# Ronald Brown (mathematician)

**Ronald Brown** is an English mathematician. Emeritus Professor in the School of Computer Science at Bangor University,[1] he has authored many books and more than 160 journal articles.

Ronald Brown | |
---|---|

Brown in a 1987 lecture video | |

Born | |

Nationality | United Kingdom |

Alma mater | University of Oxford |

Scientific career | |

Fields | Mathematics |

Institutions | University of Liverpool University of Hull Bangor University |

Thesis | Some problems of algebraic topology (1962) |

Doctoral advisors | J. H. C. Whitehead Michael G. Barratt |

Doctoral students | 21 |

## Education and career

Born on 4 January 1935 in London, Brown attended Oxford University, obtaining a B.A. in 1956 and a D.Phil. in 1962.[2] Brown began his teaching career during his doctorate work, serving as an assistant lecturer at the University of Liverpool before assuming the position of Lecturer. In 1964, he took a position at the University of Hull, serving first as a Senior Lecturer and then as a Reader before becoming a Professor of pure mathematics at Bangor University, then a part of the University of Wales, in 1970.

Brown served as Professor of Pure Mathematics for 30 years; he also served during the 1983–84 term as a Professor for one month at Louis Pasteur University in Strasbourg.[2] In 1999, Brown took a half-time research professorship until he became Professor Emeritus in 2001. He was elected as a Fellow of the Learned Society of Wales in 2016.

## Editing and writing

Brown has served as an editor or on the editorial board for a number of print and electronic journals. He began in 1968 with the *Chapman & Hall Mathematics Series*, contributing through 1986.[2] In 1975, he joined the editorial advisory board of the London Mathematical Society, remaining through 1994. Two years later, he joined the editorial board of Applied Categorical Structures,[3] continuing through 2007. From 1995 and 1999, respectively, he has been active with the electronic journals *Theory and Applications of Categories*[4] and *Homology, Homotopy and Applications*,[5] which he helped found. Since 2006, he has been involved with *Journal of Homotopy and Related Structures*.[6] His mathematical research interests range from algebraic topology and groupoids, to homology theory, category theory, mathematical biology, mathematical physics and higher-dimensional algebra.[7][8][9][10][11]

Brown has authored or edited a number of books and over 160 academic papers published in academic journals or collections. His first published paper was "Ten topologies for X × Y", which was published in the *Quarterly Journal of Mathematics* in 1963[12] Since then, his publications have appeared in many journals, including but not limited to the *Journal of Algebra*, *Proceedings of the American Mathematical Society*, *Mathematische Zeitschrift*, *College Mathematics Journal*, and *American Mathematical Monthly*. He is also known for several recent co-authored papers on categorical ontology.[13]

Among his several books and standard topology and algebraic topology textbooks are: *Elements of Modern Topology* (1968), *Low-Dimensional Topology* (1979, co-edited with T.L. Thickstun), *Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid* (1998),[14][15] *Topology and Groupoids* (2006)[16] and *Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids* (EMS, 2010).[16][17][18][19][20][21][22][23][24][25]

His recent fundamental results that extend the classical Van Kampen theorem to higher homotopy in higher dimensions (HHSvKT) are of substantial interest for solving several problems in algebraic topology, both old and new.[26] Moreover, developments in algebraic topology have often had wider implications, as for example in algebraic geometry and also in algebraic number theory. Such higher-dimensional (HHSvKT) theorems are about homotopy invariants of structured spaces, and especially those for filtered spaces or *n*-cubes of spaces. An example is the fact that the relative Hurewicz theorem is a consequence of HHSvKT, and this then suggested a triadic Hurewicz theorem.

