Higher-genus wall-crossing in the gauged linear sigma model

We introduce a technique for proving all-genus wall-crossing formulas in the gauged linear sigma model as the stability parameter varies, without assuming factorization properties of the virtual class. We implement this technique explicitly for the hybrid model, which generalizes our previous work to the Landau--Ginzburg phase.Comment: 42 pages, 2 figures. v2: Added an appendix (by Yang Zhou) proving the n=0 case of the main theorem; additional substantial changes to Sections 2.5 (broad vanishing) and 4.3 (localization contributions

Open rr-spin theory II: The analogue of Witten's conjecture for rr-spin disks

We conclude the construction of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open $r$-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the $r$th Gelfand--Dickey integrable hierarchy. This provides an analogue of Witten's $r$-spin conjecture in the open setting and a first step toward the construction of an open version of Fan--Jarvis--Ruan--Witten theory. As an unexpected consequence, we establish a mysterious relationship between open $r$-spin theory and an extension of Witten's closed theory.Comment: The more foundational parts of the previous version, v3, were moved to the article arXiv:2003.01082. These include the description of objects, constructions of moduli spaces and bundles and proofs of orientations theorems. The name of the paper and the abstract were changed accordingl

Topological recursion relations from Pixton's formula

For any genus g \leq 26, and for n \leq 3 in all genus, we prove that every degree-g polynomial in the psi-classes on Mbar_{g,n} can be expressed as a sum of tautological classes supported on the boundary with no kappa-classes. Such equations, which we refer to as topological recursion relations, can be used to deduce universal equations for the Gromov-Witten invariants of any target.Comment: 17 page