Abstract: The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions in the study of tautological classes on the moduli space following ideas and conjectures of Mumford, Faber-Zagier, and Pixton. Cohomological Field Theories (CohFTs) play an important role. The talk is about the search for a cohomology calculus for the moduli space of curves parallel to what is known for better understood geometries. My goal is to give a presentation of the progress in the past decade and the current state of the field
https://people.math.ethz.ch/~rahul/Rio2.pdf
https://eta.impa.br/dl/PL017.pdf
https://arxiv.org/abs/1712.02528
本文研究曲线的模空间M_g的上同调，尤其是M_g的Miller-Morita-Mumford上同调类R*(M_g)中的Faber-Zagier关系的三种证明，其中一种运用了上同调场论。然后讨论紧化模空间\bar{M_{g, n}}上的Pixton关系，证明利用上同调场论。
