This is the second talk of the series started by Nitin Chidambaram on a “negative” spin analogue of the Witten r-spin theory. In this second talk, we will exploit the relation between cohomological field theories and topological recursion to prove W-algebra constraints satisfied by the descendant potential of the class (constructed in Nitin’s talk). Furthermore, we conjecture that this descendant potential is the r-BGW tau function of the r-KdV hierarchy, and prove it for r=2 (confirming a conjecture of Norbury) and r=3.
This is based on the following joint work with Nitin Chidambaram (who gave the first talk) and Alessandro Giacchetto: https://arxiv.org/pdf/2205.15621.pdf