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CATEGORIES:Theoretical computer science seminar
SUMMARY:From curves to train tracks to compressed words -
Saul Schleimer (Maths\, Warwick)
DTSTART:20180112T110000Z
DTEND:20180112T120000Z
UID:TALK3054AT
URL:/talk/index/3054
DESCRIPTION:Abstract - A _curve_ is a smooth embedding of a ci
rcle into some other space. A famous theorem of J
ordan and Sch\\"onflies\nstates that all curves in
the plane bound disks. Thus\, to the eyes of a t
opologist\, all of these curves are really the sam
e ---\nthey are\nequivalent up to _isotopy_. Curv
es in the once- or twice-punctured plane are not m
uch more interesting\; each of these is\nisotopic
into a small neighborhood of one of the punctures.
\n\nIn the three-times punctured plane\, and in su
rfaces in general\, there is a much more interesti
ng story due to Dehn\, Nielsen\,\nThurston\, and\n
others. Thurston's theory of _train tracks_ allow
s us to describe curves purely combinatorially. Th
is will lead us to the\nidea of straight-line comp
ression of curves. Combining this with a theorem
of Plandowski\, and some work\, we will arrive at
a new\npolynomial-time solution to the word proble
m in the mapping class group.\n\n
LOCATION:217\, School of Computer Science
CONTACT:Paul Taylor
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