Research

My research interests lie in the area of complex geometry and number theory, in particular, the relationship between Nevanlinna theory (the theory of complex hyperbolicities) and Diophantine approximation.

The theory of diophantine geometry has a long rich history dating back all the way to the Greek schools and culminating in the great breakthrough in the 1980s by Faltings in the resolution of the Mordell Conjecture and the proof by Wiles of Fermat's Last Theorem in 1994 concerning the non-existence of integer solutions of the Fermat polynomial x^n+y^n=x^n. Similar questions arise in higher dimension as well, namely, solutions of polynomials of more variables. Analogous questions are also investigated by algebraic geometers, searching for solutions over function fields and by complex geometers, searching for meromorphic solutions. Such theory is called the Nevanlinna theory. Research in this domain has been carried out by many outstanding mathematicians, starting from Nevanlinna's time until recent years. It is perhaps worth noticing that the first Fields Medal was awarded, in 1936, to Lars Ahlfors for his works in this field. Some notable well-known mathematicians like S.S. Chern, P.H. Griffiths, Yum-Tong Siu, J.P. Demailly all have worked in this subject. The research in Diophantine geometry itself also produced at least five Fields medalists (Roth, Baker, Bombieri, Faltings and Wiles).

In 1983, C.H. Osgood was the first one who noticed the striking analogy between the subject of Nevanliina theory in complex geometry and Diophantine approximation in number theory. The link between these two theories, since then, has been deeply investigated, notably by Serge Lang, Paul Vojta, P.M. Wong, and myself etc. The research in exploring the deep relationship betweek these two subjects has spurred great advances in both fields. Lang conjectured that if M is a projective variety defined over a number field K and is hyperbolic (i.e. f every entire map f from the complex plane C to M is constant), then there are only finitely many K-rational points on M. This serves a guideline of our study.

My another research interest is the value distribution properties of the Gauss maps of minimal surfaces in R^n, a program initiated by S.S.Chern and Robert Osserman in early sixties.

For complete information, see my CV.