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SUMMARY:Toposes as 'bridges'  for unifying Mathematics - Olivia Caramello\
 , DPMMS
DTSTART:20111115T141500Z
DTEND:20111115T151500Z
UID:TALK34480@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:In the paper "The unification of Mathematics via Topos Theory"
  I introduced a new point of view on the concept of Grothendieck topos\, n
 amely the idea of a topos as a 'bridge' which can be effectively used for 
 transferring\ninformation between distinct mathematical theories. The topo
 s-theoretic techniques resulting from an implementation of this idea have 
 already proved themselves to be very fruitful in Mathematics\; indeed\, th
 ey have generated a great number of non-trivial applications in distinct m
 athematical fields including Algebra\, Topology\, Algebraic Geometry\, Mod
 el Theory and Proof Theory. This naturally stimulates a wider reflection o
 n the reasons why toposes are so effective in allowing a transfer of knowl
 edge between distinct fields. In the talk I will present substantial speci
 fic evidence for this\, by identifying several crucial features of the con
 cept of topos which are responsible for its technical effectiveness with r
 espect to the\ngoal of 'unifying Mathematics'\; I shall also put the techn
 ique 'toposes as bridges' in a broader perspective by extracting the real 
 essence of the idea of 'bridge' and discussing other incarnations of the c
 oncept both in Mathematics and in different scientific fields. The analysi
 s will be complemented by analogies with Astronomy\, Linguistics and Genet
 ics.
LOCATION:MR5\, Centre for Mathematical Sciences
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