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SUMMARY:On the enumeration of random maps with three tight boundaries and 
 its probabilistic consequences - Gregory Miermont (Lyon)
DTSTART:20220906T090000Z
DTEND:20220906T100000Z
UID:TALK178469@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:We consider the enumeration problem of graphs on surfaces\, or
  maps\, with three boundaries\, also colloquially called pairs of pants. P
 erhaps surprisingly\, a formula due to Eynard and extended by Collet-Fusy 
 shows that this problem has a very simple and explicit solution\, which be
 comes even simpler when one asks that the boundaries are tight\, meaning t
 hat they have smallest possible length in their free homotopy class. We pr
 ovide a bijective approach to this formula which consists in decomposing t
 he graph into elementary pieces in a way that is reminiscent of certain ge
 ometric constructions of pairs of pants in hyperbolic geometry. I will als
 o discuss the probabilistic consequences of this bijective approach by stu
 dying statistics of minimal separating loops in random maps with boundarie
 s.  (Based on joint work with J\\'er\\'emie Bouttier and Emmanuel Guitter.
 )
LOCATION:MR9\, Centre for Mathematical Sciences
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