Tian Gang (Chinese: 田刚; pinyin: Tián Gāng; born 24 November 1958) is a Chinese mathematician and an academician of the Chinese Academy of Sciences. He is known for his contributions to geometric analysis and quantum cohomology, among other fields. He was born in Nanjing, China, was a professor of mathematics at MIT from 1995–1998, but now divides his time between Princeton University and Peking University.
Tian graduated from Nanjing University in 1982, and received a master's degree from Peking University in 1984. In 1988, he received a Ph.D. in mathematics from Harvard University, after having studied under Shing-Tung Yau. This work was so exceptional he was invited to present it at the Geometry Festival that year. In 1998, he was appointed as a Cheung Kong Scholar professor at the School of Mathematical Sciences at Peking University, under the "Cheung Kong Scholars Programme" (长江计划) of the Ministry of Education. Later his appointment was changed to Cheung Kong Scholar chair professorship. He was awarded the Alan T. Waterman Award in 1994, and the Veblen Prize in 1996. In 2004 Tian was inducted into the American Academy of Arts and Sciences.
Much of Tian's earlier work was about the existence of Kähler–Einstein metrics on complex manifolds under the direct of Yau. In particular he solved the existence question for Kähler–Einstein metrics on compact complex surfaces with positive first Chern class, and showed that hypersurfaces with a Kähler–Einstein metric are stable in the sense of geometric invariant theory. He proved that a Kähler manifold with trivial canonical bundle has trivial obstruction space, known as the Bogomolov–Tian–Todorov theorem.
He (jointly with Jun Li) constructed the moduli spaces of maps from curves in both algebraic geometry and symplectic geometry and studied the obstruction theory on these moduli spaces. He also (jointly with Y. Ruan) showed that the quantum cohomology ring of a symplectic manifold is associative.
In 2006, together with John Morgan of Columbia University, amongst others, Tian helped verify the proof of the Poincaré conjecture given by Grigori Perelman.
* Morgan, John; Gang Tian (2007). Ricci Flow and the Poincaré Conjecture. Clay Mathematics Institute. ISBN 0821843281.
1. ^ http://www.ams.org/notices/199603/comm-veblen.pdf
2. ^ Morgan, John W.; Gang Tian (25 July 2006). Ricci Flow and the Poincaré Conjecture. arXiv:math.DG/0607607.
* Veblen prize citation
* Gang Tian at the Mathematics Genealogy Project
* M.I.T. home page for Gang Tian
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