Symplectic topology, mirror symmetry and integrable systems.

Paolo Rossi (1)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies

Using Sympelctic Field Theory as a computational tool, we compute Gromov-Witten theory of target curves using gluing formulas and quantum integrable systems. In the smooth case this leads to a relation of the results of Okounkov and Pandharipande with the quantum dispersionless KdV hierarchy, while in the orbifold case we prove triple mirror symmetry between GW theory of target P^1 orbifolds of positive Euler characteristic, singularity theory of a class of polynomials in three variables and extended affine Weyl groups of type ADE.

Mots clés: Gromov-Witten theory; Symplectic Field Theory; Integrable Systems

Domaines: Géométrie symplectique [math.SG]; Géométrie algébrique [math.AG]; Physique mathématique [math-ph]

Paolo Rossi. Symplectic topology, mirror symmetry and integrable systems.. Symplectic Geometry [math.SG]. SISSA - Trieste, 2008. English. ⟨NNT : ⟩. ⟨tel-00690265⟩