||This biographical article needs additional citations for verification. (June 2014)|
Gang Tian at Oberwolfach in 2005
24 November 1958 |
Nanjing, Jiangsu, China
|Alma mater||Harvard University
|Doctoral advisor||Shing-Tung Yau|
|Doctoral students||Zhiqin Lu|
|Known for||Bogomolov–Tian–Todorov theorem|
|Notable awards||Veblen Prize (1996)
Waterman Prize (1994)
Tian Gang (simplified Chinese: 田刚; traditional Chinese: 田剛; pinyin: Tián Gāng; born 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, and was a professor of mathematics at MIT from 1995–2006 (holding the chair of Simons Professor of Mathematics from 1996), but now divides his time between Princeton University and Peking University. His employment at Princeton started from 2003, and now he is entitled Higgins Professor of Mathematics; starting 2005, he has been the director of Beijing International Center for Mathematical Research (BICMR).
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 direction 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.
|This section does not cite any references or sources. (June 2014)|
Tian, Gang. Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric. Mathematical aspects of string theory (San Diego, Calif., 1986), 629—646, Adv. Ser. Math. Phys., 1, World Sci. Publishing, Singapore, 1987.
Tian, Gang. On Kähler-Einstein metrics on certain Kähler manifolds with $C\sb 1(M)>0$. Invent. Math. 89 (1987), no. 2, 225—246.
Tian, G.; Yau, Shing-Tung. Complete Kähler manifolds with zero Ricci curvature. I. J. Amer. Math. Soc. 3 (1990), no. 3, 579—609.
Tian, G. On Calabi's conjecture for complex surfaces with positive first Chern class. Invent. Math. 101 (1990), no. 1, 101—172.
Tian, Gang. On a set of polarized Kähler metrics on algebraic manifolds. J. Differential Geom. 32 (1990), no. 1, 99—130.
Ruan, Yongbin; Tian, Gang. A mathematical theory of quantum cohomology. J. Differential Geom. 42 (1995), no. 2, 259—367.
Tian, Gang. Kähler-Einstein metrics with positive scalar curvature. Invent. Math. 130 (1997), no. 1, 1--37.
Ruan, Yongbin; Tian, Gang. Higher genus symplectic invariants and sigma models coupled with gravity. Invent. Math. 130 (1997), no. 3, 455—516.
Li, Jun; Tian, Gang. Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties. J. Amer. Math. Soc. 11 (1998), no. 1, 119—174.
Liu, Gang; Tian, Gang. Floer homology and Arnold conjecture. J. Differential Geom. 49 (1998), no. 1, 1--74.
Liu, Xiaobo; Tian, Gang. Virasoro constraints for quantum cohomology. J. Differential Geom. 50 (1998), no. 3, 537—590.
Tian, Gang. Gauge theory and calibrated geometry. I. Ann. of Math. (2) 151 (2000), no. 1, 193—268.
Tian, Gang; Zhu, Xiaohua. Uniqueness of Kähler-Ricci solitons. Acta Math. 184 (2000), no. 2, 271—305.
Cheeger, J.; Colding, T. H.; Tian, G. On the singularities of spaces with bounded Ricci curvature. Geom. Funct. Anal. 12 (2002), no. 5, 873—914.
Tao, Terence; Tian, Gang. A singularity removal theorem for Yang-Mills fields in higher dimensions. J. Amer. Math. Soc. 17 (2004), no. 3, 557—593.
Tian, Gang; Viaclovsky, Jeff. Bach-flat asymptotically locally Euclidean metrics. Invent. Math. 160 (2005), no. 2, 357—415.
Cheeger, Jeff; Tian, Gang. Curvature and injectivity radius estimates for Einstein 4-manifolds. J. Amer. Math. Soc. Vol. 19, No. 2 (2006), 487—525.
Morgan, John; Tian, Gang. Ricci flow and the Poincaré conjecture. Clay Mathematics Monographs, 3. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2007, 525pp.
Song, Jian; Tian, Gang. The Kähler-Ricci flow on surfaces of positive Kodaira dimension. Invent. Math. 170 (2007), no. 3, 609—653.
Chen, X. X.; Tian, G. Geometry of Kähler metrics and foliations by holomorphic discs. Publ. Math. Inst. Hautes Études Sci. No. 107 (2008), 1--107.
Kołodziej, Sławomir; Tian, Gang A uniform $L^\infty$L∞ estimate for complex Monge-Ampère equations. Math. Ann. 342 (2008), no. 4, 773–787.
Mundet i Riera, I.; Tian, G. A compactification of the moduli space of twisted holomorphic maps. Adv. Math. 222 (2009), no. 4, 1117–1196.
Rivière, Tristan; Tian, Gang The singular set of 1-1 integral currents. Ann. of Math. (2) 169 (2009), no. 3, 741–794.
Tian, Gang Finite-time singularity of Kähler-Ricci flow. Discrete Contin. Dyn. Syst. 28 (2010), no. 3, 1137–1150.
Vladimir Bozin, MIT, 2004 
Xiaodong Cao, MIT, 2002;
Sandra Francisco, MIT, 2005;
Zuoliang Hou, MIT, 2004;
Ljudmila Kamenova, MIT, 2006;
Peng Lu, State University of New York at Stony Brook, 1996;
Zhiqin Lu, New York University, 1997;
Dragos Oprea, MIT, 2005;
Yanir Rubinstein, MIT, 2008;
Sema Salur, Michigan State University, 2000;
Bianca Santoro, MIT, 2006;
Natasa Sesum, MIT, 2004;
Jake Solomon, MIT, 2006;
Jun S. Song, MIT, 2001;
Michael Usher, MIT, 2004;
Lijing Wang, MIT, 2003;
Hao Wu, MIT, 2004;
Zhiyu Wu, Columbia University, 1998;
Baozhong Yang, MIT, 2000;
Zhou Zhang, MIT, 2006;
Aaron Naber, Princeton, 2009;
Hans-Joachim Hein, Princeton, 2010;
Richard Bamler, Princeton, 2011
Chi Li, Princeton, 2012;
Mohammad Farajzadeh Tehrani, Princeton 2012;
Giulia Saccà, Princeton 2013;
Guangbo Xu, Princeton 2013;
Liangming Shen, Princeton(current);
Heather Macbeth, Princeton(current)
- The history about Tian-Todorov Lemma
- Morgan, John W.; Gang Tian (25 July 2006). "Ricci Flow and the Poincaré Conjecture". arXiv:math.DG/0607607.
- Vladimir Bozin, MIT, 2004;http://genealogy.math.ndsu.nodak.edu/id.php?id=84790
- Richard Bamler, Princeton, 2011;http://genealogy.math.ndsu.nodak.edu/id.php?id=158616
- Veblen prize citation
- Yum-Tong Siu's 3 letters on Tian's plagiarism
- Shing-Tung Yau slams academic corruption in China
- Donaldson's comments on Tian's recent plagiarism
- Gang Tian at the Mathematics Genealogy Project
- M.I.T. home page for Gang Tian (probably out of date).