Geometry of the moduli space of curves – Rahul Pandharipande – ICM2018

Plenary Lecture 3
Geometry of the moduli space of curves
Rahul Pandharipande

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.

ICM 2018 – International Congress of Mathematicians ©
 
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