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SUMMARY:Well adapted models in Synthetic Differential Geometry - Filip Bá
 r\, DPMMS
DTSTART:20130430T131500Z
DTEND:20130430T141500Z
UID:TALK44709@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:Synthetic Differential Geometry (SDG) is an approach to differ
 ential geometry that builds on an algebro-geometric theory of infinitesima
 ls. The notion of infinitesimal is made rigorous by the Kock-Lawvere axiom
  scheme. One strength of this approach is that the formalization agrees wi
 th the intuitive use of infinitesimals in differential geometry as employe
 d by geometers like E. Cartan and S. Lie.\n\nThe simplicity and intuition 
 of this approach comes with a price: It turns out that SDG has no non-triv
 ial models in the realm of classical logic\, i.e.\, in any boolean topos. 
 However\, one can construct toposes that yield models of SDG. Of particula
 r interest are the so called well-adapted models. These are topos models t
 ogether with a 'nice' embedding of the category of smooth manifolds.\n\nTh
 is talk will consist of three parts. In the first part I shall introduce t
 he basic concepts and notions of SDG\, in particular the Kock-Lawvere axio
 m scheme. In the second part I will introduce well-adapted models axiomati
 cally and present some consequences of the axioms. Finally\, in the third 
 part I shall sketch how one can construct well-adapted models using C-infi
 nity rings. 
LOCATION:MR5\, Centre for Mathematical Sciences
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