Notices of the International Consortium of Chinese Mathematicians

Volume 5 (2017)

Number 1

From Riemann and Kodaira to Modern Developments on Complex Manifolds

Pages: 1 – 21



Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


We survey the theory of complex manifolds that are related to Riemann surface, Hodge theory, Chern class, Kodaira embedding and Hirzebruch–Riemann-Roch, and some modern development of uniformization theorems, Kähler–Einstein metric and the theory of Donaldson–Uhlenbeck–Yau on Hermitian Yang–Mills connections. We emphasize mathematical ideas related to physics. At the end, we identify possible future research directions and raise some important open questions.

Reprinted with permission from the Japanese Journal of Mathematics 11, 263–303 (2016). DOI: 10.1007/s11537-016-1565-6.

Published 16 October 2017