## See also

## References

- http://www.bangor.ac.uk/~mas010/ Page at Bangor University, UK
- "Ronald Brown: Biographical Sketch".
*Bangor University*. Retrieved 2010-04-23. - "
*Applied Categorical Structures*".*Springer Publishers, Berlin*. 2010-12-08. Retrieved 2010-12-11. - EDITORIAL BOARD of the International journal
*Theory and Applications of Categories*http://www.tac.mta.ca/tac/geninfo.html#edlist - EDITORIAL BOARD of the International journal
*Homology, Homotopy and Applications*http://www.intlpress.com/HHA/editors.htm - Listed in the Editors' List of the International
*Journal of Homotopy and Related Structures*http://tcms.org.ge/Journals/JHRS/editors.htm - Editor Ronald Brown's research interests: Category theory, higher-dimensional algebra, holonomy, groupoids and crossed objects in algebraic topology. http://emis.kaist.ac.kr/journals/JHRS/interests.htm
- Cited by John C. Baez, James Dolan., in Higher-Dimensional Algebra III: n-categories and the Algebra of Opetopes, quantum algebra and Topology, Adv. Math. 135 (1998), 145-206.
- Cited by Georgescu, George and Popescu, Andrei., in "A common generalization for MV-algebras and Łukasiewicz-Moisil algebras",
*Archive for Mathematical Logic*, Vol. 45, No. 8. (November 2006), pp. 947-981. (in reference to Heyting-algebra higher-dimensional-algebra hyperalgebras Łukasiewicz-Moisil-algebras meta-logics MV-algebras on 2007-07-11) - Cited by John C. Baez, Laurel Langford., in "Higher-Dimensional Algebra IV: 2-Tangles", (
*Quantum Algebra*(math.QA);*Algebraic Topology*(math.AT);*Category Theory*(math.CT)),*Adv. Math.*. 180 (2003), 705-764 http://www.azimuthproject.org/azimuth/show/John+Baez - Cited in "Higher-dimensional Algebra and Topological Quantum Field Theory"
*J.Math.Phys*.**36**(1995) 6073-6105, by John C. Baez, James Dolan, (2004) https://arxiv.org/abs/q-alg/9503002 doi:10.1063/1.531236 - "Ronald Brown Publications".
*Bangor University*. 2008-04-19. Archived from the original on 2008-04-24. Retrieved 2010-04-23. - Cited in Online research in philosophy Entries: http://philpapers.org/
- Cited in Encyclopaedia of Mathematics - ISBN 1-4020-0609-8
- Referenced in
*Algebraic homotopy*http://eom.springer.de/A/a130170.htm - Cited in "Bibliography For Groupoids And Algebraic Topology" http://myyn.org/m/article/bibliography-for-groupoids-and-algebraic-topology/
- http://sz0009.ev.mail.comcast.net/service/home/~/Tracts_vol15.pdf?auth=co&loc=en_US&id=128480&part=2 and www.ems-ph.org :
*EMS Tracts in Mathematics*, Vol. 15 - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.6444 CiteSeerX accessed on 12/10/2010
- Review of "Nonabelian Algebraic Topology" in
*nLab* - A Review of "Nonabelian Algebraic Topology" by Prof. J. Baez on June 6, 2009 http://golem.ph.utexas.edu/category/2009/06/nonabelian_algebraic_topology.html
- Addebook • Apr 22nd, 2009 • Category: Mathematics :
*Nonabelian Algebraic Topology*http://www.addebook.com/tech2/mathematics/nonabelian-algebraic-topology_4164.html - Cited on p. xi as a basic reference in "Non-abelian Theories" http://myyn.org/m/article/non-abelian-theories/
- [ALGTOP-L] available full draft of book on
*Nonabelian algebraic topology*https://lists.lehigh.edu/pipermail/algtop-l/2009q2/000443.html - Cited in "Towards Higher Categories" By John C. Baez and J. Peter May, Publisher: Springer Verlag,Published Date: 2009-10-01, ISBN 978-1-4419-1523-8 http://www.isbnlib.com/author/John_C__Baez
- Referenced in nonabelian cohomology in
*nLab* - The higher Van Kampen Theorems and computation of the unstable homotopy groups of spheres and complex spaces https://mathoverflow.net/q/39818

## External links

- Ronald Brown at the Mathematics Genealogy Project
- "Ronald Brown's Biography and publications".
- "Ronald Brown's Home Page".
- "MathOverflow user page".
- Higher-Dimensional Algebra citations list
*Editorial Board of Journal of Homotopy and Related Structures (JHRS*)- nLab Abstract Mathematics Website
- Editorial Board of
*Homology, Homotopy and Applications (HHA)* - The Origins of `Pursuing Stacks' by Alexander Grothendieck
- Homology, Homotopy and Applications
- Theory and Applications of Categories