Gang Tian

This is a Chinese name; the family name is Tian.
Gang Tian

Gang Tian at Oberwolfach in 2005
Born 24 November 1958
Nanjing, Jiangsu, China
Nationality China
Fields Mathematics
Institutions Princeton University
Peking University
Alma mater Harvard University
Peking University
Nanjing University
Doctoral advisor Shing-Tung Yau
Doctoral students Aaron Naber
Eaman Eftekhary
Known for Bogomolov–Tian–Todorov theorem
Notable awards Veblen Prize (1996)
Alan T. Waterman Award (1994)

Tian Gang (simplified Chinese: 田刚; traditional Chinese: 田剛; pinyin: Tián Gāng; born November 1958)[1] is a Chinese-American mathematician and an academician of the American Academy of Arts and Sciences. He is known for his contributions to geometric analysis and quantum cohomology especially Gromov-Witten invariants, 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) and also dean of School of Mathematical Sciences, Peking University. He with John Milnor involved as Senior Scholars of The Clay Mathematics Institute (CMI). Since 2011, Gang Tian become director of Sino-French Research Program in Mathematic in "le Centre National de la Recherche Scientifique"(CNRS) in Paris. Since 2010, He become Scientific council for International Center for Theoretical Physics in Trieste in Italy.

Biography

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.

Mathematical contributions

Much of Tian's earlier work was about the existence of Kähler–Einstein metrics on complex manifolds. In particular he solved the existence question for Kähler–Einstein metrics on compact complex surfaces with positive first Chern class,[2] defined (jointly with Weiyue Ding) a generalized Futaki invariant for a class of singular varieties as new obstructions to the existence of Kähler-Einstein orbifold metrics,[3] and proved (jointly with Yau) a noncompact version of Calabi's conjecture on quasiprojective manifolds.[4] He proved that a Kähler manifold with trivial canonical bundle has trivial obstruction space, known as the Bogomolov–Tian–Todorov theorem[5][6]

For Einstein manifolds, he (jointed with Cheeger) studied the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay [7] and the curvature and injectivity radius estimates for Einstein 4-manifolds.[8]

In sympletic geometry, 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.[9]He also (jointly with Y. Ruan) showed that the quantum cohomology ring of a symplectic manifold is associative.[10]

In Yang-Mills theory, he (jointed with Terence Tao) proved a singularity removal theorem for Yang-Mills fields in higher dimensions[11]

For Kähler-Ricci flow, he (jointed with Xiuxiong Chen) proved some convergence results.[12]

He introduced the Analytical Minimal Model program which is known as Tian-Song MMP theory in Birational Geometry. In Kähler geometry he has a new theory which is known as Cheeger-Colding-Tian's theory.

In 2006, together with John Morgan of Columbia University (now at Stony Brook University), amongst others, Tian helped verify the proof of the Poincaré conjecture given by Grigori Perelman.[13]

Gang Tian was once one of the five members of the Abel Prize Committee, which is sometimes considered to be the second most important prize in mathematics after the Fields medal.[14]

Gang Tian was also once one of the five members of the Ramanujan Prize selection committee.

Since 2012 he became member of Leroy P. Steele Prize Committee in AMS.[15]

Editorial Positions

Gang Tian, is member of the editorial boards of a number of high ranking journals in Mathematics.

1. Annals of Mathematics[16]

2.Annali della Scuola Normale Superiore[17]

3.Journal of Symplectic Geometry[18]

3.Journal of the American Mathematical Society,1995-1998.[19]

4.Geometry & Topology[20]

5.The Journal of Geometric Analysis[21]

6.Geometric and Functional Analysis[22]

7.Advances in Mathematics [23]

8.International Mathematics Research Notices[24]

9-Pacific Journal of Mathematics, 1994-1998.

10-Communications in Analysis and Geometry, 1994-2000.

11-Acta Mathematica Sinica,[25]

12-Mathematics Revista Matemática Complutense [26]

13-Communications in Mathematics and Statistics, [27]

14.Communication in Contemporary Mathematics,[28]

Publications

(Selected)

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.

