J. D. Brown, [[Marc Henneaux]], _Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity_, Commun. Math. Phys. (1986) 104: 207 ([doi:10.1007/BF01211590](https://doi.org/10.1007/BF01211590))

* O. Coussaert, [[Marc Henneaux]], P. van Driel, _The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant_, Class. Quant. Grav. 12 (1995) 2961-2966 ([arXiv:gr-qc/9506019](https://arxiv.org/abs/gr-qc/9506019))

* [[Marc Henneaux]], [[Wout Merbis]], Arash Ranjbar, _Asymptotic dynamics of $AdS_3$ gravity with two asymptotic regions_ ([arXiv:1912.09465](https://arxiv.org/abs/1912.09465))

On [[self-dual higher gauge fields]]:

* {#HenneauxTeitelboim88} [[Marc Henneaux]], [[Claudio Teitelboim]], _Dynamics of chiral (self-dual) $p$-forms_, Physics Letters B **206** 4 (1988) 650-654 [doi:10.1016/0370-2693(88)90712-5]

On [[BV-formalism|BV-]][[BRST complex|BRST]]-[[quantization]] of [[gauge theories]]:

* [[Marc Henneaux]], [[Claudio Teitelboim]], *[[Quantization of Gauge Systems]]*, Princeton University Press (1992) [[ISBN:9780691037691](https://press.princeton.edu/books/paperback/9780691037691/quantization-of-gauge-systems), [doi:10.2307/j.ctv10crg0r](https://doi.org/10.2307/j.ctv10crg0r), [jstor:j.ctv10crg0r](https://www.jstor.org/stable/j.ctv10crg0r)]

On the [[BTZ black hole]]:

* [[Máximo Bañados]], [[Marc Henneaux]], [[Claudio Teitelboim]], [[Jorge Zanelli]], _Geometry of the 2+1 Black Hole_, Phys. Rev. D **48** (1993) 1506-1525 [[arXiv:gr-qc/9302012](https://arxiv.org/abs/gr-qc/9302012)]

On [[local BRST cohomology]] and [[BV-formalism]]:

* {#BarnichBrandtHenneaux94} [[Glenn Barnich]], [[Friedemann Brandt]], [[Marc Henneaux]], _Local BRST cohomology in the antifield formalism: I. General theorems_, Commun. Math. Phys. **174** (1995) 57-92 [[arXiv:hep-th/9405109](https://arxiv.org/abs/hep-th/9405109), [doi:10.1007/BF02099464](https://doi.org/10.1007/BF02099464)]

* {#BarnichHenneaux96} [[Glenn Barnich]], [[Marc Henneaux]], _Isomorphisms between the Batalin-Vilkovisky antibracket and the Poisson bracket_, J. Math. Phys. **37** (1996) 5273-5296 [[arXiv:hep-th/9601124](https://arxiv.org/abs/hep-th/9601124), [doi:10.1063/1.531726](https://doi.org/10.1063/1.531726)]

* {#BarnichBrandtHenneaux00} [[Glenn Barnich]], [[Friedemann Brandt]], [[Marc Henneaux]], _Local BRST cohomology in gauge theories_, Phys. Rept. **338** (2000) 439-569 [doi:10.1016/S0370-1573(00)00049-1[arXiv:hep-th/0002245](https://arxiv.org/abs/hep-th/0002245)]

and application to [[gravity]] and/or [[Yang-Mills theory]] ([[Einstein-Yang-Mills theory]]):

* [[Glenn Barnich]], [[Friedemann Brandt]], [[Marc Henneaux]], _Local BRST cohomology in Einstein-Yang-Mills theory_, Nucl. Phys. B **455** (1995) 357-408 [doi:10.1016/0550-3213(95)00471-4[arXiv:hep-th/9505173](https://arxiv.org/abs/hep-th/9505173)]

## Related entries

* [[gauge theory]]

* [[BV-BRST formalism]]

* [[local BRST cohomology]]

category: people


Marc Hindry

* [webpage](https://www.imj-prg.fr/~marc.hindry/)

category: people


Marc Hoyois

* [webpage](http://www.mathematik.ur.de/hoyois/index.html)

## Selected writings

On [[Grothendieck's six operations]] in [[equivariant motivic homotopy theory]]:

* [[Marc Hoyois]], *The six operations in equivariant motivic homotopy theory*, Adv. Math. **305** (2017) 197-279 [[arXiv:1509.02145](https://arxiv.org/abs/1509.02145), [doi:10.1016/j.aim.2016.09.031](https://doi.org/10.1016/j.aim.2016.09.031)]

On [[representable functor|representability]] in [[motivic homotopy theory]]:

and [[representable functor|representability]]:

* [[Aravind Asok]], [[Marc Hoyois]], [[Matthias Wendt]], *Affine representability results in $\mathbb{A}^1$-homotopy theory I: Vector bundles*, Duke Math. J. **166** 10 (2017) 1923-1953 [[arXiv:1506.07093](http://arxiv.org/abs/1506.07093), [doi:10.1215/00127094-0000014X](https://doi.org/10.1215/00127094-0000014X)]

* [[Aravind Asok]], [[Marc Hoyois]], [[Matthias Wendt]], _Affine representability results in $\mathbb{A} ^1$-homotopy theory II: Principal  bundles and homogeneous spaces_, Geom. Topol. **22** (2018) 1181-1225 [[arXiv:1507.08020](http://arxiv.org/abs/1507.08020), [doi:10.2140/gt.2018.22.1181](https://doi.org/10.2140/gt.2018.22.1181)]

On [[Joyal loci|Joyal $\infty$-loci]]:

* {#Hoyois19} [[Marc Hoyois]], *Topoi of parametrized objects*, Theory and Applications of Categories, **34** 9 (2019) 243-248 [[arXiv:1611.02267](https://arxiv.org/abs/1611.02267), [tac:34-09](http://www.tac.mta.ca/tac/volumes/34/9/34-09abs.html)]

On the [[Quillen plus construction]] in [[(∞,1)-category theory]]:

* {#Hoyois19} [[Marc Hoyois]], *On Quillen's plus construction*, 2019 ([pdf](http://www.mathematik.ur.de/hoyois/papers/acyclic.pdf))

On a construction of [[algebraic cobordism]] as a non-[[A1-homotopy theory|$\mathbb{A}^1$-invariant]] [[cohomology theory]] on [[derived schemes]], and the resulting [[Conner-Floyd isomorphism]]:

* Toni Annala, [[Marc Hoyois]], Ryomei Iwasa, _Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory_ [[arXiv:2303.02051](https://arxiv.org/abs/2303.02051)]

## Related entries

* [[motivic homotopy theory]]
* [[étale homotopy]]

category: people


Marc Lackenby

* [home page](https://people.maths.ox.ac.uk/lackenby/)

## Selected writings

Lecture notes on [[covering space]]-theory:

* {#Lackenby08} [[Marc Lackenby]], *Topology and Groups* (2008, 2018) [[pdf](http://people.maths.ox.ac.uk/lackenby/tg050908.pdf), [[Lackenby-TopologyAndGroups.pdf:file]]]

category: people


Marc Levine

**Marc Levine** is an American [[algebraic geometry|algebraic geometer]], a specialist on [[motives]], [[algebraic cycles]] and [[algebraic K-theory]]. He proposed several constructions of the (triangulated) category of [[motive]]s and constructed [[algebraic cobordism]] together with [[Fabien Morel]].

* [web](http://www.esaga.uni-due.de/marc.levine/)

* [[motives]]
  * [[mixed motives]]
  * [[motivic homotopy theory]]
  * [[motivic cohomology]]
* [[algebraic cycles]]
* [[algebraic K-theory]]
* [[algebraic cobordism]]

category: people

[[!redirects M. Levine]]


Marc Olschok

* [Home page](http://is.muni.cz/www/183259/index.html)

category: people


Marc Pauly

## Selected writings

On [[modal logic]] in [[game theory]] and [[information science]]:

* [[Wiebe van der Hoek]], [[Marc Pauly]], *Modal logic for games and information*, Ch. 20 in: *The Handbook of Modal Logic*, Studies in Logic and Practical Reasoning **3** (2007) 85-183 $[$doi:10.1016/S1570-2464(07)80023-1, [book webpage](https://cgi.csc.liv.ac.uk/~frank/MLHandbook/)$]$

## Related entries

* [[epistemic logic]]

category: people


Marc Rieffel

* [webpage](http://math.berkeley.edu/~rieffel/)

## Selected writings

On the [[Stone-von Neumann theorem]]:

* [[Marc Rieffel]], _On the uniqueness of the Heisenberg commutation relations_, Duke Math. J. **39**  4 (1972) 745-752 [[doi:10.1215/S0012-7094-72-03982-8](https://projecteuclid.org/journals/duke-mathematical-journal/volume-39/issue-4/On-the-uniqueness-of-the-Heisenberg-commutation-relations/10.1215/S0012-7094-72-03982-8.short)]

On [[noncommutative tori]]:

* {#Rieffel81} [[Marc A. Rieffel]], _$C^\ast$-algebras associated with irrational rotations_, Pacific Journal of Mathematics 93:2 (1981), 415–429 ([pdf](https://msp.org/pjm/1981/93-2/pjm-v93-n2-p12-s.pdf), [doi:10.2140/pjm.1981.93.415](http://dx.doi.org/10.2140/pjm.1981.93.415), [euclid:pjm/1102736269](https://projecteuclid.org/euclid.pjm/1102736269))

* [[Marc Rieffel]], [[Albert Schwarz]], _Morita equivalence of multidimensional noncommutative tori_, Int. J. Math. 10 (1999) 289-299 ([arXiv:math/9803057](https://arxiv.org/abs/math/9803057))

Introducing the notion of [[C-star algebraic deformation quantization]] ([[strict deformation quantization]]):

* [[Marc A. Rieffel]], *Deformation quantization of Heisenberg manifolds*, Communications in Mathematical Physics **122** (1989) 531–562 [[doi:10.1007/BF01256492](https://doi.org/10.1007/BF01256492)]

* {#Rieffel90} [[Marc Rieffel]], _Deformation quantization and operator algebras_, in: Operator theory: operator algebras and applications, Part 1 (Durham, NH, 1988), 411-423, Proc. Sympos. Pure Math. __51__, Part 1, Amer. Math. Soc. (1990) [[pdf](http://math.berkeley.edu/~rieffel/papers/deformation.pdf), [[Rieffel-DefQuantization.pdf:file]] [MR91h:46120](http://www.ams.org/mathscinet-getitem?mr=1077400)]

* [[Marc Rieffel]], _Deformation quantization for actions of $\mathbb{R}^d$_, Mem. Amer. Math. Soc. __106__ 506 (1993) [[ams:memo-106-506](https://bookstore.ams.org/memo-106-506), [MR94d:46072](http://www.ams.org/mathscinet-getitem?mr=1184061)]

* [[Marc Rieffel]], _Quantization and $C^\ast$-algebras_, Contemporary Mathematics **167** (1994) [[pdf](http://math.berkeley.edu/~rieffel/papers/quantization.pdf), [[Rieffel-CStarQuantization.pdf:file]]]

Specifically on [[Lie group|Lie]]-[[group algebras]] as strict deformation quantization of [[Lie-Poisson structures]]:

* [[Marc A. Rieffel]], *Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures*, American Journal of Mathematics **112** 4 (1990) 657-685 [[doi:10.2307/2374874](https://doi.org/10.2307/2374874), [jstor:2374874](https://www.jstor.org/stable/2374874)]

Review with open questions:

* [[Marc Rieffel]], _Questions on quantization_, Contemp. Math. **228** (1998) 315-326 [[arXiv:quant-ph/9712009](http://arxiv.org/abs/quant-ph/9712009)]

## Related entries

* [[C-star algebraic deformation quantization]]

category: people

[[!redirects Marc A. Rieffel]]
[[!redirects Marc Aristide Rieffel]]


Marc Stephan

* [webpage](https://sites.google.com/view/mstephan/home)

## related $n$Lab entries

* [[equivariant homotopy theory]]

* [[Elmendorf's theorem]]

category: people


Marcel Berger

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

## Selected writings

Introducing [[Berger's theorem]]:

* {#Berger} [[Marcel Berger]], _Sur les groupes d'holonomie homogène des variétés à connexion affine et des variétés riemanniennes_, Bull. Soc. Math. France 83 (1955) ([doi:10.24033/bsmf.1464](https://doi.org/10.24033/bsmf.1464))

On [[geometry]] ([[Euclidean space]], [[projective space]], [[rotation groups]], [[group actions]], ...):

* {#Berger87} [[Marcel Berger]], *Geometry I*, Springer 1987 ([doi:10.1007/978-3-540-93815-6](https://doi.org/10.1007/978-3-540-93815-6))

