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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Higher Genus Polylogarithms

## Higher Genus PolylogarithmsAdd to your list(s) Download to your calendar using vCal - Hain, R (Duke University)
- Wednesday 10 April 2013, 09:00-10:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Grothendieck-Teichmller Groups, Deformation and Operads Are there polylogarithms in higher genus? Classical polylogarithms are defined on P1-{0, 1,1}, which is the moduli spaceM0,4 of 4-pointed genus 0 curves. The elliptic polylogarithms of Beilinson and Levin are defined on M1,1, the moduli space of elliptic curves and on M1,2, the punctured universal elliptic curve over it. In this talk I will give a uniform definition of polylogarithms of all genera which specializes to these in genera 0 and 1. I will then explain that there are are countable many polylogarithms in genus 2 though they appear to be less interesting than elliptic polylogarithms and that, when g > 2, there are very few. The upside of this rigidity of higher genus moduli spaces is that one can construct a theory of characteristic classes of rational points of curves of genus g > 2. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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