Students

Vladimir Bozin, MIT, 2004 [29]

Xiaodong Cao, MIT, 2002;[30]

Alessandro Ghigi, Scuola Normale Superiore, Pisa, 2003,[31]

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[32]

Chi Li, Princeton, 2012;

Eaman Eftekhary,Princeton;2004[33]

Mohammad Farajzadeh Tehrani, Princeton 2012;

Giulia Saccà, Princeton 2013;

Guangbo Xu, Princeton 2013;

Liangming Shen, Princeton(current);

Heather Macbeth, Princeton(current);

Anibal Patricio Velozo Ruiz, Princeton(current);

Hassan Jolany, University of Lille1, France(current)[34]

References

  1. ↑ http://www.ams.org/notices/199603/comm-veblen.pdf
  2. ↑ Tian, G. On Calabi's conjecture for complex surfaces with positive first Chern class. Invent. Math. 101 (1990), no. 1, 101—172.
  3. ↑ Ding, Wei Yue; Tian, Gang Kähler-Einstein metrics and the generalized Futaki invariant. Invent. Math. 110 (1992), no. 2, 315–335.
  4. ↑ Tian, G.; Yau, Shing-Tung. Complete Kähler manifolds with zero Ricci curvature. I. J. Amer. Math. Soc. 3 (1990), no. 3, 579—609.
  5. ↑ 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.
  6. ↑ The history about Tian-Todorov Lemma
  7. ↑ Cheeger, Jeff; Tian, Gang On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay. Invent. Math. 118 (1994), no. 3, 493–571.
  8. ↑ Cheeger, Jeff; Tian, Gang Curvature and injectivity radius estimates for Einstein 4-manifolds. J. Amer. Math. Soc. 19 (2006), no. 2, 487–525
  9. ↑ Li, Jun; Tian, Gang Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties. J. Amer. Math. Soc. 11 (1998), no. 1, 119–174.
  10. ↑ Ruan, Yongbin; Tian, Gang. A mathematical theory of quantum cohomology. J. Differential Geom. 42 (1995), no. 2, 259—367.
  11. ↑ 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.
  12. ↑ Chen, X. X.; Tian, G. Ricci flow on Kähler-Einstein surfaces. Invent. Math. 147 (2002), no. 3, 487–544.
  13. ↑ Morgan, John W.; Gang Tian (25 July 2006). "Ricci Flow and the Poincaré Conjecture". arXiv:math.DG/0607607.
  14. ↑ http://www.ams.org/notices/201304/rnoti-p480.pdf
  15. ↑ http://www.eusja.org/top-secret-of-abel-prize/
  16. ↑ http://annals.math.princeton.edu/board
  17. ↑ http://annaliscienze.sns.it/index.php?page=EditorialBoard
  18. ↑ http://intlpress.com/site/pub/pages/journals/items/jsg/_home/editorial/index.html
  19. ↑ http://www.ams.org/publications/journals/journalsframework/jams/editorial_history_jams
  20. ↑ http://www.msp.warwick.ac.uk/gt/about/journal/editorial.html
  21. ↑ http://www.springer.com/mathematics/geometry/journal/12220?detailsPage=editorialBoard
  22. ↑ http://www.springer.com/birkhauser/mathematics/journal/39?detailsPage=editorialBoard
  23. ↑ http://www.journals.elsevier.com/advances-in-mathematics/editorial-board/
  24. ↑ http://www.oxfordjournals.org/our_journals/imrp/editorial_board.html
  25. ↑ http://www.springer.com/mathematics/journal/10114
  26. ↑ http://www.springer.com/mathematics/journal/13163
  27. ↑ http://www.springer.com/mathematics/journal/40304
  28. ↑ http://www.worldscientific.com/page/ccm/editorial-board
  29. ↑ Vladimir Bozin, MIT, 2004;http://genealogy.math.ndsu.nodak.edu/id.php?id=84790
  30. ↑ http://genealogy.math.ndsu.nodak.edu/id.php?id=66077
  31. ↑ http://www.matapp.unimib.it/~ghigi/
  32. ↑ Richard Bamler, Princeton, 2011;http://genealogy.math.ndsu.nodak.edu/id.php?id=158616
  33. ↑ http://math.ipm.ac.ir/~eftekhary/
  34. ↑ http://math.univ-lille1.fr/~jolany

External links