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CATEGORIES:Applied and Computational Analysis
SUMMARY:Undecidability in geometry and topology - Henry Wi
lton (University of Cambridge)
DTSTART;TZID=Europe/London:20171012T150000
DTEND;TZID=Europe/London:20171012T160000
UID:TALK72433AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72433
DESCRIPTION:There is a beautiful tension in topology between p
ositive classification theorems and negative “no-g
o” theorems. The positive results come from geomet
ry\, and often derive ultimately from analysis. Th
e negative results\, by contrast\, come from undec
idability results in logic. I’ll give a survey of
the history of this tension\, and mention the hig
hlight theorems — examples include Markov’s theore
m that 4-manifolds cannot be classified (on the ne
gative side)\, and Perelman’s Geometrization Theor
em in dimension 3 (on the positive side). I’ll t
hen go on to describe some recent undecidability r
esults\, which limit possible computations in matr
ix groups. This is joint work with Martin Bridson
.\n
LOCATION:MR 14\, CMS
CONTACT:Dr Hansen
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