Tonghai Yang specializes in number theory, arithmetic geometry,
and automorphic representation, and in particular their interaction.
He studies L-functions of elliptic curves and abelian varieties using
tools from representation theory and then obtains its arithmetic
consequences. An L-function provides a beautiful bridge between the
arithmetic of a geometric object (say elliptic curve) and the local
information one can get from this object. Tonghai is also
exploring some connection between Eisenstein series
(some explicit modular forms) and arithmetic on Shimura curves.