## Related $n$Lab entries

* [[Berger's theorem]]

category: people


Marcel Bökstedt

* webpage

## Selected writings

On the [[ordinary cohomology]] of [[cyclic loop spaces]] ("[[string cohomology]]"):

* {#BokstedtOttosen05} [[Marcel Bökstedt]], [[Iver Ottosen]], *A spectral sequence for string cohomology*, Topology Volume 44, Issue 6, November 2005, Pages 1181-1212 ([arXiv:math/0411571](https://arxiv.org/abs/math/0411571), [doi:10.1016/j.top.2005.04.006](https://doi.org/10.1016/j.top.2005.04.006))

and specifically for [[complex projective spaces]]:

* [[Marcel Bökstedt]], [[Iver Ottosen]], *String cohomology groups of complex projective spaces*, Algebr. Geom. Topol. 7(4): 2165-2238 (2007). ([arXiv:math/0605754](https://arxiv.org/abs/math/0605754), [doi:10.2140/agt.2007.7.2165](https://projecteuclid.org/journals/algebraic-and-geometric-topology/volume-7/issue-4/String-cohomology-groups-of-complex-projective-spaces/10.2140/agt.2007.7.2165.full))

On the [[homotopy groups]] of the [[embedded cobordism category]]:

* [[Marcel Bökstedt]], [[Anne Marie Svane]], _A geometric interpretation of the homotopy groups of the cobordism category_, Algebr. Geom. Topol. 14 (2014) 1649-1676 ([arXiv:1208.3370](https://arxiv.org/abs/1208.3370))

* [[Marcel Bökstedt]], [[Johan Dupont]], [[Anne Marie Svane]], _Cobordism obstructions to independent vector fields_, Q. J. Math. 66 (2015), no. 1, 13-61 ([arXiv:1208.3542](https://arxiv.org/abs/1208.3542))

On the [[EHP spectral sequence]]:

* [[Marcel Bökstedt]], [[Anne Marie Svane]], _A generalization of the stable EHP spectral sequence_ ([arXiv:1208.3938](http://arxiv.org/abs/1208.3938))

## Related $n$Lab entries

* [[topological cyclic homology]]

category: people


Marcel Franz

* [personal page](https://phas.ubc.ca/~franz/)

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

## Selected writings

On [[topological insulators]]:

*  [[Marcel Franz]], [[Laurens Molenkamp]] (eds.), *Topological Insulators*, Contemporary Concepts of Condensed Matter Science **6** (2013) [[ISBN:978-0-444-63314-9](https://www.sciencedirect.com/bookseries/contemporary-concepts-of-condensed-matter-science/vol/6/suppl/C)]

On ([[non-perturbative effect|strongly]]) [[interaction|interacting]] [[topological phases of matter]] (such as [[topological order]]):

* [[Jason Alicea]], [[Matthew Fisher]], [[Marcel Franz]], [[Yong-Baek Kim]],  *Strongly Interacting Topological Phases*, report on Banff workshop [15w5051](http://www.birs.ca/events/2015/5-day-workshops/15w5051) (2015) [[pdf](https://www.birs.ca/workshops/2015/15w5051/report15w5051.pdf), [[AliceaEtAl-InteractingTopPhases.pdf:file]]]

category: people


Marcel Rubió

I'm a PhD student at KU Leuven.

* ([website](http://marcelrubio.wordpress.com/))


Marcello Bernardara

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

## related $n$Lab entries

* [[noncommutative motive]]

category: people


Marcelo Aguiar

__Marcelo Aguiar__ works on [[category theory]], [[higher category theory]]/[[higher structures]], and their applications to [[combinatorics]].

* [personal page](http://www.math.cornell.edu/~maguiar)

## Selected writings

On [[noncartesian internal categories]] and [[quantum groups]]:

* [[Marcelo Aguiar]],  *Internal categories and quantum groups*, PhD thesis, Cornell 1997 ([pdf](http://pi.math.cornell.edu/~maguiar/thesis2.pdf), [[Aguiar_InternalCategoriesAndQuantumGroups.pdf:file]])

On [[separable algebras]]:

* [[Marcelo Aguiar]], *A note on strongly separable algebras*, Boletín de la Academia Nacional de Ciencias (Córdoba, Argentina), special issue in honor of Orlando Villamayor, **65** (2000) 51-60  [[pdf](http://www.math.cornell.edu/~maguiar/strongly.pdf)]

On [[monoidal functors]], [[species]] and [[Hopf algebras]]:

* [[Marcelo Aguiar]], [[Swapneel Mahajan]], _[[Monoidal Functors, Species and Hopf Algebras]]_, With forewords by [[Kenneth Brown]], [[Stephen Chase]] and [[André Joyal]], CRM Monograph Series __29__ Amer. Math. Soc. 2010. lii+784 pp. ([ISBN:978-0-8218-4776-3](https://bookstore.ams.org/crmm-29/), [pdf](http://www.math.cornell.edu/~maguiar/a.pdf))

category: people

[[!redirects M. Aguiar]]


Marcelo Aguilar

## Selected writings

On [[algebraic topology]] and [[homotopy theory]]:

* [[Marcelo Aguilar]], [[Samuel Gitler]], and [[Carlos Prieto]], *Algebraic topology from a homotopical viewpoint*, Springer Science & Business Media, 2008 ([doi:10.1007/b97586](https://link.springer.com/book/10.1007/b97586))

category: people


Marcelo Fiore

* [website](http://www.cl.cam.ac.uk/~mpf23/)

## Selected writings

On [[linear logic]]:

* *Differential Structure in Models of Multiplicative Biadditive Intuitionistic Linear Logic*, in *Typed Lambda Calculi and Applications. TLCA 2007*,  Lecture Notes in Computer Science **4583** [[pdf](http://www.cl.cam.ac.uk/~mpf23/papers/Types/diff.pdf), [doi:10.1007/978-3-540-73228-0_13](https://doi.org/10.1007/978-3-540-73228-0_13)]

On [[higher-order abstract syntax]]:

* [[Marcelo Fiore]], [[Gordon Plotkin]], [[Daniele Turi]]. _Abstract syntax and variable binding_, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158). IEEE (1999) [[doi:10.1109/LICS.1999.782615](https://doi.org/10.1109/LICS.1999.782615), [pdf](https://homepages.inf.ed.ac.uk/gdp/publications/Abstract_Syn.pdf), [webpage](https://www.dcs.ed.ac.uk/home/dt/abstractsyn.html)]

* [[Marcelo Fiore]], [[Chung-Kil Hur]]. _Second-order equational logic_, International Workshop on Computer Science Logic. Springer, Lecture Notes in Computer Science **6247** (2010) [[doi:10.1007/978-3-642-15205-4_26](https://doi.org/10.1007/978-3-642-15205-4_26), [pdf](https://www.cl.cam.ac.uk/~mpf23/papers/Types/soeqlog.pdf)]

On [[simple type theory]]:

* [[Nathanael Arkor]], [[Marcelo Fiore]], *Algebraic models of simple type theories: a polynomial approach*, Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, July 2020, Pages 88-101 ([doi:10.1145/3373718.3394771](https://doi.org/10.1145/3373718.3394771), [arXiv:2006.16949](https://arxiv.org/abs/2006.16949))

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

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

category: people

[[!redirects Marcelo P. Fiore]]


Marco Benini

* [institute page](https://mathphys.dima.unige.it/index.php/home/group-members/marco-benini/)

* [cv](http://fisica.unipv.it/personale/PersFiles/Curr_308.pdf)

## Selected writings

On [[self-dual higher gauge theory]] on [[Lorentzian spacetimes]] via [[ordinary differential cohomology]]:

* [[Christian Becker]], [[Marco Benini]], [[Alexander Schenkel]], [[Richard Szabo]], _Abelian duality on globally hyperbolic spacetimes_, Commun. Math. Phys. **349** (2017) 361-392 [[arXiv:1511.00316](https://arxiv.org/abs/1511.00316), [doi:10.1007/s00220-016-2669-9](https://doi.org/10.1007/s00220-016-2669-9)]

On relating [[homotopy AQFT|homotopy]] [[algebraic quantum field theory]] via [[local nets of observables]] to [[factorization algebras]]:

* [[Marco Benini]], [[Marco Perin]], [[Alexander Schenkel]], _Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds_, Communications in Mathematical Physics volume 377, pages 971–997 (2020) ([arXiv:1903.03396v2](https://arxiv.org/abs/1903.03396), [doi:10.1007/s00220-019-03561-x](https://doi.org/10.1007/s00220-019-03561-x))

* [[Marco Benini]], Giorgio Musante, [[Alexander Schenkel]], *Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory* [[arXiv:2212.02546](https://arxiv.org/abs/2212.02546)]

Discussion of [[orbifold|orbifolding]] via [[categorification]], in [[homotopical algebraic quantum field theory]]:

* [[Marco Benini]], [[Marco Perin]], [[Alexander Schenkel]], [[Lukas Woike]], _Categorification of algebraic quantum field theories_, Lett. Math. Phys. 2021 ([arXiv:2003.13713](https://arxiv.org/abs/2003.13713))

On rigorous [[semi-topological 4d Chern-Simons theory]] via [[homotopical AQFT]]:

* [[Marco Benini]], [[Alexander Schenkel]], Benoit Vicedo, _Homotopical analysis of 4d Chern-Simons theory and integrable field theories_ ([arXiv:2008.01829](https://arxiv.org/abs/2008.01829))

On 1d [[AQFT]] and [[smooth stacks]]:

* [[Marco Benini]], [[Marco Perin]], [[Alexander Schenkel]], *Smooth 1-dimensional algebraic quantum field theories* ([arXiv:2010.13808](https://arxiv.org/abs/2010.13808))

On [[non-perturbative quantum field theory|non-perturbative]] aspects of the [[BV-formalism]]:

* [[Marco Benini]], [[Pavel Safronov]], [[Alexander Schenkel]], *Classical BV formalism for group actions* ([arXiv:2104.14886](https://arxiv.org/abs/2104.14886))

On [[2d CFT]] in terms of [[AQFT on curved spacetimes]]:

* [[Marco Benini]], [[Luca Giorgetti]], [[Alexander Schenkel]], *A skeletal model for 2d conformal AQFTs* ([arXiv:2111.01837](https://arxiv.org/abs/2111.01837))

On the [[time slice axiom]] in [[homotopical AQFT]]:

* [[Marco Benini]], [[Victor Carmona]], [[Alexander Schenkel]], *Strictification theorems for the homotopy time-slice axiom* [[arxiv:2208.04344](https://arxiv.org/abs/2208.04344)]

On [[model structure on modules in a monoidal model category|model structure on modules]] for representations of higher [[local nets of observables]] in [[homotopical AQFT]]:

* Angelos Anastopoulos, [[Marco Benini]], *Homotopy theory of net representations*, Rev. Math. Phys. [[arXiv:2201.06464](https://arxiv.org/abs/2201.06464), [doi:10.1142/S0129055X23500083](https://doi.org/10.1142/S0129055X23500083)]

Formulation of the [[CS/WZW correspondence]] in [[homotopical AQFT]]:

* [[Marco Benini]], [[Alastair Grant-Stuart]], [[Alexander Schenkel]], *The linear CS/WZW bulk/boundary system in AQFT*, Annales Henri Poincaré (2023) [[arXiv:2302.06990](https://arxiv.org/abs/2302.06990)]

## Related $n$Lab entries

* [[AQFT]]

* [[homotopical AQFT]]

category: people


Marco Chiodaroli

* [institute page](https://www.katalog.uu.se/profile/?id=N16-907)

* [GoogleScholar page](https://scholar.google.de/citations?user=Pk1sRsMAAAAJ&hl=en)

## Selected writings

On the "[[double copy]]" [[KLT relations]]-approach to [[scattering amplitudes]] in [[perturbative quantum gravity]] and [[supergravity]]:

* [[Zvi Bern]], [[John Joseph Carrasco]], [[Marco Chiodaroli]], [[Henrik Johansson]], [[Radu Roiban]], *Supergravity amplitudes, the double copy and ultraviolet behavior*, in *[[Handbook of Quantum Gravity]]*, Springer (2023) [[arXiv:2304.07392](https://arxiv.org/abs/2304.07392)]

category: people


Marco Fazzi

* [webpage](https://phys.technion.ac.il/en/people/person/902)

## Selected writings

On [[geometric engineering of QFT]] and on [[AdS/CFT]] for [[D6-D8 brane bound states]] on [[NS5-branes]] in [[massive type IIA string theory]]:

* Fabio Apruzzi, [[Marco Fazzi]], Dario Rosa, [[Alessandro Tomasiello]],  _All $AdS_7$ solutions of type II supergravity_, JHEP 04 (2014) 064 ([arxiv:1309.2949](https://arxiv.org/abs/1309.2949))

