BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Affine algebra - Vaughan Pratt (Stanford University)
DTSTART:20080925T131500Z
DTEND:20080925T150000Z
UID:TALK13803@talks.cam.ac.uk
CONTACT:Helen Innes
DESCRIPTION:We axiomatize affine algebra equationally in terms of the geom
 etric\nprimitives of reflection and centroid.  This reduces the usual\nthr
 ee-stage algebraic development of affine geometry (fields then\nvector spa
 ces then torsors) to a single stage.  The expansion of\nthis variety with 
 a lawless constant is equivalent to vector spaces\nover the rationals (or 
 complex rationals when further expanded with\nquarter-turn rotation).  Com
 pletion to the continuum is accomplished\nentirely within this framework v
 ia a notion of convergence of\npairs of point sets constituting a partial 
 equivalence relation\,\nwith Cauchy sets defined as those sets that conver
 ge with themselves.\nThe additive fragment based on reflection\, whose mod
 els we call groves\,\nis of independent interest as a weak generalization 
 of heaps/herds\nas an affine counterpart of abelian groups.\n
LOCATION:MR12
END:VEVENT
END:VCALENDAR