Brief Description of Dr. Dihua Jiang's Research

General Introduction

The classical theory of automorphic forms, in particular modular forms, was initiated by H. Poincar{\'e} and F. Klein. Rooted in the work of Gauss, Riemann, Jacobi, Eisenstein, it was further developed by Hecke, Siegel, Maass, Selberg, and then by many others. It became early on a meeting ground for analysis and number theory, and has developed as an indispensable tool in analytic number theory, algebraic number theory, Diophantine problems, arithmetic and algebraic geometry, and recently in infinite dimensional Lie algebras and mathematical physics. These relations of automorphic forms with other fields of mathematics can often be summarized as the modularity problem. The Taniyama-Shimura-Weil conjecture on elliptic curves is a typical example. About fifty years ago, it was realized first by Gelfand and Fomin and then in greater generality by Harish-Chandra that the theory of automorphic forms might be better understood in terms of harmonic analysis over locally compact topological groups, especially in terms of the representation theory of complex, real, and p-adic reductive algebraic groups. Then Langlands gave a systematic conjectural description of relations between L-functions in number theory or algebraic geometry and those arising in the theory of automorphic forms. This is the well-known Langlands Program. It has been actively developed in the last thirty years. The recent striking advances on the Langlands Conjectures bring another new exciting moment to this subject.

Description of My Work

  • My Lecture Notes for The Seconed ICCM 2001
    ( (2002)
  • Selection of My Papers
    selected work