The kappa classes on the moduli spaces of curves

TL;DR

This paper introduces recent advances in the algebra of kappa classes on moduli spaces of curves, highlighting new results and open questions in algebraic geometry.

Contribution

It provides an accessible overview of recent progress and open problems regarding kappa classes on moduli spaces of curves.

Findings

Progress in understanding kappa class algebra

New results on moduli space structure

Open questions in algebraic geometry

Abstract

In the past few years, substantial progress has been made in the understanding of the algebra of kappa classes on the moduli spaces of curves. My goal here is to provide a short introduction to the new results. Along the way, I will discuss several open questions. The article accompanies my talk at "A celebration of algebraic geometry" at Harvard in honor of the 60th birthday of J. Harris.