This is the first of two talks about a “negative” spin analogue of the Witten $r$-spin theory. In the first talk, we will present the construction and properties of a cohomological field theory (without a flat unit) that parallels the famous Witten r-spin class for negative spin. The class for $r=2$ was constructed and studied by Norbury in 2017. By studying certain deformations of this class, we use Teleman’s reconstruction theorem to 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.
This is based on the following joint work with Elba Garcia-Failde (who will give the second talk) and Alessandro Giacchetto: https://arxiv.org/pdf/2205.15621.pdf