/ Center for Mathemaitcal Challenges
My research interests lie in number theory. More specifically, I am mainly interested in the beautiful relation between the arithmetic invariants and the special L-values of elliptic curves, modular forms, and Galois representations via Iwasawa theory. Iwasawa theory concerns the nature of “functions” from arithmetic objects to their arithmetic invariants of the “variables” arising from infinite Galois extensions via base change and p-adic families of modular forms. I study explicit arithmetic problems including the celebrated Birch and Swinnerton-Dyer conjecture, one of the Millennium Prize Problems, using special values of L-functions and Iwasawa theory. I am also interested in the refined nature of Iwasawa theory. What can we see more than the main conjecture in Iwasawa theory?