SeminarsMirror theorem, Seidel representation, and holomorphic disks.
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The quantum cohomology ring QH^*(X) of a projective toric manifold X can be computed in several ways. A presentation of QH^*(X) can be derived from the toric mirror theorem of Givental, Lian-Liu-Yau, and Iritani. McDuff-Tolman used Seidel representations to derive a presentation of QH^*(X). More recently, Fukaya-Oh-Ohta-Ono showed that QH^*(X) is isomorphic to the Jacobian ring of the Lagrangian Floer superpotential of X, which is defined in terms of counting of holomorphic disks in X. The purpose of this talk is to explain the geometric reason underlying the equivalence of these three seemingly very different approaches, when X is semi-Fano.
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Hsian-Hua Tseng
2013-07-08
15:00:00 - 16:00:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
The quantum cohomology ring QH^*(X) of a projective toric manifold X can be computed in several ways. A presentation of QH^*(X) can be derived from the toric mirror theorem of Givental, Lian-Liu-Yau, and Iritani. McDuff-Tolman used Seidel representations to derive a presentation of QH^*(X). More recently, Fukaya-Oh-Ohta-Ono showed that QH^*(X) is isomorphic to the Jacobian ring of the Lagrangian Floer superpotential of X, which is defined in terms of counting of holomorphic disks in X. The purpose of this talk is to explain the geometric reason underlying the equivalence of these three seemingly very different approaches, when X is semi-Fano.