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UID:20260610T062828EDT-1993uMZXSv@132.216.98.100
DTSTAMP:20260610T102828Z
DESCRIPTION: \n\nSeminar Geometric Group Theory\n	 \n\nNew bounds for `homot
 opical Ramsey theory' on surfaces\n	\n	Farb and Leininger asked: How many di
 stinct (isotopy classes of) simple closed curves on a finite-type surface 
 S may pairwise intersect at most k times? Przytycki has shown that this nu
 mber grows at most as a polynomial in |χ(S)| of degree k^2+k+1. We present
  narrowed bounds by showing that the above quantity grows slower than |χ(S
 )|^{3k}. The most interesting case is that of k=1\, in which case the size
  of a `maximal 1-system' grows sub-cubically in |χ(S)|. Following Przytyck
 i\, the proof uses the hyperbolic geometry of a surface of negative Euler 
 characteristic essentially. In particular\, we require bounds for the maxi
 mum size of a collection of curves of length at most L on a hyperbolic sur
 face homeomorphic to S of the form F(L)·|χ|\, a point of view that yields 
 intriguing questions in its own right. This is joint work with Tarik Aouga
 b and Ian Biringer.\n\n \n\nWeb site : http://www.math.mcgill.ca/ggt/\n
DTSTART:20170405T190000Z
DTEND:20170405T190000Z
LOCATION:BURN 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Jonah Gaster\, Boston College
URL:https://www.mcgill.ca/mathstat/channels/event/jonah-gaster-boston-colle
 ge-267429
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