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.
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.