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SUMMARY:Higher Genus Polylogarithms - Hain\, R (Duke University)
DTSTART:20130410T080000Z
DTEND:20130410T090000Z
UID:TALK44418@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Are there polylogarithms in higher genus? Classical polylogari
 thms are defined on P1-{0\, 1\,1}\, which is the moduli spaceM0\,4 of 4-po
 inted genus 0 curves. The elliptic polylogarithms of Beilinson and Levin a
 re defined on M1\,1\, the moduli space of elliptic curves and on M1\,2\, t
 he punctured universal elliptic curve over it. In this talk I will give a 
 uniform definition of polylogarithms of all genera which specializes to th
 ese in genera 0 and 1. I will then explain that there are are countable ma
 ny polylogarithms in genus 2  though they appear to be less interesting th
 an elliptic polylogarithms  and that\, when g > 2\, there are very few. Th
 e upside of this rigidity of higher genus moduli spaces is that one can co
 nstruct a theory of characteristic classes of rational points of curves of
  genus g > 2.\n
LOCATION:Seminar Room 1\, Newton Institute
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