2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67861Let V be a vector space with a nondegenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH^*(OG) and show that its product structure is determined by the ring of (P~)-polynomials. A "quantum Schubert calculus" is formulated, which includes quantum Pieri and Giambelli formulas, as well as algorithms for computing Gromov-Witten invariants. As an application, we show that the table of 3-point, genus zero Gromov-Witten invariants for OG coincides with that for a corresponding Lagrangian Grassmannian LG, up to an involution.20 pages, LaTeX, to appear in Compositio MathematicaAlgebraic Geometry14M15 (Primary) 05E15 (Secondary)text