# Colloquium abstracts

**Nitin K Chidambaram***

MPIM, Bonn

April 7, 2022

**r-th roots: better negative than positive**: I will talk about the construction and properties of a cohomological field theory that parallels the famous Witten r-spin class. In particular, one can view it as the negative r analogue of the Witten r-spin class. For r=2, it was constructed by Norbury and called the Theta class, and we generalize this construction to any r. By studying certain deformations of this class, we prove relations in the tautological ring, and in the special case of r=2 they reduce to relations involving only Kappa classes (which were recently conjectured by Norbury-Kazarian). Finally, I will also discuss some relations to the W-algebra constraints and the r-KdV hierarchy. This is joint work-in-progress with Alessandro Giacchetto and Elba Garcia-Failde.