* [[Marco Fazzi]], _Higher-dimensional field theories from type II supergravity_ ([arxiv:1712.04447](https://arxiv.org/abs/1712.04447))

and for the [[orientifold]] version of [[heterotic M-theory on ADE-singularities]] (with [[half M5-branes]]):

* Fabio Apruzzi, [[Marco Fazzi]], Section 2.1.2 of: _AdS7/CFT6 with orientifolds_, JHEP 01 (2018) 124 ([arXiv:1712.03235](https://arxiv.org/abs/1712.03235))

On the [[Coulomb branch]] of [[D=3 N=4 SYM]] from [[heterotic string theory]] on [[ADE-singularities]]:

* [[Michele Del Zotto]], [[Marco Fazzi]], Suvendu Giri, *A new vista on the Heterotic Moduli Space from Six and Three Dimensions* [[arXiv:2307.10356](https://arxiv.org/abs/2307.10356)]

## Related entries

* [[NS5-brane]]

* [[geometric engineering of quantum field theory]]

category:people


Marco Grandis

* [website](http://www.dima.unige.it/~grandis/)

* [list of publications](http://www.dima.unige.it/~grandis/rec.public_grandis.html)

## Selected writings

On [[category theory]]:

* [[Marco Grandis]], _Category Theory and Applications: A Textbook for Beginners_, World Scientific 2021 ([doi:10.1142/12253](https://doi.org/10.1142/12253))

## Related entries

* [[directed space]]

* [[Cospans in Algebraic Topology]]

* [[multispan]]

* [[Puppe exact category]]

* [[cube category]]

category: people


Marco Gualtieri

* [website](http://www.math.toronto.edu/mgualt/)

#related $n$Lab entries#

* [[generalized complex geometry]]

category: people


Marco Mackaay

* [publications](http://en.scientificcommons.org/marco_mackaay)

## Selected writings

Introducing [[twisted vector bundles]] and discussing their [[holonomy]]:

* [[Marco Mackaay]], _A note on the holonomy of connections in twisted bundles_, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 1, pp. 39-62.  ([arXiv:math/0106019](http://arxiv.org/abs/math/0106019), [numdam:CTGDC_2003__44_1_39_0](http://www.numdam.org/item/?id=CTGDC_2003__44_1_39_0))

On the [[cobordism category]] of "foams" (from [Khovanov 2004](Khovanov+homology#Khovanov04)) for studying [[link homology]]:

* [[Marco Mackaay]], [[Pedro Vaz]], *The universal $sl_3$-link homology*, Algebr. Geom. Topol. **7** (2007) 1135-1169 [[doi:10.2140/agt.2007.7.1135](https://doi.org/10.2140/agt.2007.7.1135)]

* [[Marco Mackaay]], [[Pedro Vaz]], *The foam and the matrix factorization $sl_3$ link homologies are equivalent*, Algebr. Geom. Topol. **8** (2008) 309-342 [[arXiv:0710.0771](https://arxiv.org/abs/0710.0771), [doi:10.2140/agt.2008.8.309](https://doi.org/10.2140/agt.2008.8.309)]

* [[Marco Mackaay]], [[Pedro Vaz]], *The diagrammatic Soergel category and $sl(N)$-foams, for $N \gt 3$ [[arXiv:0911.2485](https://arxiv.org/abs/0911.2485)]

category: people


Marco Maggesi

* [personal page](https://sites.google.com/unifi.it/maggesi/?pli=1)

## Selected writings

On [[univalent bicategory|univalent]] [[bicategories]] in [[homotopy type theory]]:

* [[Benedikt Ahrens]], [[Dan Frumin]], [[Marco Maggesi]], [[Niels van der Weide]], _Bicategories in Univalent Foundations_, Mathematical Structures in Computer Science **31** 10 (2022) 1232-1269 [[arXiv:1903.01152](https://arxiv.org/abs/1903.01152), [doi:10.1017/S0960129522000032](https://doi.org/10.1017/S0960129522000032)&rbrack

category: people


Marco Manetti

* [webage](http://www1.mat.uniroma1.it/people/manetti/)

## related $n$Lab entries

* [[deformation theory]]

* [[model structure for L-infinity algebras]]

category: people


Marco Perin

* [Institute page](https://www.nottingham.ac.uk/mathematics/people/marco.perin)

* [GoogleScholar page](https://scholar.google.com/citations?user=T43xleQAAAAJ&hl=en)

## Selected writings

On relating [[algebraic quantum field theory]] via [[local nets of observables]] to [[factorization algebras]]:

* [[Marco Benini]], [[Marco Perin]], [[Alexander Schenkel]], _Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds_, Communications in Mathematical Physics volume 377, pages 971–997 (2020) ([arXiv:1903.03396v2](https://arxiv.org/abs/1903.03396), [doi:10.1007/s00220-019-03561-x](https://doi.org/10.1007/s00220-019-03561-x))

Discussion of [[orbifold|orbifolding]] via [[categorification]], in [[homotopical algebraic quantum field theory]]:

* [[Marco Benini]], [[Marco Perin]], [[Alexander Schenkel]], [[Lukas Woike]], _Categorification of algebraic quantum field theories_, Lett. Math. Phys. 2021 ([arXiv:2003.13713](https://arxiv.org/abs/2003.13713))

On 1d [[AQFT]] and [[smooth stacks]]:

* [[Marco Benini]], [[Marco Perin]], [[Alexander Schenkel]], *Smooth 1-dimensional algebraic quantum field theories* ([arXiv:2010.13808](https://arxiv.org/abs/2010.13808))

category: people


Marco Robalo

Marco Robalo works on [[derived algebraic geometry]], [[motives]], [[higher category theory]] and [[higher algebra]]. He was a Ph.D. student under the direction of [[Bertrand Toen]].

* [webpage](https://webusers.imj-prg.fr/~marco.robalo/)

## selected writings

* {#Robalo12} [[Marco Robalo]], _Noncommutative Motives I: A Universal Characterization of the Motivic Stable Homotopy Theory of Schemes_, June 2012 ([arxiv:1206.3645](http://arxiv.org/abs/1206.3645))

* {#Robalo15} [[Marco Robalo]], _K-theory and the bridge from motives to noncommutative motives_, Advances in Mathematics Volume 269, 10 January 2015 ([doi:10.1016/j.aim.2014.10.011](https://doi.org/10.1016/j.aim.2014.10.011))

## Related $n$Lab entries

* [[noncommutative motives]]

* [[stabilization]]

category: people


Marco Schlichting

Marco Schlichting is associate professor of [[mathematics]] at Warwick.

* [webpage](http://www2.warwick.ac.uk/fac/sci/maths/people/staff/marco_schlichting/)

## Selected writings

On [[Hermitian K-theory]]:

* [[Max Karoubi]], [[Marco Schlichting]], [[Charles Weibel]], *The Witt group of real algebraic varieties*, Journal of Topology **9** 4 (2016) 1257-1302 [[arXiv:1506.03862](https://arxiv.org/abs/1506.03862), [doi:10.1112/jtopol/jtw024]( https://doi.org/10.1112/jtopol/jtw024)]

* [[Marco Schlichting]], *Higher $K$-Theory of Forms I. From Rings to Exact Categories*, Journal of the Institute of Mathematics of Jussieu **20** 4 (2021) 1205-1273 [[doi:10.1017/S1474748019000410](https://doi.org/10.1017/S1474748019000410)]

## Related entries

* [[Waldhausen K-theory of a dg-category]]

category: people


Marco Toller

* [InSpire page](https://inspirehep.net/authors/1049013)

## Selected writings

On [[coset spaces]] ([[homogeneous spaces]]) of the [[Lorentz group]], such as the [[celestial sphere]]:

* {#Toller03} [[Marco Toller]], *Homogeneous Spaces of the Lorentz Group* [[arXiv:math-ph/0301014](https://arxiv.org/abs/math-ph/0301014)]

category: people


Marco Vergura

* [webpage](https://u.osu.edu/vergura.1/)

## Selected writings

On [[localization of an (infinity,1)-category|localization]] of [[(infinity,1)-topos|$\infty$-toposes]] motivated by [[modal homotopy type theory]]:

* [[Marco Vergura]], *Localization Theory in an Infinity Topos*, 2019 ([pdf](https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=8583&context=etd), [ir.lib.uwo.ca:etd/6257](https://ir.lib.uwo.ca/etd/6257))

category: people


Marco Volpe

* [GoogleScholar page](https://scholar.google.com/citations?user=kcDp8p8AAAAJ&hl=en)

## Selected writings

On a [[Grothendieck yoga of six operations]] for [[sheaves]] on [[topological spaces]]:

* [[Marco Volpe]], *The six operations in topology* [[arXiv:2110.10212](https://arxiv.org/abs/2110.10212)]

category: people


Marco Zambon

* [webpage](http://www.uam.es/personal_pdi/ciencias/mzambon/)

## Selected writings

On [[generalized Spin(7)-manifold|generalized]] [[Spin(7)-manifolds]] and [[M-theory on G2-manifolds]]:

* [[Mariana Graña]], [[Carlos S. Shahbazi]], [[Marco Zambon]], _$Spin(7)$-manifolds in compactifications to four dimensions_, JHEP11(2014)046 [[arXiv:1405.3698](http://arxiv.org/abs/1405.3698)]

category: people


Marcos Mariño

* [webpage](http://www.unige.ch/math/en/people/marino/)

## Selected writings

On [[Chern-Simons theory as topological string theory]]:

* [[Marcos Marino]], _Chern-Simons Theory and Topological Strings_, Rev. Mod. Phys. 77:675-720, 2005 ([arXiv:hep-th/0406005](https://arxiv.org/abs/hep-th/0406005))

On [[topological string theory]] and [[integrable systems]]:

* [[Mina Aganagic]], [[Robbert Dijkgraaf]], [[Albrecht Klemm]], [[Marcos Marino]], [[Cumrun Vafa]], *Topological Strings and Integrable Hierarchies*, Commun. Math. Phys. **261** (2006) 451-516 [[arXiv:hep-th/0312085](https://arxiv.org/abs/hep-th/0312085), [doi:10.1007/s00220-005-1448-9](https://doi.org/10.1007/s00220-005-1448-9)]

On [[quantum Seiberg-Witten curves]]:

* Alba Grassi, Jie Gu, [[Marcos Mariño]], *Non-perturbative approaches to the quantum Seiberg-Witten curve*,  J. High Energ. Phys. **2020** 106 (2020) [[arXiv:1908.07065](https://arxiv.org/abs/1908.07065), doi:10.1007/JHEP07(2020)106 ]

## Related entries

* [[non-perturbative effect]]

* [[instanton in QCD]]

* [[topological recursion]]

* [[topological string]]

category: people

[[!redirects Marcos Marino]]


Marcos Riojas

* [InSpire page](https://inspirehep.net/authors/1879703)

* [GoogleScholar page](https://scholar.google.com/citations?user=sbbDAK8AAAAJ&hl=en)

## Selected writings

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

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

and on what to do about it:

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

category: people


Marcus Grisaru

* [webpage](http://www.brandeis.edu/departments/physics/people/faculty/gris.html)

## selected writings

* {#GatesGrisaruRocekSiegel83} [[Jim Gates]] Jr, [[Marcus Grisaru]], [[Martin Roček]], [[Warren Siegel]], _Superspace, or One thousand and one lessons in supersymmetry_, Front.Phys. 58 (1983) 1-548  (1983) ([arXiv:hep-th/0108200](https://arxiv.org/abs/hep-th/0108200), [spire:195126](inspirehep.net/record/195126))

  (on [[superspace]])

category: people


Marcus Kracht

**Marcus Kracht** is a German modal logician and (mathematical) linguist. His work in linguistics comprises among others mathematical models of the Chomskian GB framework, application of modal logic to syntax, application of [[dynamic logic]] to argument structure ("referent systems"), and, the study of [[compositionality]].

He currently helds the chair in Computational Linguistics and Mathematical Linguistics at Universität Bielefeld.

