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Theses Year : 2008

Symplectic topology, mirror symmetry and integrable systems.

Abstract

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.
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Dates and versions

tel-00690265 , version 1 (22-04-2012)

Identifiers

  • HAL Id : tel-00690265 , version 1

Cite

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

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