Studies on modular and quasimodular forms arising in various contexts in mathematics and physics

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We mainly studied the elliptic modular function, modular forms, and quasimodular forms. In particular, we found a very interesting phenomena concerning the behavior of the j-function at real quadratic numbers. Related topics such as Markoff irrationalities and the caliber of real quadratic fields were studied. Other topics we studied include 2-adic modular forms, quadratic version of Serre's modularity conjecture, monodromies of Painleve equations, mirror symmetries of Calabi-Yau varieties, and free energy of lens spaces, which are related to automorphic forms.