2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64446We study a reduction of the Toda lattice in the limit of infintesimal lattice spacing. Using this reduction, we formulate a conjecture for the equivariant Gromov-Witten invariants of the sphere, which we prove in genus 0. This conjecture follows from recent work of Okounkov and Pandharipande (math.AG/0207233), combined with results from the sequel to this paper.Small corrections in Section 2Algebraic GeometryHigh Energy Physics - TheoryMathematical PhysicsExactly Solvable and Integrable Systems37K10; 53D45text