He has resolved various conjectures by applying estimates of the complex Neumann problem and the theory of multiplier ideal sheaves to algebraic geometry.

[3] Siu completed his doctoral dissertation, titled "Coherent Noether-Lasker decomposition of subsheaves and sheaf cohomology", under the supervision of Robert C.

[6] In 1993, Siu received the Stefan Bergman Prize[7] of the American Mathematical Society.

[10][11] He has been an invited speaker at the International Congress of Mathematicians in Helsinki (1978), Warsaw (1983) and Beijing (2002).

Currently, Siu is a member of the Scientific Advisory Board of the Clay Mathematics Institute (since 2003); the Advisory Committee for the Shaw Prize In Mathematical Sciences (since 2010);[12] the Advisory Committee for the Millennium Prize Problems under the sponsorship of the Clay Mathematics Institute; the Scientific Advisory Board for the Institute for Mathematics Sciences, National University of Singapore[13] (since 2009) and the Institute of Advanced Studies, Nanyang Technological University, Singapore (since 2006).