W-constraints and the Eynard-Orantin topological recursion

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800003
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• 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
• Keywords: period integrals / vertex algebras / Gromov-Witten invariants

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.

Free Research Field

Representation theory