Abstract We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP integrability of the differentials of blobbed topological recursion for the input data that include KP-integrable blobs. This result generalizes, unifies, and gives a new proof of the KP integrability of nonperturbative differentials conjectured by Borot–Eynard and recently proved by the authors.

Abstract We prove a formula for the cycle class of the supersingular locus in the Chow ring with rational coefficients of the moduli space of principally polarized abelian varieties of dimension g in characteristic p. This formula determines this class as a monomial in the Chern classes of the Hodge bundle up to a factor that is a polynomial in p. This factor is known for $$g\le 3$$ g ≤ 3 . We also determine the factor for $$g=4$$ g = 4 .

Abstract We formulate a precise connection between the new Drinfeld presentation of a quantum affine algebra $$U_q\widehat{{\mathfrak {g}}}$$ U q g ^ and the new Drinfeld presentation of affine coideal subalgebras of split type recently discovered by Lu and Wang. In particular, we establish a “factorization formula”, expressing the commuting “Drinfeld–Cartan”-type operators $$\Theta _{i,k}$$ Θ i , k in the coideal subalgebra in terms of the corresponding Drinfeld generators of $$U_q\widehat{{\mathfrak {g}}}$$ U q g ^ , modulo the “Drinfeld positive half” of $$U_q\widehat{{\mathfrak {g}}}$$ U q g ^ . We study the spectra of these operators on finite dimensional representations, and describe them in terms of rational functions with an extra symmetry. These results can be seen as the starting point of a q-character theory for affine Kac–Moody quantum symmetric pairs. Additionally, we prove a compatibility result linking Lusztig’s and the Lu-Wang-Zhang braid group actions.