1400 - 1440, December 27, 2017 (Wednesday)
Room 202, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 202室)
Topics on the Geometry and Arithmetic of Congruence and Noncongruence Modular Forms
Wen-Ching Winnie Li ( Pennsylvania State University )


In this talk I shall report on two recent results concerning the geometry and arithmetic of mod-ular forms for congruence and noncongruence subgroups of SL(2;Z). The rst is Will Chen's work on the moduli interpretation of the modular curves for nite index subgroups of SL(2;Z), extending the well-known moduli structure on curves for congruence subgroups. The second is congruence relations on the Fourier coecients of congruence forms with CM, resulting from our eort to understand holomorphic dierentials on the (noncongruence) Fermat elliptic curve x3 + y3 = z3 over the eld of rationals. This is an on-going joint work with Ling Long and Fang-Ting Tu.