A calculus for the moduli space of curves

@article{Pandharipande2018ACF,
  title={A calculus for the moduli space of
 curves},
  author={Rahul Pandharipande},
  journal={Algebraic Geometry: Salt Lake City
                    2015},
  year={2018}
}
  • R. Pandharipande
  • Published 16 March 2016
  • Mathematics
  • Algebraic Geometry: Salt Lake City 2015
This article accompanies my lecture at the 2015 AMS summer institute in algebraic geometry in Salt Lake City. I survey the recent advances in the study of tautological classes on the moduli spaces of curves. After discussing the Faber-Zagier relations on the moduli spaces of nonsingular curves and the kappa rings of the moduli spaces of curves of compact type, I present Pixton's proposal for a complete calculus of tautological classes on the moduli spaces of stable curves. Several open… 

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