Ronald Brown (mathematician)
Encyclopedia
Ronald Brown is an English
mathematician
. Emeritus Professor in the School of Computer Science at Bangor University
, he has authored many books and journal articles.
, Brown attended Oxford University, obtaining a B.A. in 1956 and a Ph.D. in 1962. Brown began his teaching career during his Ph.D. work, serving as an assistant lecturer at Liverpool University before assuming the position as lecturer. In 1964, he took a position at Hull University, 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 29 years, also serving briefly during the 1983-1984 term as an associate professor at Louis Pasteur University
in Strasbourg
. In 1999, Brown took a half-time research professorship until he became Professor Emeritus in 2001.
or on the editorial board
for a number of print and electronic journal
s. He began in 1968 with the Chapman & Hall Mathematics Series, contributing through 1986. 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
, continuing through 2007. From 1995 and 1999, respectively, he has been active with the electronic journals [Theory and Applications of Categories http://www.tac.mta.ca/tac/] and [Homology, Homotopy and Applications http://www.intlpress.com/ ], which he helped found. Since 2006, he has been involved with Journal of Homotopy and Related Structures
. His mathematical research interests range from algebraic topology
and groupoid
s, to homology theory
, category theory
, mathematical biology
, mathematical physics
and higher dimensional algebra.
Brown has authored or edited a number of books and over 150 academic papers published in academic journals or collections. His first published paper was "Ten topologies for $X\times Y$", which was published in the Quarterly Journal of Math in 1963 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
.
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), Topology and Groupoids (2006) and Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids (EMS, 2010).
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. 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. A nice example is the fact that the relative Hurewicz theorem is a consequence of HHSvKT, and this then suggested a triadic Hurewicz theorem
.
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. Emeritus Professor in the School of Computer Science at Bangor University
Bangor University
Bangor University is a university based in the city of Bangor in the county of Gwynedd in North Wales-United Kingdom.It was officially known for most of its history as the University College of North Wales...
, he has authored many books and journal articles.
Education and career
Born on 4 January 1935 in LondonLondon
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
, Brown attended Oxford University, obtaining a B.A. in 1956 and a Ph.D. in 1962. Brown began his teaching career during his Ph.D. work, serving as an assistant lecturer at Liverpool University before assuming the position as lecturer. In 1964, he took a position at Hull University, serving first as a senior lecturer and then as a reader before becoming a professor of pure mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
at Bangor University, then a part of the University of Wales
University of Wales
The University of Wales was a confederal university founded in 1893. It had accredited institutions throughout Wales, and formerly accredited courses in Britain and abroad, with over 100,000 students, but in October 2011, after a number of scandals, it withdrew all accreditation, and it was...
, in 1970.
Brown served as professor of pure mathematics for 29 years, also serving briefly during the 1983-1984 term as an associate professor at Louis Pasteur University
Louis Pasteur University
Louis Pasteur University , also known as Strasbourg I or ULP was a large university in Strasbourg, Alsace, France. As of January 15, 2007, there were 18,847 students enrolled at the university, including around 3,000 foreign students. Research and teaching at ULP concentrates on the natural...
in Strasbourg
Strasbourg
Strasbourg is the capital and principal city of the Alsace region in eastern France and is the official seat of the European Parliament. Located close to the border with Germany, it is the capital of the Bas-Rhin département. The city and the region of Alsace are historically German-speaking,...
. In 1999, Brown took a half-time research professorship until he became Professor Emeritus in 2001.
Editing and writing
Brown has served as an editorEditor
The term editor may refer to:As a person who does editing:* Editor in chief, having final responsibility for a publication's operations and policies* Copy editing, making formatting changes and other improvements to text...
or on the editorial board
Editorial board
The editorial board is a group of people, usually at a publication, who dictate the tone and direction the publication's editorial policy will take.- Board makeup :...
for a number of print and electronic journal
Electronic journal
Electronic journals, also known as ejournals, e-journals, and electronic serials, are scholarly journals or intellectual magazines that can be accessed via electronic transmission. In practice, this means that they are usually published on the Web...
s. He began in 1968 with the Chapman & Hall Mathematics Series, contributing through 1986. In 1975, he joined the editorial advisory board of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
, remaining through 1994. Two years later, he joined the editorial board of Applied Categorical Structures
Springer Science+Business Media
- Selected publications :* Encyclopaedia of Mathematics* Ergebnisse der Mathematik und ihrer Grenzgebiete * Graduate Texts in Mathematics * Grothendieck's Séminaire de géométrie algébrique...
