W-constraints and the Eynard-Orantin topological recursion
Project/Area Number |
26800003
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | The University of Tokyo |
Principal Investigator |
MILANOV Todor 東京大学, カブリ数物連携宇宙研究機構, 准教授 (80596841)
|
Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
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)
|
Keywords | period integrals / vertex algebras / Gromov-Witten invariants / Frobenius structures / vertex operators / Eynard-Orantin recursion / Eynard―Orantin recursion |
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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Report
(4 results)
Research Products
(17 results)