Paris seminar

[Ronnie Brown <r.brown@bangor.ac.uk>]

Paris Seminar Notice:
http://www.di.ens.fr/~longo/geocogni.html

Groupe de Travail
GÉOMÉTRIE ET COGNITION
(Giuseppe LONGO*, Jean PETITOT°, Bernard TEISSIER*)
30 Mai : R. Brown (Math., Univ. of Wales)
"The intuitions of higher dimensional algebra for the study of structured
space."

16h,  SALLE U ou V, étage -2 ,  Dépts. de Math. et d'Informatique, ENS, 45,
Rue D'Ulm,  75005  Paris:

ABSTRACT

One definition of  Higher Dimensional Algebra is that it is about
algebraic structures whose operations are partially defined under
geometric conditions, and whose axioms are defined by the geometry
- so for example one considers composing squares and cubes in
various directions. This allows for a more detailed transition
from geometry to algebra. One overall aim is to provide new tools
for local-to-global problems by the procedure `algebraic inverses
to subdivision'. The pursuit of this aim has led to a range of new
algebraic structures, new understanding and computations in
algebraic topology, as well as new tools for concurrency problems.
Its potential relevance to this seminar is the speculative idea
that a mathematics `on a line' cannot be adequate for describing
the complex modular and hierarchical interactions of the brain. So
Higher Dimensional Algebra can perhaps open out new modelling
possibilities for future development. For more background, see
http://www.bangor.ac.uk/~mas010/hdaweb2.htm

The structure of the talk will be
 1. Origins and intuitions
 2. Landmark theorems: these are of the type
    (a) equivalent descriptions of the algebraic structures
    (b) gluing (colimit) theorems
    (c) realisation of algebra by spaces
 3. Computational issues
 4. The future?

 (The aim is to give an impression of this area for a more general
 audience, and so consideration of `weak structures' and many other
 applications will be omitted.)

Ronnie Brown