His webpage is [here](http://wwwhomes.uni-bielefeld.de/mkracht/index-en.html).

category: people


Marcus Sperling

* [webpage](http://ymsc.tsinghua.edu.cn/content/show/146-146.html)

## Selected writings

Review of [[Coulomb branches]] of [[D=3 N=4 super Yang-Mills theory]]:

* [[Marcus Sperling]], _Two aspects of gauge theories : higher-dimensional instantons on cones over Sasaki-Einstein spaces and Coulomb branches for 3-dimensional $\mathcal{N}=4$ gauge theories_ ([spire:1495766/](http://inspirehep.net/record/1495766),  [pdf](https://www.itp.uni-hannover.de/fileadmin/arbeitsgruppen/ag_lechtenf/Theses/sperling.pdf), [[SperlingGaugeTheory.pdf:file]])

On [[KK-compactification]] of [[D=6 N=(1,0) SCFT]] on [[Riemann surfaces]] [[4d superconformal gauge field theory]]:

* [[Jin Chen]], [[Babak Haghighat]], [[Shuwei Liu]], [[Marcus Sperling]], _4d $\mathcal{N}=1$ from 6d D-type $\mathcal{N}=(1,0)$_,  J. High Energ. Phys. **2020** 152 (2020) [[arXiv:1907.00536](https://arxiv.org/abs/1907.00536), doi:10.1007/JHEP01(2020)152]

On [[D=6 N=(1,0) SCFT]] and [[heterotic M-theory on ADE-orbifolds]]:

* Santiago Cabrera, [[Amihay Hanany]], [[Marcus Sperling]], _Magnetic Quivers, Higgs Branches, and 6d $\mathcal{N}=(1,0)$ Theories_, J. High Energ. Phys. (2019) 2019: 71 ([arXiv:1904.12293](https://arxiv.org/abs/1904.12293))

On [[quantum Seiberg-Witten curves]] in relation to [[class S-theories]] and "[[M3]]"-[[defect branes]] inside [[M5-branes]]:

* [[Jin Chen]], [[Babak Haghighat]], [[Hee-Cheol Kim]], [[Marcus Sperling]], *Elliptic Quantum Curves of Class $\mathcal{S}_k$*,  J. High Energ. Phys. **2021** 28 (2021) [[arXiv:2008.05155](https://arxiv.org/abs/2008.05155), doi:10.1007/JHEP03(2021)028]

On [[quantum Seiberg-Witten curves]] of [[E-string]]-theories in relation to [[D6-D8-brane bound states]]:

* [[Jin Chen]], [[Babak Haghighat]], [[Hee-Cheol Kim]], [[Marcus Sperling]], [[Xin Wang]], *E-string Quantum Curve*, Nuclear Physics B **973** (2021) 115602 [[arXiv:2103.16996](https://arxiv.org/abs/2103.16996), [doi:10.1016/j.nuclphysb.2021.115602](https://doi.org/10.1016/j.nuclphysb.2021.115602)]

category: people


Marcus Spradlin

* [Institute page](https://vivo.brown.edu/display/mspradli)

## Selected writings

On [[twistor string theory]]:

* {#RoibanSpradlinVolovich04} [[Radu Roiban]], [[Marcus Spradlin]], [[Anastasia Volovich]], *On the Tree-Level S-Matrix of Yang-Mills Theory*, Phys. Rev. D70 : 026009, 2004 ([arXiv:hep-th/0403190](https://arxiv.org/abs/hep-th/0403190))

* {#Spradlin} [[Marcus Spradlin]], *Progress and Prospects in Twistor String Theory* ([pdf](https://conservancy.umn.edu/bitstream/handle/11299/130081/1/spradlin.pdf))

On [[configuration spaces of points]] in general poisition inside [[complex projective spaces]]:

* [[Nima Arkani-Hamed]], [[Thomas Lam]], [[Marcus Spradlin]], *Positive configuration space*, Commun. Math. Phys. **384** (2021) 909–954  [[arXiv:2003.03904](https://arxiv.org/abs/2003.03904), [doi:10.1007/s00220-021-04041-x](https://doi.org/10.1007/s00220-021-04041-x)]

category: people


Marcus Tressl

Marcus Tressl is a mathematical logician working in the [Model theory group](https://www.maths.manchester.ac.uk/research/expertise/model-theory/) of the University of Manchester (UK).

* [Home page](https://personalpages.manchester.ac.uk/staff/Marcus.Tressl/index.php)

## Selected writings

* [[Max Dickmann]], [[Niels Schwartz]], [[Marcus Tressl]], _Spectral Spaces_. New Mathematical Monographs 35 (2019).  Cambridge: Cambridge University Press. ISBN 9781107146723.

category:people


Marcy Robertson

Marcy Robertson is a lecturer at the University of Melbourne. She works on [[operad]] theory, [[homotopy theory]], and [[higher category theory]].

* [webpage](http://www.marcyrobertson.com)

category: people


Marek A. Bednarczyk

* [Academia page](https://pja.academia.edu/MarekBednarczyk)

## Selected writings

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

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

category: people

[[!redirects Marek Bednarczyk]]


Marek Filakovský

* [institute group page](https://ist.ac.at/en/research/wagner-group/)

## Selected writings

Discussion of ([[equivariant homotopy theory|equivariant]]) [[homotopies]] and [[homotopy groups]] in [[computational topology]]:

* [[Marek Filakovský]], [[Lukáš Vokřínek]], _Are two given maps homotopic? An algorithmic viewpoint_, Found Comput Math (2019) ([arXiv:1312.2337](https://arxiv.org/abs/1312.2337), [doi:10.1007/s10208-019-09419-x](https://doi.org/10.1007/s10208-019-09419-x))

* [[Marek Filakovsky]], [[Peter Franek]], [[Uli Wagner]], Stephan Zhechev, _Computing simplicial representatives of homotopy group elements_, J Appl. and Comput. Topology (2018) 2: 177. ([arXiv:1706.00380](https://arxiv.org/abs/1706.00380))

category: people

[[!redirects Marek Filakovsky]]


Marek Gluza

* [Institute page](https://www.physik.fu-berlin.de/en/einrichtungen/ag/ag-eisert/people/gluza/index.html)

## Selected writings

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

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

based on:

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

category: people


Marek Golasiński

Marek Golasiński is a [[homotopy theory|homotopy theorist]] working at the University of Warmia and Mazury, Poland.

## Selected writings

On the [[model structure on crossed complexes]]:

* [[Ronald Brown]], [[Marek Golasiński]]: _A model structure for the homotopy theory of crossed complexes_, Cahiers de Topologie et Géométrie Différentielle Catégoriques, **30** 1 (1989) 61-82 [[numdam:CTGDC_1989__30_1_61_0](http://www.numdam.org/item/?id=CTGDC_1989__30_1_61_0)]

On [[twisted Bredon cohomology]]:

* [[Marek Golasiński]], _Equivariant cohomology with local coefficients_, Mathematica Slovaca (1997) Volume: 47, Issue: 5, page 575-586 ([dml:34467](https://eudml.org/doc/34467))

On [[vector G-spaces]] and [[equivariant dgc-algebras]] in [[equivariant rational homotopy theory]]:

* [[Marek Golasiński]], _Componentwise injective models of functors to DGAs_, Colloquium Mathematicum, Vol. 73, No. 1 (1997)  ([dml:21048](https://eudml.org/doc/210480), [[GolasinskiInjectiveModels.pdf:file]])

* [[Marek Golasiński]], _Injective models of $G$-disconnected simplicial sets_,  Annales de l'Institut Fourier, Volume 47 (1997) no. 5, p. 1491-1522 ([numdam:AIF_1997__47_5_1491_0](http://www.numdam.org/item/?id=AIF_1997__47_5_1491_0))

On the [[model structure on equivariant dgc-algebras]] and the [[fundamental theorem of dg-algebraic rational homotopy theory]]:

* [[Marek Golasiński]], _Equivariant rational homotopy theory as a closed model category_, Journal of Pure and Applied Algebra Volume 133, Issue 3, 30 December 1998, Pages 271-287 (doi:10.1016/S0022-4049(97)00127-8)

On [[group cohomology]] of [[cyclic groups]] with [[coefficients]] in cyclic groups:

* {#GolasińskiGonçalves11} [[Marek Golasiński]], [[Daciberg Lima Gonçalves]], *On cohomologies and extensions of cyclic groups*, Topology and its Applications **158** (2011) 1858–1865 [[doi:10.1016/j.topol.2011.06.022](https://doi.org/10.1016/j.topol.2011.06.022)]

category:people

[[!redirects Marek Golasiński]]
[[!redirects Marek Golasinski]]
[[!redirects Golasiński]]
[[!redirects Golasinski]]


Marek Krčál

## Selected writings

On [[Cohomotopy]]-sets in [[computational topology]]:

* [[Martin Čadek]], [[Marek Krčál]], [[Jiří Matoušek]], [[Francis Sergeraert]], [[Lukáš Vokřínek]], [[Uli Wagner]], _Computing all maps into a sphere_, Journal of the ACM, Volume 61 Issue 3, May 2014 Article No. 1 ([arxiv:1105.6257](https://arxiv.org/abs/1105.6257))

Discussion of [[homotopy groups]] in [[computational topology]]:

* [[Martin Čadek]], [[Marek Krčál]], [[Jiří Matoušek]], [[Lukáš Vokřínek]], [[Uli Wagner]], _Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension_, SIAM J. Comput., 43(5), 1728–1780  ([arXiv:1211.3093](https://arxiv.org/abs/1211.3093), [doi:10.1137/120899029](https://doi.org/10.1137/120899029))

* [[Martin Čadek]], [[Marek Krčál]], [[Jiří Matoušek]], [[Lukáš Vokřínek]], [[Uli Wagner]], _Extendability of continuous maps is undecidable_, Discrete Comput Geom (2014) 51: 24 ([arXiv:1302.2370](https://arxiv.org/abs/1302.2370), [doi:10.1007/s00454-013-9551-8](https://doi.org/10.1007/s00454-013-9551-8))

On [[persistent Cohomotopy]] and its improvement over [[well groups]]:

* [[Peter Franek]], [[Marek Krčál]], _On Computability and Triviality of Well Groups_, Discrete Comput Geom (2016) 56: 126 ([arXiv:1501.03641](https://arxiv.org/abs/1501.03641), [doi:10.1007/s00454-016-9794-2](https://doi.org/10.1007/s00454-016-9794-2))

* [[Peter Franek]], [[Marek Krčál]], _Persistence of Zero Sets_, Homology, Homotopy and Applications, Volume 19 (2017) Number 2 ([arXiv:1507.04310](https://arxiv.org/abs/1507.04310), [doi:10.4310/HHA.2017.v19.n2.a16](http://dx.doi.org/10.4310/HHA.2017.v19.n2.a16))

* [[Peter Franek]], [[Marek Krčál]], _Cohomotopy groups capture robust Properties of Zero Sets via Homotopy Theory_, talk at [ACAT meeting 2015](https://www2.ist.ac.at/acat) ([pfd slides](https://www2.ist.ac.at/fileadmin/user_upload/events_pages/acat/ACAT2015_Marek_Krcal.pdf))

* [[Peter Franek]], [[Marek Krčál]], [[Hubert Wagner]], _Solving equations and optimization problems with uncertainty_, J Appl. and Comput. Topology (2018) 1: 297 ([arxiv:1607.06344](https://arxiv.org/abs/1607.06344), [doi:10.1007/s41468-017-0009-6](https://doi.org/10.1007/s41468-017-0009-6))

category: people

[[!redirects Marek Krcal]]


Marek Radzikowski

* [webpage](https://www.auaf.edu.af/academics/undergraduate-departments/science-and-mathematics/marek-radzikowski/)

## related $n$Lab entries

* [[Hadamard distribution]]

* [[locally covariant perturbative quantum field theory]]

category: people


Maren Justesen

Maren Justesen is a mathematician in Denmark who wrote a thesis on the bicategory of [[profunctors]] as master's student of [[Anders Kock]] in 1968.

