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SUMMARY:Exponential volumes of moduli spaces of hyperbolic surfaces and re
 cursions
DTSTART:20231027T143000Z
DTEND:20231027T160000Z
DTSTAMP:20260614T032900Z
UID:indico-event-10744@indico.math.cnrs.fr
CONTACT:volodya@univ-angers.fr\;+33(0)663168700
DESCRIPTION:Speakers: Alexander B. Goncharov (Yale University and IHES)\n\
 nThis is a joint work with Zhe Sun.   A decorated surface S is an orien
 ted topological surface with boundary\, equipped with marked points on the
  boundary considered modulo the isotopy.   We consider the moduli space 
 M(S) of hyperbolic structures on S with geodesic boundary\, such that the
  hyperbolic structure near each marked point is a cusp\,  equipped with 
  a horocycle. The  space M(S) carries a canonical volume form. However\,
   if the cusps are present\,  the volume of the space M(S)\, as well as 
 its   variant without horocycles\,  are infinite.   We introduce the
  exponential  volume form\, given by the volume form multiplied by the e
 xponent of a canonical function on M(S).  We show that  the exponential 
 volume is finite. We prove  recursion formulas  for the exponential vo
 lumes\,  generalising Mirzakhani's recursions for the volumes of  moduli
  spaces of hyperbolic surfaces.    We suggest that the moduli space M(
 S)  with the exponential volume form is the true analog of the moduli spa
 ce M_{g\,n}\, relevant to the open string theory. \n\nhttps://indico.math
 .cnrs.fr/event/10744/
LOCATION:salle 314 (IHP\, Paris)
URL:https://indico.math.cnrs.fr/event/10744/
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