Ngaiming Mok | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Born | 1956 (age 66–67) Hong Kong | ||||||||||||
Scientific career | |||||||||||||
Doctoral advisor | Yum-Tong Siu | ||||||||||||
Chinese name | |||||||||||||
Chinese | 莫 毅 明 | ||||||||||||
|
Ngaiming Mok (Chinese :莫毅明; pinyin :Mò Yìmíng; born 1956) is a Hong Kong mathematician specializing in complex differential geometry and algebraic geometry. He is currently a professor at the University of Hong Kong. [1]
After graduating from St. Paul's Co-educational College in Hong Kong in 1975, [2] Mok studied at the University of Chicago and Yale University, obtaining his M.A. in Mathematics from Yale in 1978. [3] He obtained his Ph.D. from Stanford University under the guidance of Yum-Tong Siu. [4] He taught at Princeton University, Columbia University and the University of Paris-Saclay before joining the faculty of the University of Hong Kong in 1994. He has been the director of the University of Hong Kong's Institute of Mathematical Research since 1999.
The awards Mok has received include a Sloan Fellowship in 1984, the Presidential Young Investigator Award in Mathematics in 1985, and the Stefan Bergman Prize in 2009. [5] Mok was an invited speaker at the 1994 International Congress of Mathematicians in Zurich and served on the Fields Medal committee at the 2010 ICM in Hyderabad. He was on the editorial board of Inventiones Mathematicae from 2002 to 2014, [6] and he is currently an editor of Mathematische Annalen. [7] He was elected as Member of the Chinese Academy of Sciences (Division of Mathematics and Physics) in 2015, [8] and a fellow of the American Mathematical Society in 2019. [9]
Mok is a polyglot, being able to speak Chinese (including Mandarin and Cantonese), English, French, German, Italian, Russian, Japanese and more.
Shing-Tung Yau is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau retired from Harvard to become a professor of mathematics at Tsinghua University.
Lev Genrikhovich Schnirelmann was a Soviet mathematician who worked on number theory, topology and differential geometry.
Nigel James Hitchin FRS is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.
Wilhelm Karl Joseph Killing was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
Shiu-Yuen Cheng (鄭紹遠) is a Hong Kong mathematician. He is currently the Chair Professor of Mathematics at the Hong Kong University of Science and Technology. Cheng received his Ph.D. in 1974, under the supervision of Shiing-Shen Chern, from University of California at Berkeley. Cheng then spent some years as a post-doctoral fellow and assistant professor at Princeton University and the State University of New York at Stony Brook. Then he became a full professor at University of California at Los Angeles. Cheng chaired the Mathematics departments of both the Chinese University of Hong Kong and the Hong Kong University of Science and Technology in the 1990s. In 2004, he became the Dean of Science at HKUST. In 2012, he became a fellow of the American Mathematical Society.
Gerhard Hessenberg was a German mathematician who worked in projective geometry, differential geometry, and set theory.
Georg August Nöbeling was a German mathematician.
Mok is a surname in various cultures. It may be a transcription of several Chinese surnames in their Cantonese or Teochew pronunciations, a Dutch surname, a Hungarian surname, or a Korean surname.
Jean-Michel Bismut is a French mathematician who has been a professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry.
Indranil Biswas is an Indian mathematician. He is professor of mathematics at the Tata Institute of Fundamental Research, Mumbai. He is known for his work in the areas of algebraic geometry, differential geometry, and deformation quantization.
Gerald Walter Schwarz is an American mathematician and Professor Emeritus at Brandeis University. Schwarz specializes in invariant theory, algebraic group actions and invariant differential operators.
Martin George Scharlemann is an American topologist who is a professor at the University of California, Santa Barbara. He obtained his Ph.D. from the University of California, Berkeley under the guidance of Robion Kirby in 1974.
Lawrence Man Hou Ein is a mathematician who works in algebraic geometry.
William Hamilton Meeks III is an American mathematician, specializing in differential geometry and minimal surfaces.
Jun-Muk Hwang is a South Korean mathematician, specializing in algebraic geometry and complex differential geometry.
Dieter Kotschick is a German mathematician, specializing in differential geometry and topology.
Thomas Schick is a German mathematician, specializing in algebraic topology and differential geometry.
Marius Nicolae Crainic is a Romanian mathematician working in the Netherlands.
Xiangyu Zhou is a Chinese mathematician, specializing in several complex variables and complex geometry. He is known for his 1998 proof of the "extended future tube conjecture", which was an unsolved problem for almost forty years.
In algebraic geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundle. The theorem states the following
Le Potier (1975): Let X be a n-dimensional compact complex manifold and E a holomorphic vector bundle of rank r over X, here is Dolbeault cohomology group, where denotes the sheaf of holomorphic p-forms on X. If E is an ample, then
from Dolbeault theorem,
By Serre duality, the statements are equivalent to the assertions: