Ronald Brown's Home Page

Information last updated: August 7, 2009

Emeritus Professor R. Brown,
School of Computer Science,
Bangor University,
Dean Street,
Bangor,
Gwynedd LL57 1UT
UK. 

01492 583608
Fax:      (01248)-361429
Email:      @btinternet.com

Groupoids in mathematics

John Robinson, artist and sculptor, died on April 6, 2007. For tributes, see Hyperseeing June and July 2007 , and an obit notice here in pdf form or html. There is also a wikipedia entry.

BOOK NOW AVAILABLE

Follow Topology and Groupoids for more information.

This is a revised and extended version of my old topology book, previously published in 1968 and 1988, and long out of print. The revised version is xxv+512 rather than xvi+460 pages, the figures have been redrawn, and the material has been reorganised to emphasise the topology/groupoids translation and analogy. The print version is available from amazon.com at $31.99 via the following ORDER NOW LINK . The e-version is available at £5 from Kagi .

Brief Biography

Publication list in html format. This also contains some links to downloads of papers.

Nonabelian Algebraic Topology :filtered spaces, crossed complexes, cubical homotopy groupoids
Click for the aims of and background to this book, and for downloads of the current draft.

Alexander Grothendieck : This is a link to an account of the origins of the 600 page 1983 manuscript `Pursuing stacks'.

Higher dimensional group theory This web paper explains some of the intuitions behind this new area of mathematics, and has a link to an extensive bibliography up to Jan, 1999, and to a fuller bibliography on the non abelian tensor product of groups. The latter has been updated with additional information in July, 2009.

Preprints/reprints in .ps or other form (Updat3ed 28 July, 2009)

Seminars and activities: 2002-2009

Research

I have come to be involved in the analysis and development of underlying stuctures across several fields, and computation with these. One such area is the foundations of algebraic topology. This has led to an interest in multiple categories, and the applications of groupoids and multiple groupoids. The aim is make the algebra model better the geometry, so that more computations are possible. The computational side leads to a current interest in rewriting and Groebner bases.

I am keeping up various research interests, particularly in Higher Dimensional Algebra, holonomy, popularisation, and some multidisciplinary contacts. See the paper:
The intuitions of higher dimensional algebra for the study of structured space (pdf file)
by R. Brown and T. Porter.
This is a development of a seminar by the first author in May, 2001, in the series of G. Longo `Géometrie et Cognition' at the ENS. (To download a .ps.gz file click here. ) The paper is addressed to a general audience.

These contacts have resulted in relevant papers, namely `Category theory and higher dimensional algebra: potential descriptive tools in neuroscience', (with T. Porter), and `Categorical language and hierarchical models for cell systems,' (with R. Paton and T. Porter).

Groupoids and crossed objects in algebraic topology
This survey article addressed originally to students on a course at Grenoble mostly concentrates on the 2-dimensional case, as the jump from the fundamental groupoid to the fundamental double groupoid of a pair was the key step, conceptually and technically. The article is downloadable from Homology, homotopy and applications.

Towards Non Commutative Algebraic Topology
This is a file of the transparencies for a seminar at University College, London, on May 7, 2003. It aims to present a quick overview of ideas, plans, and some achievements.

Doctoral students supervised
This gives some idea of the great contributions of Bangor research students to the research programme at Bangor.

Popularisation and teaching projects:

Quality Assurance in Higher Education: a discussion document, particularly related to mathematics.

The site for the Centre for the Popularisation of Mathematics has been reorganised to give new animations and a new look, by Mike Yates under an EPSRC Popularisation Grant.

A Celebration of Mathematics in the Arts in honour of the ninetieth birthday of H.S.M. (Donald) Coxeter.
These are the slides for the presentation on February 9, 1997, at the Fields Insitute, Toronto.

What should be the output of mathematical education?

Letter on Science Funding to `Science and Public Affairs', August 1999.

Review for the London Math. Soc. Newsletter, January, 2000, 25-27, of `History of Topology' (ed. I.M. James).

Editorships:

Theory and Applications of Categories

Homology, Homotopy and Applications

Journal of Homotopy and Related Structures

Health:

This is information for those who want to know of a hampering illness in 2000-2001, and the progress towards the current recovery. This might help others with the same acoustic neuroma problem.