## Selected writings

On the [[bicategory]] [[Prof]] of [[categories]] with [[profunctors]] between them:

* [[Maren Justesen]], *Bikategorien af Profunktorer*, Aarhus 1968 ([[Justesen_Profunktoren.pdf:file]])

category: people

[[!redirects M. Justesen]]


Maria Basterra

* [webpage](https://ceps.unh.edu/person/maria-basterra)

* [Mathematics Genealogy Page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=23591)

## Selected writings

On [[equivariant elliptic genera]]:

* [[Matthew Ando]], [[Maria Basterra]], _The Witten genus and equivariant elliptic cohomology_, Math Z 240, 787–822 (2002) ([arXiv:math/0008192](https://arxiv.org/abs/math/0008192), [doi:10.1007/s002090100399](https://doi.org/10.1007/s002090100399))

category: people


Maria Emilia Descotte

* [website](https://www.labri.fr/perso/mdescotte/)

## Relevant entries

* [[2-pro-object]]

category: people


Maria Maietti

* [webpage](http://www.math.unipd.it/~maietti/)

## Selected writings

On [[arithmetic pretoposes]]:

* {#Maietti05a} [[Maria Maietti]], _Reflection Into Models of Finite Decidable FP-sketches in an Arithmetic Universe_, Electronic Notes in Theoretical Computer Science
**122** (2005) 105-126 [[doi:10.1016/j.entcs.2004.06.054](https://doi.org/10.1016/j.entcs.2004.06.054)]

* {#Maietti05} [[Maria Maietti]], _Modular correspondence between dependent type theories and categories including pretopoi and topoi_, Mathematical Structures in Computer Science **15**  6 (2005) 1089-1149 [[doi:10.1017/S0960129505004962](https://doi.org/10.1017/S0960129505004962), [pdf](https://www.math.unipd.it/~maietti/papers/tumscs.pdf)]

* {#Maietti10} [[Maria E. Maietti]], _Joyal's arithmetic universe as list-arithmetic pretopos_ , TAC **24** 3 (2010) 39-83 [[tac:24-03](http://www.tac.mta.ca/tac/volumes/24/3/24-03abs.html), [pdf](http://www.tac.mta.ca/tac/volumes/24/3/24-03.pdf)]

* {#MaettiVickers12} [[Maria E. Maietti]], [[Steve Vickers]], _An induction principle for consequence in arithmetic universes_, JPAA **216** (2012) pp.2049-2067. [[doi:10.1016/j.jpaa.2012.02.040](https://doi.org/10.1016/j.jpaa.2012.02.040), [pdf](http://www.math.unipd.it/~maietti/papers/aumv12.pdf)]

## Related entries

* [[list-arithmetic pretopos]], [[incompleteness theorem]]

* [[relation between category theory and type theory]]

category: people

[[!redirects Maria E. Maietti]]
[[!redirects Maria Emilia Maietti]]


Maria Manuel Clementino

* [homepage](http://www.mat.uc.pt/~mmc/)

* [list of publications](http://www.mat.uc.pt/~mmc/publications.html)

category:people


Maria P. Garcia del Moral

* [InSpirePage](https://inspirehep.net/authors/1019914)

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

## Selected writings

On the [[super 2-brane in 4d]]-[[D=4 supergravity]]:

* [[Maria P. Garcia del Moral]], J. M. Pena, [[Alvaro Restuccia]], _$\mathcal{N}=1$ 4D Supermembrane from $11D$_, JHEP0807 039 (2008) [[arXiv:0709.4632](http://arxiv.org/abs/0709.4632)]

Lift of T-duality from [[string theory]] to a [[SL(2,Z)]]-[[U-duality]] acting on the [[M2-brane]]-[[Green-Schwarz action functional|sigma-model]]:

* [[Maria P. Garcia del Moral]], I. Martin, [[Alvaro Restuccia]], *Nonperturbative $SL(2,\mathbb{Z})$ $(p,q)$-strings manifestly realized on the quantum M2* [[arXiv:0802.0573](https://arxiv.org/abs/0802.0573)]

* [[Maria P. Garcia del Moral]], J. M. Pena, [[Alvaro Restuccia]], *Aspects of the T-duality construction for the Supermembrane theory*, J. Phys.: Conf. Ser. **720** (2016) 012025 [[arXiv:1504.06907](https://arxiv.org/abs/1504.06907), [doi:10.1088/1742-6596/720/1/012025](https://doi.org/10.1088/1742-6596/720/1/012025)]

On [[gauged supergravity|gauged]] [[D=9 supergravity]] from [[SL(2,Z)]]-[[U-duality]] acting on the [[M2-brane]]:

* [[Maria P. Garcia del Moral]], J. M. Pena, [[Alvaro Restuccia]], _Supermembrane origin of type II gauged supergravities in 9D_, JHEP 1209 (2012) 063 [[arXiv:1203.2767](http://arxiv.org/abs/1203.2767)]

* [[Maria P. Garcia del Moral]], C. Las Heras, P. Leon, J. M. Pena, [[Alvaro Restuccia]], _Fluxes, Twisted tori, Monodromy and $U(1)$ Supermembranes_,  J. High Energ. Phys. **2020** 97 (2020) [[arXiv:2005.06397](https://arxiv.org/abs/2005.06397), doi:10.1007/JHEP09(2020)097]

On [[massive type IIA supergravity]] via [[M2-branes]]:

* [[Maria P. Garcia del Moral]], [[Alvaro Restuccia]], *10D Massive Type IIA Supergravities as the uplift of Parabolic M2-brane Torus bundles*, Forthsch. d. Phys. **64** 4-5 (2016) [[arXiv:1511.04784](https://arxiv.org/abs/1511.04784), [doi:10.1002/prop.201500087](https://doi.org/10.1002/prop.201500087)]

* [[Maria P. Garcia del Moral]], P. Leon, [[Alvaro Restuccia]], *Wordsheet description of a* massive *type IIA superstring in 10D*, J. High Energ. Phys. **2023** 104 (2023) [[arXiv:2306.16620](https://arxiv.org/abs/2306.16620), doi:10.1007/JHEP11(2023)104]

category: people

[[!redirects Maria Garcia del Moral]]


Maria Smizanska

* [institute page](https://www.lancaster.ac.uk/physics/about-us/people/maria-smizanska)

## Selected writings

On [[B meson]]-[[decays]] and [[flavour anomalies]]:

* [[Patrick Koppenburg]], [[Zdenek Dolezal]], [[Maria Smizanska]], _Rare decays of b hadrons_, Scholarpedia, 11(6):32643 ([doi:10.4249/scholarpedia.32643](http://dx.doi.org/10.4249/scholarpedia.32643))

category: people


Mariana Graña

* [website](http://ipht.cea.fr/Pisp/39/mariana.grana.html)

## Selected writings

On the [[Myers effect]] in [[M-theory]] for [[M2-branes]] polarizing into [[M5-branes]] of [[fuzzy 3-sphere|fuzzy]] [[3-sphere]]-shape:

* [[Iosif Bena]], [[Mariana Graña]], Stanislav Kuperstein, Stefano Massai, _Tachyonic Anti-M2 Branes_, JHEP 1406:173, 2014 ([arXiv:1402.2294](https://arxiv.org/abs/1402.2294))

On [[generalized Spin(7)-manifold|generalized]]  [[Spin(7)-manifolds]] and [[M-theory on G2-manifolds]]:

* [[Mariana Graña]], [[Carlos S. Shahbazi]], [[Marco Zambon]], _$Spin(7)$-manifolds in compactifications to four dimensions_, JHEP11(2014)046 [[arXiv:1405.3698](http://arxiv.org/abs/1405.3698)]

category: people

[[!redirects Mariana Grana]]


Marianne Smith

* [Mathematics genealogy project](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=4032)

## Selected writings

* [[Marianne Smith]], _The Pontrjagin duality theorem in linear spaces_, Annals of Mathematics. 56(2): 248–253, ([doi:10.2307/1969798](https://doi.org/10.2307%2F1969798)).

## Related $n$Lab entries

* [[Smith space (functional analysis)]]

category: people


Marie Bjerrum

* [MO page](https://mathoverflow.net/users/26360/marie-bjerrum)

## Selected writings

On [[commutativity of limits with colimits]]:

* [[Marie Bjerrum]], [[Peter Johnstone]], [[Tom Leinster]], [[William F. Sawin]], *Notes on commutation of limits and colimits*, Theory and Applications of Categories **30** (2015), 527-532 [[arXiv:1409.7860](http://arxiv.org/abs/1409.7860), [tac:3015](http://www.tac.mta.ca/tac/volumes/30/15/30-15abs.html)]

category: people


Marie La Palme Reyes

* [webpage](http://reyes-reyes.com)

## Selected writings

An introduction to [[topos theory]] with emphasis on [[presheaf toposes]]:

* [[Marie La Palme Reyes]], [[Gonzalo E. Reyes]], [[Houman Zolfaghari]], _Generic figures and their glueings.  A constructive approach to functor categories_, Polimetrica (2008) [[pdf](https://marieetgonzalo.files.wordpress.com/2004/06/generic-figures.pdf), ISBN:8876990046]

## Related entries

* [[Gonzalo Reyes]]

* [[syllogism]]

category: people


Marie-Louise Michelsohn

* [webpage](http://www.math.sunysb.edu/~mlm/)

## Publications

* _[[Spin geometry]]_

category: people


Marija Zamaklar

* [webpage](https://www.dur.ac.uk/research/directory/staff/?mode=staff&id=5081)

## selected writings

* [[Kasper Peeters]], [[Marija Zamaklar]], _Euclidean Field Theory_, Lecture notes 2009-2011 ([web](http://maths.dur.ac.uk/users/kasper.peeters/eft.html), [pdf](http://maths.dur.ac.uk/users/kasper.peeters/pdf/eft.pdf))

## related $n$Lab entries

* [[Euclidean field theory]]

* [[lattice gauge theory]]

category: people


Marina Nielsen

## Selected writings

On [[hadron supersymmetry]] via [[light cone gauge|light cone]] [[supersymmetric quantum mechanics]] in [[holographic light front QCD]];

* {#NielsenBrodsky18} [[Marina Nielsen]], [[Stanley Brodsky]], _Hadronic Superpartners from Superconformal and Supersymmetric Algebra_, Phys. Rev. D 97, 114001 (2018) ([arXiv:1802.09652](https://arxiv.org/abs/1802.09652))

* [[Marina Nielsen]], [[Stanley Brodsky]], Guy F. de Téramond, [[Hans Günter Dosch]], Fernando S. Navarra, [[Liping Zou]], _Supersymmetry in the Double-Heavy Hadronic Spectrum_, Phys. Rev. D 98, 034002 (2018) ([arXiv:1805.11567](https://arxiv.org/abs/1805.11567))

In view of [[tetraquarks]]:

* [[Hans Günter Dosch]], [[Stanley Brodsky]], [[Guy de Teramond]], [[Marina Nielsen]], [[Liping Zou]], _Exotic States in a Holographic Theory_ ([arXiv:2012.02496](https://arxiv.org/abs/2012.02496))

category: people


Marino Gran

* [Homepage](http://perso.uclouvain.be/marino.gran/)

## Selected writings

On the [[exact completion]] of the [[classical homotopy category]] $Ho(Top)$ being a [[pretopos]]:

* [[Marino Gran]], [[Enrico Vitale]], *On the exact completion of the homotopy category*, Cahiers de Topologie et Géométrie Différentielle Catégoriques **39** 4 (1998)  287-297 [[numdam:CTGDC_1998__39_4_287_0](http://www.numdam.org/item/CTGDC_1998__39_4_287_0)]

On the category of [[internal categories]] in a [[Malcev category]]:

* {#Gran99} [[Marino Gran]], _Internal categories in Mal’cev categories_, Journal of Pure and Applied Algebra **143** 1-3 (1999) 221-229 [doi:10.1016/S0022-4049(98)00112-1]

For the characterisation of [[categories]] which are [[localizations]] of [[Maltsev varieties]]:

* [[Marino Gran]] and [[Enrico Vitale]], _Localizations of Maltsev varieties_, Theory and Applications of Categories **5** 12 (1999) 281-291 [[TAC](http://www.tac.mta.ca/tac/volumes/1999/n12/5-12abs.html)]

On [[regular categories]] and [[protomodular categories]]:

* [[Dominique Bourn]], [[Marino Gran]], _Regular, Protomodular, and Abelian Categories_, Chapter IV, pp.165-211 in: Maria Pedicchio, [[Walter Tholen]] (eds.), _Categorical Foundations_, Cambridge University Press 2004 ([doi:10.1017/CBO9781107340985.007](https://doi.org/10.1017/CBO9781107340985.007))

* {#Gran20} [[Marino Gran]], *An introduction to regular categories*, in: New Perspectives in Algebra, Topology and Categories,  Coimbra Mathematical Texts, Springer (2021) [[arXiv:2004.08964](https://arxiv.org/abs/2004.08964), [ISBN:978-3-030-84319-9](https://www.springerprofessional.de/en/new-perspectives-in-algebra-topology-and-categories/19764096)]

On [[Goursat categories]]:

* [[Marino Gran]], [[Diana Rodelo]], *A New Characterisation of Goursat Categories*, Applied Categorical Structures **20** (2012) 229–238 [[doi:10.1007/s10485-010-9236-x](https://doi.org/10.1007/s10485-010-9236-x)]

On the [[Beck-Chevalley condition]] in [[Goursat categories]]:

* [[Marino Gran]], [[Diana Rodelo]], *Beck-Chevalley condition and Goursat categories*, Journal of Pure and Applied Algebra **221** 10 (2017) 2445-2457 [[arXiv:1512.04066](https://arxiv.org/abs/1512.04066), [doi:10.1016/j.jpaa.2016.12.031](https://doi.org/10.1016/j.jpaa.2016.12.031)]

Presenting a [[pretorsion theory]] on [[Cat]] whose torsion(-free) objects are the [[groupoids]] ([[skeletal categories]], respectively), hence whose "trivial objects" are the [[skeletal groupoids]]:

* [[Francis Borceux]], [[Federico Campanini]], [[Marino Gran]], [[Walter Tholen]], *Groupoids and skeletal categories form a pretorsion theory in $Cat$* [[arXiv:2207.08487](https://arxiv.org/abs/2207.08487)]

category:people


Mario Bunge

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

* [institute page](https://www.mcgill.ca/philosophy/people/emeritus-faculty/bunge)

* Martin Mahner: *Mario Bunge (1919–2020): Conjoining Philosophy of Science and Scientific Philosophy*, Journal for General Philosophy of Science **52** (2021) 3–23 [[doi:10.1007/s10838-021-09553-7](https://doi.org/10.1007/s10838-021-09553-7)]

