Witten's conjecture and Virasoro conjecture for genus up to two

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69006This is an expository paper based on the results in [12] and [16]. The main goal is to prove the following two conjectures for genus up to two. (1) Witten's conjecture on the relations between higher spin curves and Gelfand-Dickey Hierarchies. (2) Virasoro conjecture for conformal semisimple Frobenius manifolds.submitted to proceedings of conference "Gromov-Witten Theory of Spin Curves and Orbifolds". Final versionAlgebraic GeometryWitten's conjecture and Virasoro conjecture for genus up to twotext