Mainly engaged in analytic number theory, matrix geometry, typical groups, automorphism function theory, multiple complex variable function theory, partial differential equations, high-dimensional numerical integration and other fields.
Contribution to mathematics:
Hua's early research field was analytic number theory, and his achievements in analytic number theory were particularly famous. The internationally famous "China Analytic Number Theory School" is a school initiated by China, which has made many significant contributions to the distribution of prime numbers and Goldbach conjecture.
Hua is also the founder and pioneer in the research of analytic number theory, matrix geometry, canonical group and automorphism function theory in China.