## Selected writings

On [[epistemic logic]] of [[necessity and possibility]] in view of [[probability|probabilistic]] theories of [[physics]] such as [[quantum mechanics]]:

* {#Bunge76} [[Mario Bunge]], *Possibility and Probability*, in: *Foundations of Probability Theory, Statistical Interference, and Statistical Theories of Science*, Reidel (1976) 17-34 [[doi:10.1007/978-94-010-1438-0_2](https://doi.org/10.1007/978-94-010-1438-0_2)]

## Related entries

* [[philosophy of science]]

* [[possible worlds]]

* [[Gell-Mann principle of quantum compulsion]]

category: people


Mario Flory

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

* [InSpire page](https://inspirehep.net/authors/1259940)

## Selected writings

On [[generalized quantum measurement channels]] and [[POVMs]]:

* {#Flory11} [[Mario Flory]], *POVMs and superoperators* (2011) [[pdf](https://wiki.physik.uni-muenchen.de/TMP/images/8/87/POVMs.pdf), [[Flory-POVM.pdf:file]]]

On [[perturbative quantum field theory]] and [[non-perturbative effects]]:

* {#FloryHellingSluka12} [[Mario Flory]], [[Robert C. Helling]], Constantin Sluka, *How I Learned to Stop Worrying and Love QFT* [[arXiv:1201.2714](https://arxiv.org/abs/1201.2714)]

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

* [[Mario Flory]], Sebastian Grieninger, Sergio Morales-Tejera, *Critical and near-critical relaxation of holographic superfluids* [[arXiv:2209.09251](https://arxiv.org/abs/2209.09251)]

category: people


Mario Garcia-Fernandez

* [Inspire page](https://inspirehep.net/authors/1072614)

* [MathGenealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=151995)

## Selected writings

On [[string Lie algebroids]]:

* [[Mario Garcia-Fernandez]], Roberto Rubio, Carl Tipler, *Holomorphic string algebroids*, Trans. Amer. Math. Soc. **373** 10 (2020) 7347-7382 [[arXiv:1807.10329](https://arxiv.org/abs/1807.10329), [doi:10.1090/tran/8149](https://doi.org/10.1090/tran/8149)]

* [[Mario Garcia-Fernandez]], Roberto Rubio, Carl Tipler, *Gauge theory for string algebroids*, Journal of Differential Geometry [[arXiv:2004.11399](https://arxiv.org/abs/2004.11399), [hal:02557365](https://hal.science/hal-02557365)]

category: people


Mario Pasquato

__Mario Pasquato__ is an astrophysicist interested in intermediate mass [[black holes]] (IMBH).

He lectured on them at [[Croatian Black Hole School]] in 2010. His other lectures
at clusters09 on *mass segregation method* for IMBH are [here](http://online.itp.ucsb.edu/online/clusters09/pasquato).

category: people


Mario Rasetti

* [institute page](https://www.theinnovationgroup.it/speakers/mario-rasetti/)

## Selected writings

The idea of [[adiabatic quantum computation]] ([[topological quantum computation]]) formulated in the generality of [[Berry phases]] for any [[loops]] in any external parameter space ([[holonomic quantum computation]]):

* [[Paolo Zanardi]], [[Mario Rasetti]], *Holonomic Quantum Computation*, Phys. Lett. A **264** (1999) 94-99 [doi:10.1016/S0375-9601(99)00803-8, [arXiv:quant-ph/9904011](https://arxiv.org/abs/quant-ph/9904011)]

* [[Jiannis Pachos]], [[Paolo Zanardi]], [[Mario Rasetti]], *Non-Abelian Berry connections for quantum computation*, Phys. Rev. A **61** (2000) 010305 [[arXiv:quant-ph/9907103](https://arxiv.org/abs/quant-ph/9907103), [doi:10.1103/PhysRevA.61.010305](https://doi.org/10.1103/PhysRevA.61.010305)]

category: people


Mario Román

I am currently undertaking a PhD at Tallinn University of Technology under the supervision of [[Pawel Sobocinski]].

* [Personal website.](https://mroman42.github.io/)

## Selected writings

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

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

category: people


Mario Tonin

* [webpage](https://www.sif.it/attivita/saggiatore/ricordo/tonin)

## Selected writings

On the [[superembedding approach]] for [[super p-branes|super $p$-branes]]/[[Green-Schwarz sigma-models]]:

* {#BPSTV95} [[Igor Bandos]], [[Paolo Pasti]], [[Dmitri Sorokin]], [[Mario Tonin]], [[Dmitry Volkov]], _Superstrings and supermembranes in the doubly supersymmetric geometrical approach_, Nucl. Phys. B **446** (1995) 79-118 [[arXiv:hep-th/9501113](https://arxiv.org/abs/hep-th/9501113)]

On [[self-dual higher gauge fields]]:

* [[Paolo Pasti]], [[Dmitri Sorokin]], [[Mario Tonin]], _On Lorentz Invariant Actions for Chiral P-Forms_, Phys.Rev. D55 (1997) 6292-6298 ([arXiv:hep-th/9611100](https://arxiv.org/abs/hep-th/9611100))

On [[10d supergravity]] and [[10d super Yang-Mills theory]]:

* {#BonoraBregolaLechnerPastiTonin87} [[Loriano Bonora]], M. Bregola, [[Kurt Lechner]], [[Paolo Pasti]], [[Mario Tonin]], _Anomaly-free supergravity and super-Yang-Mills theories in ten dimensions_, Nuclear Physics B
Volume 296, Issue 4, 25 January 1988 (doi:10.1016/0550-3213(88)90402-6)

* {#BonoraBregolaLechnerPastiTonin90} [[Loriano Bonora]], M. Bregola; [[Kurt Lechner]], [[Paolo Pasti]], [[Mario Tonin]], _A discussion of the constraints in $N=1$ SUGRA-SYM in 10-D_,  International Journal of Modern Physics A, February 1990, Vol. 05, No. 03 : pp. 461-477 (doi:10.1142/S0217751X90000222)

* {#BBDFLPPRRTZ} L. Bonora, M. Bregola, [[Riccardo D'Auria]], [[Pietro Fre]], [[Kurt Lechner]], [[Paolo Pasti]], I. Pesando, M. Raciti, F. Riva, [[Mario Tonin]] and D. Zanon, _Some remarks on the supersymmetrization of the Lorentz Chern-Simons form in $D = 10$ $N= 1$ supergravity theories_, Physics Letters B 277 (1992) ([[BonoraSuperGS.pdf:file]])

* {#LechnerTonin08} [[Kurt Lechner]], [[Mario Tonin]], _Superspace formulations of ten-dimensional supergravity_, JHEP 0806:021,2008 ([arXiv:0802.3869](https://arxiv.org/abs/0802.3869))

On [[dual heterotic string theory]]:

* [[Kurt Lechner]], [[Mario Tonin]], _Worldvolume and target space anomalies in the D=10 super--fivebrane sigma--model_ ([arXiv:hep-th/9603094](http://arxiv.org/abs/hep-th/9603094))

On the [[Green-Schwarz sigma-model]] for the [[M5-brane]]:

* {#BLNPST97} [[Igor Bandos]], [[Kurt Lechner]], [[Alexei Nurmagambetov]], [[Paolo Pasti]], [[Dmitri Sorokin]], [[Mario Tonin]], _Covariant Action for the Super-Five-Brane of M-Theory_, Phys. Rev. Lett. 78 (1997) 4332-4334 ([arXiv:hep-th/9701149](http://arxiv.org/abs/hep-th/9701149))

* {#PST97} [[Paolo Pasti]], [[Dmitri Sorokin]] and [[Mario Tonin]], _Covariant Action for a D=11 Five-Brane with the Chiral Field_, Phys. Lett. B398 (1997) 41 ([arXiv:hep-th/9701037](https://arxiv.org/abs/hep-th/9701037))

Formulation of ([[Lagrangian densities]] for) [[type II supergravity]] with "democratic"/"[[pregeometric RR-field|pregeometric]]" [[RR-fields]] subject to [[self-dual higher gauge theory|self-duality]]:

* [[Gianguido Dall'Agata]], [[Kurt Lechner]], [[Mario Tonin]], *$D=10$, $N=IIB$ Supergravity: Lorentz-invariant actions and duality*, JHEP 9807:017 (1998) [[arXiv:hep-th/9806140](https://arxiv.org/abs/hep-th/9806140), [doi:10.1088/1126-6708/1998/07/017](https://doi.org/10.1088/1126-6708/1998/07/017)]

## Related entries

* [[heterotic supergravity]]

* [[supergravity torsion constraints]]

* [[M5-brane]]

category: people


Mario Trigiante

* [InSpire page](https://inspirehep.net/authors/985668)

* [Institute page](https://www.polito.it/personale?p=013490)

## Selected writings

Usage of full [[supergravity]] (retaining the [[gravitino]]) for [[AdS-CMT]], with application to [[graphene]]-like systems:

* [[Laura Andrianopoli]], [[Bianca L. Cerchiai]], [[Riccardo D'Auria]], [[Mario Trigiante]], *Unconventional Supersymmetry at the Boundary of $AdS_4$ Supergravity*,  J. High Energ. Phys. **2018** 7 (2018) [[arXiv:1801.08081](https://arxiv.org/abs/1801.08081), doi:10.1007/JHEP04(2018)007]

* [[Laura Andrianopoli]], [[Bianca L. Cerchiai]], [[Riccardo D'Auria]], A. Gallerati, R. Noris, [[Mario Trigiante]], [[Jorge Zanelli]], *$\mathcal{N}$-Extended $D=4$ Supergravity, Unconventional SUSY and Graphene*, JHEP 01 (2020) 084 [[arXiv:1910.03508](https://arxiv.org/abs/1910.03508), doi:10.1007/JHEP01(2020)084]

On the [[self-dual higher gauge field]] on the [[M5-brane]] lifted to [[superspace]] in the [[D'Auria-Fré formulation of supergravity]]:

* {#ACDGMNRT22} [[Laura Andrianopoli]], [[C. A. Cremonini]], [[Riccardo D'Auria]], [[Pietro A. Grassi]], R. Matrecano, R. Noris, [[Lucrezia Ravera]], [[Mario Trigiante]], *M5-brane in the superspace approach*, Phys. Rev. D **106** 2 (2022) 026010 [[arXiv:2206.06388](https://arxiv.org/abs/2206.06388), [doi:10.1103/PhysRevD.106.026010](https://doi.org/10.1103/PhysRevD.106.026010)]

category: people


Mario Velásquez

* [personal page](https://sites.google.com/site/mavelasquezm/)

* [Google Scholar page](https://scholar.google.com.co/citations?user=lDakQSoAAAAJ&hl=en)

## Selected writings

On the analog of the [[Atiyah-Hirzebruch spectral sequence]] for [[twisted equivariant K-theory]] via the [[universal equivariant PU(H)-bundle|universal equivariant $PU(\mathcal{H})$-bundle]]:

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

category: people

[[!redirects Mario Velasquez]]


Marius Crainic

* [website](http://www.staff.science.uu.nl/~crain101/)

## Selected writings

On the [[cyclic homology]] of [[groupoid convolution algebras]] of [[étale groupoids]]:

* [[Marius Crainic]], *Cyclic Cohomology of Étale Groupoids; The General Case*, K-Theory 17: 319–362, 1999 ([arXiv:funct-an/9712001](https://arxiv.org/abs/funct-an/9712001), [published pdf](https://access.portico.org/Portico/rest/au/getAUContent?auId=ark:/27927/pgg1zfpvw2x&fileName=pgg1zfprgx2.pdf&viewType=PDF))

On [[Lie integration]] in the generality of [[Lie algebroids]] integrating to [[Lie groupoids]] (cf. [[Lie's three theorems]]):

* [[Marius Crainic]], [[Rui Loja Fernandes]], *Integrability of Lie brackets*, Ann. of Math. **157** 2 (2003) 575-620 [[arXiv:math.DG/0105033](http://arxiv.org/abs/math.DG/0105033), [doi:10.4007/annals.2003.157.575](https://doi.org/10.4007/annals.2003.157.575)]

* [[Rui Loja Fernandes]], [[Marius Crainic]], Ioan Mărcuţ, *Lectures on Integrability of Lie Brackets*, Geometry & Topology Monographs **17** (2011) 1–107 [[arxiv:math.DG/0611259](https://arxiv.org/abs/math/0611259), [doi:10.2140/gtm.2011.17.1](http://dx.doi.org/10.2140/gtm.2011.17.1)]

On [[differential geometry]] (including [[G-structures]]):

* [[Marius Crainic]], _[Differential geometry course](https://webspace.science.uu.nl/~crain101/DG-2015/)_, 2015 ([pdf](https://webspace.science.uu.nl/~crain101/DG-2015/main10.pdf), [[CrainicDifferentialGeometry15.pdf:file]])

On [[Poisson geometry]]:

* [[Marius Crainic]], [[Rui Loja Fernandes]], Ioan Mărcuţ, *Lectures on Poisson Geometry*, Graduate Studies in Mathematics **217**, Amer. Math. Soc. (2021) [[ISBN:978-1-4704-6430-1](https://bookstore.ams.org/view?ProductCode=GSM/217)]

On [[characteristic class]]es for [[Lie algebroid]]s

* [[Marius Crainic]], [[Rui Loja Fernandes]], _Secondary characteristic classes of Lie algebroids_, In: Carow-Watamura, U., Maeda, Y., Watamura, S. (eds) Quantum Field Theory and Noncommutative Geometry. Lecture Notes in Physics __662__, Springer [doi](https://doi.org/10.1007/113427869)

category: people


Marius Dadarlat

**Marius Dādārlat** is a Professor of Mathematics at [Purdue University](http://www.math.purdue.edu), working in [[operator algebras]] and [[noncommutative geometry]], including the methods of [[KK-theory]], [[E-theory]] and homotopy and [[shape theory]] for [[operator algebras]].

