Dear colleagues This introduction to SDG will occur tomorrow Weds 18 January in MR4, CMS; as part of the SDG series. Best, Jeremy
------ Jeremy Butterfield: http://en.wikipedia.org/wiki/Jeremy_Butterfield Homepage: http://www.trin.cam.ac.uk/butterfield/ Trinity College, Cambridge CB2 1TQ (tel = 01223 761524 (direct) or 07896 471002 (mobile)). Visit the journal, Studies in the History and Philosophy of Modern Physics http://www.sciencedirect.com/science/journal/13552198 ----------------- Synthetic Differential Geometry - An Overview by Filip Bar (U of Cambridge) http://talks.cam.ac.uk/talk/index/35506 ABSTRACT: This talk is the first talk of a seminar on SDG I'm organizing this term. I intend to give a small introduction to SDG as well as various impressions what it involves. In a nutshell SDG is concerned with the analysis and geometry of infinitesimals in the spirit of Leibniz, one of the founding fathers of Calculus. It starts off with 'crazy' axioms like that any function f: R -> R is differentiable, or that any function f: [0,1] -> R is integrable. To realize SDG as a rigorous and interesting mathematical discipline input from Category Theory and Logic (in particular logical aspects of Topos Theory), Algebraic Geometry and Differential Geometry is needed. But the original motivation for SDG lies in physics, in particular in classical dynamics. It is an offspring of F.W. Lawvere's famous lectures on Categorical Dynamics. In fact, the notion of infinitesimality in SDG (modelled by nilpotents) corresponds to the intuition of physicists, namely that of a small perturbation, which is negligible up from a certain order. _____________________________________________________ Sent by the CamPhilEvents mailing list. To unsubscribe or change your membership options, please visit the list information page: http://bit.ly/CamPhilEvents Posts are now archived here: http://bit.ly/CamPhilEventsArchive
