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This is a conference in honor of Motohico Mulase-s 65th birthday. It will cover recent advances around the following themes Quantization of moduli spaces, in particular the Hitchin moduli space of Higgs bundles Gromov-Witten theory, Frobenius manifolds, integrable hierarchies, cohomological field theories Geometry of quiver varieties, wall-crossing phenomena Mirror symmetry, topological string theory, quantum invariants of 3-manifolds Topological recursion, quantum curves, and application to geometry and enumerative problems (Hurwitz theory, random matrix theory, ribbon graphs) Connections between these fields are apparent from the physics perspective and research is trying to make rigorous sense of these relationships. Encouraging the exchanges between mathematicians and theoretical physicists will thus be an important dimension of the conference. More details available soon.