* [homepage](http://www.math.purdue.edu/~mdd)

* [publications](http://www.math.purdue.edu/~mdd/Papersd.html)

## Selected writings

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

* [[Marius Dadarlat]], [[Ulrich Pennig]], *Unit spectra of K-theory from strongly self-absorbing $C^\ast$-algebras*, Algebr. Geom. Topol. 15 (2015) 137-168 ([arXiv:1306.2583](https://arxiv.org/abs/1306.2583))

category: people

[[!redirects Marius Dadarlat]]
[[!redirects M. Dadarlat]]
[[!redirects Marius Dādārlat]]
[[!redirects M. Dādārlat]]


Mariusz Wodzicki

* [institute page](https://math.berkeley.edu/people/faculty/mariusz-wodzicki)

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

## Selected writings

Introducing the [[Wodzicki residue]]:

* [[Mariusz Wodzicki]], *Spectral asymmetry and noncommutative residue*, PhD thesis, Steklov Institute (1984)

* [[Mariusz Wodzicki]], *Noncommutative residue. I. Fundamentals*, in: *K-theory, arithmetic and geometry*, Lecture Notes in Math. __1289__, Springer (1987) 320-399 [[doi:10.1007%2FBFb0078372](http://dx.doi.org/10.1007%2FBFb0078372), [MR923140](http://www.ams.org/mathscinet-getitem?mr=923140)]

On [[Hermitian K-theory]]:

* [[Max Karoubi]], [[Mariusz Wodzicki]], *Algebraic and Hermitian K-theory of $\mathcal{K}$-rings*, The Quarterly Journal of Mathematics **64** 3 (2013) 903–940 [[arXiv:1310.4123](https://arxiv.org/abs/1310.4123), [doi:10.1093/qmath/hat030](https://doi.org/10.1093/qmath/hat030)]

category: people


Marja Kankaanrinta

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=15129)

## selected writings

* {#Kankaanrinta07} [[Marja Kankaanrinta]], _Equivariant collaring, tubular neighbourhood and gluing theorems for proper Lie group actions_,     Algebr. Geom. Topol. Volume 7, Number 1 (2007), 1-27 ([euclid:agt/1513796653](https://projecteuclid.org/euclid.agt/1513796653))

## related $n$Lab entries

* [[equivariant differential topology]]

category: people


Marjorie Batchelor

__Marjorie Batchelor__ is an American mathematician known for her work on [[coalgebra]]s ([[measuring coalgebra]]s in particular) and [[supermanifold]]s.

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

**(Batchelor's theorem)**

Every supermanifold is [[isomorphism|isomorphic]] to one of the form $\Pi E$ where $E$ is an ordinary smooth [[vector bundle]].

### Work on supermanifolds

### Work on coalgebras

* _Measuring coalgebras, quantum group-like objects, and non-commutative geometry_, In: Bartocci, C., [[Ugo Bruzzo|Bruzzo, U.]], Cianci, R. (eds) Differential Geometric Methods in Theoretical Physics. Lecture Notes in Physics __375__ [doi](https://doi.org/10.1007/3-540-53763-5_45)
* _Measuring comodules - their applications_, J.  Geom. Physics __36__:3-4 (2009) 251-269 (doi)
* _Difference operators, measuring coalgebras and quantum group like objects_, Adv. Math. __105__, 190-218 (1994) [pdf](https://core.ac.uk/download/pdf/81927027.pdf)

category: people
[[!redirects Marj Batchelor]]


Marjorie Senechal

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

## Selected writings

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

* [[Peter Engel]], [[Louis Michel]], [[Marjorie Senechal]], *Lattice Geometry*, IHES/P/04/45 (2004) $[$[pdf](https://cds.cern.ch/record/859509/files/cer-002542451.pdf), [cds:859509](https://cds.cern.ch/record/859509)$]$

category: people


Mark Behrens

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

## Selected writings

On the [[Boardman homomorphism]] (generalized [[Hurewicz homomorphism]]) to [[tmf]]:

* [[Mark Behrens]], [[Mark Mahowald]], J.D. Quigley, _The 2-primary Hurewicz image of $tmf$_ ([arXiv:2011.08956](https://arxiv.org/abs/2011.08956))

## Related $n$Lab entries

* [[tmf]]

* [[Goerss-Hopkins-Miller theorem]]

category: people


Mark Grant

## Selected writings

On [[topological complexity]] of [[configuration space]]:

* {#FarberGrant08} [[Michael Farber]], [[Mark Grant]], _Topological Complexity of the Klein bottle_ (2008), [arXiv:0806.4111](https://arxiv.org/pdf/0806.4111.pdf)


Mark Gross

__Mark Gross__ is an [[algebraic geometer]] at University of California at San Diego. Much of his research focuses on [[mirror symmetry]].

+ [webpage](http://www.math.ucsd.edu/~mgross/)

## Selected writings

On [[tropical geometry]] and [[mirror symmetry]]:

* _Tropical geometry and mirror symmetry_, CBMS regional conf. ser. 114 (2011), based on the CBMS course in Kansas, [AMS book page](http://www.ams.org/bookstore-getitem/item=CBMS-114), [pdf](http://www.math.ucsd.edu/~mgross/kansas.pdf)

* [slides](http://www.math.ucsd.edu/~mgross/current.pdf)

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))

category:people


Mark Haiman

* [personal page](https://math.berkeley.edu/~mhaiman/)

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

## Selected writings

On [[Lie groups]] and [[quantum groups]]:

* [[Richard Borcherds]], [[Mark Haiman]], [[Theo Johnson-Freyd]], [[Nicolai Reshetikhin]], [[Vera Serganova]], *Berkeley Lectures on Lie Groups and Quantum Groups*, 2020 ([pdf](http://categorified.net/LieQuantumGroups.pdf))

On [[double affine Hecke algebra]]s:

* [[Mark Haiman]], _Cherednik algebras, Macdonald polynomials and combinatorics_, Proc. ICM, Madrid 2006, Vol. III, 843--872, [djvu scan](http://www.mathunion.org/ICM/ICM2006.3/Main/icm2006.3.0843.0872.ocr.djvu), [author's pdf](https://math.berkeley.edu/~mhaiman/ftp/icm-2006/comb-mac-chered.pdf)

category: people


Mark Hovey

* [website](http://mhovey.web.wesleyan.edu/)

## Selected writings

On the [[Conner-Floyd isomorphism]] for the [[Atiyah-Bott-Shapiro orientation]] of [[KU]] and [[KO]] ([[cobordism theory determining homology theory]]):

* {#HopkinsHovey92} [[Michael Hopkins]], [[Mark Hovey]], _Spin cobordism determines real K-theory_, Mathematische Zeitschrift volume 210, pages 181–196 (1992) ([doi:10.1007/BF02571790](https://doi.org/10.1007/BF02571790), [[HopkinsHoveyCobordismK.pdf:file]])

On [[stable homotopy theory]]:

* [[Mark Hovey]], [[John Palmieri]], [[Neil Strickland]],  *Axiomatic stable homotopy theory*, Memoirs Amer. Math. Soc. **610** (1997) [[ISBN:978-1-4704-0195-5](https://bookstore.ams.org/memo-128-610), [pdf](http://www.math.rochester.edu/people/faculty/doug/otherpapers/axiomatic.pdf)]

On [[monoidal model categories]]:

* {#Hovey98} [[Mark Hovey]], _Monoidal model categories_ ([arXiv:math/9803002](https://arxiv.org/abs/math/9803002))

On [[model categories]]:

* [[Mark Hovey]], _[[Model Categories]]_, Mathematical Surveys and Monographs, Volume 63, AMS (1999) ([ISBN:978-0-8218-4361-1](https://bookstore.ams.org/surv-63-s),   [doi:10.1090/surv/063](https://doi.org/http://dx.doi.org/10.1090/surv/063), [pdf](https://www.math.rochester.edu/people/faculty/doug/otherpapers/hovey-model-cats.pdf), [Google books](http://books.google.co.uk/books?id=Kfs4uuiTXN0C&printsec=frontcover))

On general [[model structures on symmetric spectra]] (applicable e.g. to [[model structures for parameterized spectra]]):

* {#Hovey00} [[Mark Hovey]], *Spectra and symmetric spectra in general model categories*, Journal of Pure and Applied Algebra **165** 1 (2001) 63-127 [[arXiv:0004051](http://arxiv.org/abs/math/0004051), doi:10.1016/S0022-4049(00)00172-9]

On [[model structures on chain complexes]] in [[homological algebra]] (and in the generality of [[abelian sheaves]] of chain complexes):

* [[Mark Hovey]], *Model category structures on chain complexes of sheaves* (1999) [[K-theory:0366](https://faculty.math.illinois.edu/K-theory/0366), [pdf](https://faculty.math.illinois.edu/K-theory/0366/sheaves.pdf), [[Hovey-SheavesOfChainComplexesPreprint.pdf:file]]]

* {#Hovey01} [[Mark Hovey]], _Model category structures on chain complexes of sheaves_, Trans. Amer. Math. Soc. **353** 6 (2001) [[ams:S0002-9947-01-02721-0](https://www.ams.org/journals/tran/2001-353-06/S0002-9947-01-02721-0), [jstor:221954](https://www.jstor.org/stable/221954)]

* [[Dan Christensen]], [[Mark Hovey]], _Quillen model structures for relative homological algebra_, Math. Proc. Cambridge Philos. Soc. **133** 2 (2002) 261-293 [[arXiv:math/0011216](https://arxiv.org/abs/math/0011216), [doi:10.1017/S0305004102006126](https://doi.org/10.1017/S0305004102006126)]

On [[algebraic topology]]:

* [[Mark Hovey]], *[Algebraic Topology Problem List](https://www-users.cse.umn.edu/~tlawson/hovey/)*

## Related entries

* [[2-model category]]

category: people

[[!redirects Hovey]]


Mark John Hopkins

I am a computer programmer and mathematician living in Sydney, Australia. My PhD was in quantum algebra, under Alex Molev.

* [website](https://antiselfdual.com/)

category: people


Mark Johnson

* [personal page](http://personal.psu.edu/mwj3/)

## Selected writings

On [[model category]]-[[structures]] on [[categories]] of [[ex-spaces]] ([[retractive spaces]]):

* Michele Intermont, [[Mark Johnson]], *Model structures on the category of ex-spaces*, Topology and its Applications **119** 3 (2002) 325-353 [doi:10.1016/S0166-8641(01)00076-1]

On [[KK-theory]] via [[homotopical structure on C*-algebras]] (and using the notion of *[[l.m.c.-C*-algebra]]*):

* {#JoachimJohnson07} [[Michael Joachim]], [[Mark Johnson]], _Realizing Kasparov's KK-theory groups as the homotopy classes of maps of a Quillen model category_ ([arXiv:0705.1971](http://arxiv.org/abs/0705.1971))

category: people


Mark Jones

* [personal page](http://web.cecs.pdx.edu/~mpj/)

* [Gofer archive](http://web.cecs.pdx.edu/~mpj/goferarc/index.html)

* Wikipedia, Gofer (programming_language)

## Selected writings

On [[monad transformers]] in [[functional programming]] with [[monadic effects]]:

* {#LiangHudakJones95} Sheng Liang, [[Paul Hudak]], [[Mark Jones]], *Monad transformers and modular interpreters*, POPL '95 (1995) 333–343 [[doi:10.1145/199448.199528](https://doi.org/10.1145/199448.199528)]

## Related pages

* [[Haskell]]

* [[monad in computer science]]

category: people


Mark Kac

Mark Kac was a mathematician at Cornell University and Rockefeller University.

