Workshop announcement

[Pieter HOFSTRA <phofstra@uottawa.ca>]

Fields Institute Workshop Announcement:

Smooth Structures in Logic, Category Theory and Physics

University of Ottawa
May 1-3, 2009


Abstract categorical approaches and analogies with the differential
calculus and the theory of smooth manifolds arise in a number of diverse
areas of mathematics.  For example, the well-known fact that the category
of manifolds and smooth maps fails to be cartesian closed motivated both
the theory of convenient vector spaces due to Froelicher, Kriegl, and
Michor, and work on categories of smooth spaces initiated by Chen and
Souriau.  In topos theory, synthetic differential geometry, developed by
Lawvere, Kock, Moerdijk, Reyes, and others, provides an appealing abstract
setting for differential geometry using the theory of nilpotent
infinitesimals.  In logic, the differential lambda-calculus, due to
Ehrhard and Regnier, was inspired by considerations from linear logic,
differential calculus, and work on locally convex topological models of
linear logic.  This theory subsequently gave rise to the recent
development of differential categories by Blute, Cockett, and Seely.  In
topology, the Goodwillie calculus, which also has connections with the
study of smooth manifolds, is an example of a ``calculus of functors''
drawing inspiration from differential calculus.  And in theoretical
physics, recent work by Baez and Schreiber on higher gauge theory exploits
some of these more abstract versions of differential geometry in order to
avoid technical difficulties implicit in the theory of
infinite-dimensional manifolds.

The Logic and Foundations of Computing group at the University of Ottawa
is happy to announces a workshop, supported by the Fields Institute, which
aims to bring together researchers from these different areas in order to
encourage further interaction in the study of smooth structures in logic,
category theory and physics.  In addition to the main invited lectures,
several of the invited speakers will give tutorials on their areas of
expertise in order to make the subject accessible to students and other
new researchers in the area.  The (confirmed) invited speakers are:

* John Baez (UC Riverside)
* Kristine Bauer (Calgary)
* Thomas Ehrhard (PPS Paris)
* Anders Kock (Aarhus)
* Andrew Stacey (NTNU Norway)


Some student support from the Fields Institute will be available.  There
will also be some time reserved in the schedule for a selection of
contributed talks.  Further details regarding student support and
contributed talks can be found on the workshop webpage:

http://www.fields.utoronto.ca/programs/scientific/08-09/smoothstructures/


With best regards,

Richard Blute (rblute@uottawa.ca)
Pieter Hofstra (phofstra@uottawa.ca)
Philip Scott (phil@site.uottawa.ca)
Michael A. Warren (mwarren@uottawa.ca)