# Open-closed Gromov-Witten theory

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Kenji Fukaya, Kyoto University
Fine Hall 314

Lagrangian Floer theory studies boundary valued problem for the maps from bordered Riemann surface with boundary condition given Lagrangian submanifold. Gromov-Witten theory studies pseudo-holomorphic maps from Riemann surface. Various relations between them is found and is expected to be useful both in symplectic geometry and the study of Mirror symmetry. I want to discuss some of such applications and several basic constructions we need for it.