He got his PhD from the University of Lwów in 1937, advised by [[Hugo Steinhaus]].

## Selected writings

On the [[Feynman–Kac formula]]:

* [[Mark Kac]], _On distributions of certain Wiener functionals_, Transactions of the American Mathematical Society 65:1 (1949), 1–13.  [doi](http://dx.doi.org/10.1090/s0002-9947-1949-0027960-x).

category: people


Mark Kleiner

* [Institute page](https://thecollege.syr.edu/people/faculty/mark-kleiner/)

## Selected writings

On the [[equivalence of categories]] between the [[Kleisli category]] over a given [[monad]] with the [[co-Kleisli category]] of an [[adjoint functor|adjoint]] [[comonad]] (if it exists):

* [[Mark Kleiner]],  *Adjoint monads and an isomorphism of the Kleisli categories*, Journal of Algebra
Volume **133** 1 (1990) 79-82 [doi:10.1016/0021-8693(90)90069-Z]

category: people


Mark Lawson > history

[[!redirects Mark Lawson>History]]
[[!redirects Mark Lawson]]

* [webpage](http://www.macs.hw.ac.uk/staff-directory/mark-lawson.htm)

## related $n$Lab entries

* [[pseudogroup]]

category: people


Mark Losik

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=134051)

* S. V. Galaev,  _In Memory of Mork Vol’fovich Losik_, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 4, pp. 118-120 ([web](https://mmi.sgu.ru/en/articles/in-memory-of-mork-volfovich-losik), [pdf](https://mmi.sgu.ru/system/files_force/pril118-122.pdf?download=1))

## Selected writings

On [[Fréchet manifolds]] forming a [[full subcategory]] of [[diffeological spaces]]:

* {#Losik92} [[Mark Losik]], _Fréchet manifolds as diffeologic spaces_, Russian Mathematics 36:5 (1992), 36–42.  English translation: [PDF](https://dmitripavlov.org/scans/losik-frechet-manifolds-as-diffeologic-spaces.pdf).  Russian original: ([mathnet:ivm4812](http://mi.mathnet.ru/eng/ivm4812))

* {#Losik94} [[Mark Losik]], _Categorical Differential Geometry_. Cah. Topol. Géom. Différ. Catég., 35(4):274–290, 1994 ([numdam:CTGDC_1994__35_4_274_0](http://www.numdam.org/item/CTGDC_1994__35_4_274_0))

category: people

[[!redirects Mark Volfovich Losik]]


Mark M. Wilde

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

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

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

## Selected writings

On [[quantum information theory]]:

* [[Mark M. Wilde]], *Quantum Information Theory*, Cambridge University Press (2013) [[doi:10.1017/CBO9781139525343](https://doi.org/10.1017/CBO9781139525343), [arXiv:1106.1445](https://arxiv.org/abs/1106.1445)]

* [[Sumeet Khatri]], [[Mark M. Wilde]], *Principles of Quantum Communication Theory: A Modern Approach* [[arXiv:2011.04672](https://arxiv.org/abs/2011.04672)]

category: people

[[!redirects Mark Wilde]]


Mark Mahowald

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

* [[Haynes Miller]], [[Doug Ravenel]], _Mark Mahowald's work on the homotopy groups of spheres_ ([pdf](http://www-math.mit.edu/~hrm/ksem/miller-ravenel.pdf))

## Selected writings

On [[stable homotopy groups of spheres]] and [[chromatic homotopy theory]]:

* {#MahowaldRavenel87} [[Mark Mahowald]], [[Doug Ravenel]], _Towards  a Global Understanding of the Homotopy Groups of Spheres_, in: [[Samuel Gitler]] (ed.): _The Lefschetz Centennial Conference: Proceedings on Algebraic Topology II_, Contemporary Mathematics volume 58, AMS 1987  ([ISBN:978-0-8218-5063-3](https://bookstore.ams.org/conm-58-2), [pdf](http://www.math.rochester.edu/people/faculty/doug/mypapers/global.pdf), [[MahowaldRavenelHomotopyGroupsOfSpheres.pdf:file]])

On [[Goodwillie calculus]] and [[chromatic homotopy theory]]:

* {#AroneMahowald98} [[Greg Arone]], [[Mark Mahowald]], _The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres_, Inventiones mathematicae, February 1999, Volume 135, Issue 3, pp 743-788 ([pdf](http://hopf.math.purdue.edu/Arone-Mahowald/ArMahowald.pdf), [doi:10.1007/s002220050300](https://doi.org/10.1007/s002220050300))

On the [[Boardman homomorphism]] (generalized [[Hurewicz homomorphism]]) to [[tmf]]:

* [[Mark Behrens]], [[Mark Mahowald]], J.D. Quigley, _The 2-primary Hurewicz image of $tmf$_ ([arXiv:2011.08956](https://arxiv.org/abs/2011.08956))

## Related entries

* [[J-homomorphism]]

category: people


Mark Meckes

* [personal page](https://case.edu/artsci/math/mwmeckes/)

* [institute page](https://mathstats.case.edu/faculty/mark-meckes/)

## Selected writings

On [[matrix analysis]] ([[Gershgorin circle theorem]], etc.):

* {#Meckes19} [[Mark Meckes]], *Lecture notes on matrix analysis*, 2019 ([pdf](https://case.edu/artsci/math/mwmeckes/matrix-analysis.pdf), [[MeckesMatrixAnalysis.pdf:file]])

category: people


Mark Mostow

* [MathematicsGenealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=92604)

## Selected writings

On [[universal connections]] via realizing [[classifying spaces]] as [[diffeological spaces]]:

* [[Mark Mostow]], _The differentiable space structures of Milnor classifying spaces, simplicial complexes, and geometric realizations_, J. Differential Geom. Volume 14, Number 2 (1979), 255-293 ([euclid:jdg/1214434974](https://projecteuclid.org/euclid.jdg/1214434974))

category people


Mark Naimark

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

## Selected writings

Introducing the [[GNS construction]]:

* {#GelfandNaimark43} [[Israel Gelfand]], [[Mark Naimark]], *On the imbedding of normed rings into the ring of operators on a Hilbert space*,  Matematicheskii Sbornik. 12 (2): 197–217 (1943)

  reprinted in:

  Robert Doran (ed.), *$C^\ast$-Algebras: 1943–1993*, Contemporary Mathematics **167**, AMS 1994 ([doi:10.1090/conm/167](http://dx.doi.org/10.1090/conm/167))

category: people

[[!redirects Mark A. Naimark]]


Mark Pollicott

* [webpage](http://homepages.warwick.ac.uk/~masdbl/)

## related $n$Lab entries

* [[zeta function]]

* [[zeta function of a dynamical system]]

category: people


Mark R. Dowling

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

## Selected writings

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

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

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

category: people

[[!redirects Mark Dowling]]


Mark Rieffel

__Marc A. Rieffel__ is a Professor of Mathematics at the University of California at Berkeley. Much of his research is in operator algebras, including in the framework of noncommutative geometry. He introduced
notions of strong Morita equivalence and of strong deformation quantization.

* personal [page](http://math.berkeley.edu/~rieffel) at Berkeley (includes links to files of some older papers)

* _Lie group convolution algebras as deformation quantizations of linear Poisson structures_, Amer. J. of Mathematics __112__, No. 4 (Aug., 1990), pp. 657-685, [jstor](http://www.jstor.org/stable/2374874)

* _Dirac operators for coadjoint orbits of compact Lie groups_,  Münster J. Math.  2  (2009), 265--297.

* Marc A. Rieffel, [[Albert Schwarz]], _Morita equivalence of multidimensional noncommutative tori_,  Internat. J. Math. __10__  (1999),  no. 2, 289--299.

* Lawrence G. Brown, Philip Green, Marc A. Rieffel, _Stable isomorphism and strong Morita equivalence of $C^\star$-algebras_,  Pacific J. Math. __71__  (1977), no. 2, 349--363,

* _Continuous fields of $C^\star$-algebras coming from group cocycles and actions_, Math. Ann. __283__ (1989), 631-643.

* _Morita equivalence for $C^{\star}$-algebras and $W^{\star}$-algebras_,  J. Pure Appl. Algebra __5__  (1974), 51--96, doi

* _Induced representations of $C^{\star}$-algebras_,  Bull. Amer. Math. Soc.  __78__  (1972), 606--609, [link](http://www.ams.org/journals/bull/1972-78-04/S0002-9904-1972-13026-X/home.html)

* _Morita equivalence for operator algebras_, Proceedings of Symposia in Pure Mathematics 38 (1982) Part I, 285-298, [file](http://math.berkeley.edu/~rieffel/papers/morita_equivalence.pdf)

category: people


Mark Ryan

[[!redirects M. D. Ryan]]
* [homepage](http://www.cs.bham.ac.uk/~mdr/research/papers/)

category:people


Mark S. Burgin

* [MathGenealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=183077)

* [MDPI obituary](https://www.mdpi.com/about/announcements/5474)

## Selected writings

Early discussion of [[categories with involution]] (now: "[[dagger categories]]"):

* {#Burgin70} [[Mark S. Burgin]], *Categories with involution, and correspondences in $\gamma$-categories*, Trudy Moskovskogo Matematicheskogo Obshchestva **22** (1970) 161–228 [[mathnet:mmo235](https://www.mathnet.ru/eng/mmo235)]

On [[information theory]]:

* [[Mark Burgin]], *Theory of information*, World Scientific (2009) [[doi:10.1142/7048](https://doi.org/10.1142/7048)]

category: people

[[!redirects Mark Burgin]]


Mark Shimozono

* [personal page](https://personal.math.vt.edu/mshimo/)

* [institute page](https://math.vt.edu/people/faculty/shimozono-mark.html)

## Selected writings

Proving the [[Peterson isomorphism]] relating the [[quantum cohomology]] of [[flag varieties]] with a [[Pontryagin ring]]:

* [[Thomas Lam]], [[Mark Shimozono]], *Quantum cohomology of $G/P$ and homology of affine Grassmannian*, Acta Mathematica **204** (2010) 49–90 [[arXiv:0705.1386](https://arxiv.org/abs/0705.1386), [doi:10.1007/s11511-010-0045-8](https://doi.org/10.1007/s11511-010-0045-8)]

The variant for [[Pontryagin products]] not in [[ordinary homology]] but in [[topological K-theory|topological]] [[K-homology]]:

* [[Thomas Lam]], [[Changzheng Li]], [[Leonardo C. Mihalcea]], [[Mark Shimozono]], *A conjectural Peterson isomorphism in K-theory*, Journal of Algebra **513** (2018) 326-343 [[doi:10.1016/j.jalgebra.2018.07.029](https://doi.org/10.1016/j.jalgebra.2018.07.029), [arXiv:1705.03435](https://arxiv.org/abs/1705.03435)]

category: people


Mark Srednicki

* [Wikipedia entry](http://web.physics.ucsb.edu/~mark/)

## related $n$Lab entries

* [[axion]]

category: people


Mark Steinberger

* [ResearchGate page](https://www.researchgate.net/profile/Mark-Steinberger)

* [Obituary](https://gordoncemerickfuneralhome.com/tribute/details/598/Dr-Mark-Steinberger/obituary.html)

## Selected writings

On [[equivariant stable homotopy theory]]:

* {#LewisMaySteinberger86} [[L. Gaunce Lewis]], [[Peter May]], [[Mark Steinberger]] (with contributions by [[James McClure|J.E. McClure]]), _Equivariant stable homotopy theory_, Springer Lecture Notes in Mathematics  **1213** (1986) [[pdf](http://www.math.uchicago.edu/~may/BOOKS/equi.pdf), [doi:10.1007/BFb0075778](https://link.springer.com/book/10.1007/BFb0075778)]

On [[H-infinity ring spectra|$H_\infty$-ring spectra]]:

* {#BrunerMayMcLureSteinberger86} [[Robert Bruner]], [[Peter May]], [[James McClure]], [[Mark Steinberger]], *$H_\infty$-Ring Spectra and their Applications*, Lecture Notes in Mathematics **1176**, Springer (1986) [[doi:10.1007/BFb0075405](https://link.springer.com/book/10.1007/BFb0075405), [pdf](http://www.math.uchicago.edu/~may/BOOKS/h_infty.pdf)]

category: people


Mark V. Lawson

Mark Lawson is a professor at Heriot-Watt University, Edinburgh.  He has published extensively on inverse semigroups, finite automata and their interactions with other parts of mathematics and computer science.

* [homepage](http://www.ma.hw.ac.uk/~markl/)

* [Heriot-Watt departmental webpage](http://www.macs.hw.ac.uk/staff-directory/mark-lawson.htm)

## related $n$Lab entries

* [[inverse semigroup]]

* [[pseudogroup]]

category:people
[[!redirects M. V. Lawson]]
[[!redirects Mark Lawson]]
[[!redirects M.V.Lawson]]