Research Interests

Complex Geometry, Holomorphic Foliations, Analytic and Arithmetic Number Theory and B-model of Mirror Symmetry related with followings:

Keywords: Calabi-Yau varities, Dwork family, Variation of Hodge structure, Gauss-Manin connection, Picard-Fuchs equation, Complex vector fields, Modular vector fields, Semicomplete vector fields, Algebraic leaves, (Quasi-)Modular forms, q-expansions, Calabi-Yau modular forms, Rankin-Cohen algebras, Chazy equation, Gromov-Witten invariants, Yukawa coupling.

Currently I am working on developing the theory of Calabi-Yau (CY) modular forms, which is considered as a modern generalization of the classical theory of (quasi-)modular forms. To obtain CY modular forms, we first consider a moduli space T of a special family of CY varieties enhanced with the differential forms. Then, we find a unique vector field, calling modular vector field, R in T that satisfies a certain equation involving the Gauss-Manin connection of the universal family of T. Calabi-Yau modular forms are defined as elements of a C-algebra generated by components of a particular solution of the modular vector field R, which are provided with natural weights.

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