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CATEGORIES:Category Theory Seminar
SUMMARY:Well adapted models in Synthetic Differential Geom
etry - Filip Bár\, DPMMS
DTSTART;TZID=Europe/London:20130430T141500
DTEND;TZID=Europe/London:20130430T151500
UID:TALK44709AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/44709
DESCRIPTION:Synthetic Differential Geometry (SDG) is an approa
ch to differential geometry that builds on an alge
bro-geometric theory of infinitesimals. The notion
of infinitesimal is made rigorous by the Kock-Law
vere axiom scheme. One strength of this approach i
s that the formalization agrees with the intuitive
use of infinitesimals in differential geometry as
employed by geometers like E. Cartan and S. Lie.\
n\nThe simplicity and intuition of this approach c
omes with a price: It turns out that SDG has no no
n-trivial models in the realm of classical logic\,
i.e.\, in any boolean topos. However\, one can co
nstruct toposes that yield models of SDG. Of parti
cular interest are the so called well-adapted mode
ls. These are topos models together with a 'nice'
embedding of the category of smooth manifolds.\n\n
This talk will consist of three parts. In the firs
t part I shall introduce the basic concepts and no
tions of SDG\, in particular the Kock-Lawvere axio
m scheme. In the second part I will introduce well
-adapted models axiomatically and present some con
sequences of the axioms. Finally\, in the third pa
rt I shall sketch how one can construct well-adapt
ed models using C-infinity rings.
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Julia Goedecke
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