Tautological Classes on the Moduli Space of K3 Surfaces

I will discuss kappa classes on the moduli space of quasi-polarized K3 surfaces and relations obtained from the moduli spaces of stable maps to the universal family. I will explain the proof of the generation of the tautological ring by Noether-Lefschetz loci. There are a number of open questions. Joint work with Qizheng Yin.