| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
The main focus of my research is on reconstructing certain type of Gromov―Witten invariants. The problem is equivalent to solving a system of equations defined by the so-called screening operators. My approach is based on the Eynard-Orantin recursion. The definition of the recursion involves a sum of residues of local meromorphic 1-forms. In order to obtain a solution to the screening equations we have to express the sum of local residues as a global contour integral and degenerate the branched covering. My proposal for branched covering is the monodromy covering space of the so-called second structure connection. I proved that this choice is correct for all simple singularities. In general, the monodromy covering space is not a classical Riemann surface, but some infinite sheet covering of P1. I developed a technique to classify semi-simple Frobenius manifolds for which the monodromy covering space is a classical Riemann surface.
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