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Impromptu Talks - IMA 2004 Summer Program:
n-Categories: Foundations and Applications
June 7-18, 2004


Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities, September 2004 - June 2005

Nils A. Baas (Department of Mathematical Sciences, Norwegian University of Science and Technology)
Slides:   pdf


Ronald Brown (School of Informatics, Mathematics Division University of Wales, Bangor) mas010@bangor.ac.uk http://www.bangor.ac.uk/~mas010/ http://www.cpm.informatics.bangor.ac.uk/

Nonabelian Algebraic Topology
Paper:
  pdf


Friday, June 11th, 2004 at 2:00 pm
Thomas M. Fiore (Department of Mathematics, University of Michigan) fioret@umich.edu

Pseudo Algebraic Structures in Conformal Field Theory (impromptu talk)
Introduction:   dvi    pdf   ps
Slides:
  dvi    pdf
   ps

This talk deals with the pseudo algebraic structure of gluing and disjoint union on the category of rigged surfaces and its role in the definition of conformal field theory. Pseudo algebras over Lawvere theories and 2-theories are treated in order to capture the pseudo algebraic structure. This work is an application of weak 2-categorical concepts to physics.


Monday, 14th, 2pm
Yves Lafont (Institut de Mathématiques de Luminy, Université de la Méditerranée, Marseille) lafont@iml.univ-mrs.fr http://iml.univ-mrs.fr/~lafont/

Geometry of Rewriting

Abstract: We show that the theory of rewriting, whose main purpose is to solve the word problem (in good cases) can also be used to compute homotopical and homological invariants (Squier) or to prove coherence theorems (Mac Lane). This is one of our motivations for generalizing the theory of rewriting to the higher dimensional case. We give some examples.

References :

Y. Lafont, A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier), Journal of Pure and Applied Algebra 98, p. 229-244, North-Holland (1995)

Y. Lafont, Towards an Algebraic Theory of Boolean Circuits, Journal of Pure and Applied Algebra 184 (2-3), p. 257-310 (2003)

Both papers are available on http://iml.univ-mrs.fr/~lafont/papers.html


Monday, 14th
Francois Metayer
(Equipe PPS, Université de Paris 7) metayer@logique.jussieu.fr http://www.logique.jussieu.fr/www.metayer

Resolutions And Computads

Abstract: We introduce a notion of resolution for n-categories, based on computads (or polygraphs), and state basic invariance theorems. This proves to be extremely well adapted to the study of rewriting systems: following Squier, we are particularily interested in understanding how confluence and termination properties of these systems relate to invariants of the stuctures they present.

Reference:

Francois Metayer, Resolutions by polygraphs, TAC vol 11, p 148-184 (2003)

Paper available on http://www.tac.mta.ca/tac/volumes/11/7/11-07abs.html


Wednesday, 16th, 2pm-5pm, EE/CS 3-180
Simona Paoli (University of Warwick simona.paoli@virgilio.it)

Title: Internal Categorical Structures in Homotopical Algebra


Wednesday, 16th, 3pm, EE/CS 3-180
Julie Bergner (Department of Mathematics, University of Notre Dame jbergner@nd.edu)

Title: Complete Segal Spaces, Segal Categories and S-Categories
Slides:   pdf


Thursday, 17th, times below, Lind 409
Title: Discussion Group on Concurrency, Etc.
2-2:30 Ronnie Brown (School of Informatics, Mathematics Division University of Wales, Bangor mas010@bangor.ac.uk http://www.bangor.ac.uk/~mas010/)
2:30-3 Uli Fahrenberg (Department of Mathematical Sciences, Aalborg University
uli@math.aau.dk http://www.math.auc.dk/~uli

A Dihomotopy Double Category of a Po-Space
Slides:
  pdf    ps

3-3:30 Timothy Porter (School of Informatics, University of Wales t.porter@bangor.ac.uk)
3:30-4 Michael Johnson (Department of Mathematics & Computer Science, Macquarie University sanjeevi@math.uchicago.edu
Sanjeevi Krishnan (Department of Mathematics, University of Chicago) sanjeevi@math.uchicago.edu)


Thursday, 17th, 2pm, EE/CS 3-180
Larry Breen (Laboratoire Analyse, Géométrie, Universite Paris 13 breen@math.univ-paris13.fr)

Title: From 1-Gerbes to 2-Gerbes


Thursday, 17th, 3pm, Lind 401
Tom Leinster (Department of Mathematics, University of Glasgow T.leinster@maths.gla.ac.uk)

Title: Generalized Operads, Generalized Multicategories, Generalized Enrichment (Featuring: a Definition of the Opetopes)



Claudio Hermida (Department of Mathematics, Queen's University) chermida@cs.queensu.ca

Title: A Roadmap to the Unification of Categorical Structures
Paper:   pdf    ps


Summer Programs

Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities, September 2004 - June 2005
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