, continuing through 2007. From 1995 and 1999, respectively, he has been active with the electronic journals [Theory and Applications of Categories http://www.tac.mta.ca/tac/] and [Homology, Homotopy and Applications http://www.intlpress.com/ ], which he helped found. Since 2006, he has been involved with Journal of Homotopy and Related Structures
ArXiv
The arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...
. His mathematical research interests range from algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
and groupoid
Groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid generalises the notion of group in several equivalent ways. A groupoid can be seen as a:...
s, to homology theory
Homology theory
In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of homology theories on topological spaces.-The general idea:...
, category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
, mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
and higher dimensional algebra.
Brown has authored or edited a number of books and over 150 academic papers published in academic journals or collections. His first published paper was "Ten topologies for $X\times Y$", which was published in the Quarterly Journal of Math in 1963 Since then, his publications have appeared in many journals, including but not limited to the Journal of Algebra
Journal of Algebra
Journal of Algebra is a leading international mathematical research journal in algebra. An imprint of Academic Press, it is presently published by Elsevier. Journal of Algebra was founded by Graham Higman, who was its editor from 1964 to 1984. From 1985 until 2000, Walter Feit served as its...
, Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society is a monthly mathematics journal published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages....
, Mathematische Zeitschrift
Mathematische Zeitschrift
Mathematische Zeitschrift is a mathematical journal for pure and applied mathematics published by Springer Verlag....
, College Mathematics Journal
College Mathematics Journal
The College Mathematics Journal, published by the Mathematical Association of America, is an expository journal aimed at teachers of college mathematics, particular those teaching the first two years. It is a continuation of Two-Year College Mathematics Journal. It covers all aspects of mathematics...
, and American Mathematical Monthly
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
. He is also known for several recent co-authored papers on Categorical ontology
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
.
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), Topology and Groupoids (2006) and Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids (EMS, 2010).
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. 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. A nice example is the fact that the relative Hurewicz theorem is a consequence of HHSvKT, and this then suggested a triadic Hurewicz theorem
Hurewicz theorem
In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism...
.
See also
- Higher dimensional algebraHigher-dimensional algebraSupercategories were first introduced in 1970, and were subsequently developed for applications in theoretical physics and mathematical biology or mathematical biophysics....
- Higher category theoryHigher category theoryHigher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities.- Strict higher categories :...
- Seifert-van Kampen theorem
- GroupoidGroupoidIn mathematics, especially in category theory and homotopy theory, a groupoid generalises the notion of group in several equivalent ways. A groupoid can be seen as a:...
s - Algebraic topologyAlgebraic topologyAlgebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
- Nonabelian algebraic topologyHigher-dimensional algebraSupercategories were first introduced in 1970, and were subsequently developed for applications in theoretical physics and mathematical biology or mathematical biophysics....
- R-algebroidR-algebroidIn mathematics, R-algebroids are constructed starting from groupoids. These are more abstract concepts than the Lie algebroids that play a similar role in the theory of Lie groupoids to that of Lie algebras in the theory of Lie groups...
s - Double groupoidDouble groupoidIn mathematics, especially in higher-dimensional algebra and homotopy theory, a double groupoid generalises the notion of groupoid and of category to a higher dimension.- Definition :...
s - Homology (mathematics)Homology (mathematics)In mathematics , homology is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group...
- Alexander GrothendieckAlexander GrothendieckAlexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
- arXivArXivThe arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...
External links
- Ronald Brown's Biography and publications
- Ronald Brown's Home Page
- Higher-Dimensional Algebra citations list
- Mathematical Genealogy Project page
- MathOverflow-- A place for mathematicians to ask and answer questions.
- 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
- Journal of Homotopy and Related Structur(JHRS) Publications
- Homology, Homotopy and Applications
- Theory and Applications of Categories