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CATEGORIES:Probability
SUMMARY:On the enumeration of random maps with three tight
boundaries and its probabilistic consequences - G
regory Miermont (Lyon)
DTSTART;TZID=Europe/London:20220906T100000
DTEND;TZID=Europe/London:20220906T110000
UID:TALK178469AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178469
DESCRIPTION:We consider the enumeration problem of graphs on s
urfaces\, or maps\, with three boundaries\, also c
olloquially called pairs of pants. Perhaps surpris
ingly\, a formula due to Eynard and extended by Co
llet-Fusy shows that this problem has a very simpl
e and explicit solution\, which becomes even simpl
er when one asks that the boundaries are tight\, m
eaning that they have smallest possible length in
their free homotopy class. We provide a bijective
approach to this formula which consists in decompo
sing the graph into elementary pieces in a way tha
t is reminiscent of certain geometric construction
s of pairs of pants in hyperbolic geometry. I will
also discuss the probabilistic consequences of th
is bijective approach by studying statistics of mi
nimal separating loops in random maps with boundar
ies. (Based on joint work with J\\'er\\'emie Bout
tier and Emmanuel Guitter.)
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Jason Miller
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