I am a second year graduate student. I am interested in algebraic geometry, both complex and arithmetic. Now I want to study some representation theory of algebraic groups, it may also involve with affine lie algebra. And I also want to study Hodge theory especially mixed hodge structure.

Recently I learn some history of modular forms, elliptic curves and the development of $L$-functions. Of course I only know the development up to 1950s. Things become quite different after 1950s, and I can not go further without a specific direction.