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SUMMARY:Double ramification cycles in the punctured setting - Xuanchun Lu\
 , University of Cambridge
DTSTART:20241025T150000Z
DTEND:20241025T160000Z
UID:TALK220627@talks.cam.ac.uk
CONTACT:Siao Chi Mok
DESCRIPTION:The complex projective line CP1 is the only compact Riemann su
 rface on which every degree 0 divisor is principal.\nFor compact Riemann s
 urfaces of higher genus\, it is thus natural to ask how often does a 'rand
 om' divisor on the surface become principal.\n\nGeneralising classical wor
 k of Abel--Jacobi and being fairly liberal with what the word 'solution' m
 eans\,\nthe above problem admits a partial solution in the form of a disti
 nguished homology class ---\nthe double ramification (DR) cycle --- on the
  moduli space of Riemann surfaces.\nThe latter space is not compact\, and 
 thus to obtain a more complete solution we need to extend\nthe DR cycle to
  a compactification of the space.\n\nIn this talk\, I will recall how the 
 DR cycle is constructed\, and how it can be extended using\nlogarithmic ge
 ometry following the works of Marcus--Wise.\nI will also highlight some of
  its downstream enumerative applications.\nIf time permits\, I will attemp
 t to shed some light on the appearance of the word 'punctured' in the titl
 e.
LOCATION:MR13
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