Abstract:In this presentation, I will introduce a new family of cohomology classes on the moduli space of curves, known as the Theta-classes. These are indexed by integers r ≥ 2 and 1 ≤ s ≤ r−1, and originate as the Euler class of vector bundles. They extend several known examples, including Norbury's class (corresponding to r = 2, s = 1). We show that the descendant integrals of the Theta-classes are computed by the generalised topological recursion on the so-called (r,s) spectral curve. As a consequence, we establish that their descendant potential is a tau function of the r-KdV integrable hierarchy, generalising the Brézin–Gross–Witten tau function. Additionally, we derive differential constraints satisfied by this tau function: it is annihilated by a set of differential operators forming a representation of the W(gl(r)) algebra at the self-dual level. This is joint work with V. Bouchard, N. K. Chidambaram, and S. Shadrin.