Tian Gang

Tian Gang (born November 24, 1958) is a Chinese mathematician.

He is a professor of mathematics at Peking University and Higgins Professor Emeritus at Princeton University.

He is known for contributions to the mathematical fields of Kähler geometry, Gromov-Witten theory, and geometric analysis.

He qualified in the second college entrance exam after Cultural Revolution in 1978.

Yau had conjectured in the 1980s, based partly in analogy to the Donaldson-Uhlenbeck-Yau theorem, that existence of a Kähler-Einstein metric should correspond to stability of the underlying Kähler manifold in a certain sense of geometric invariant theory.

He 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, under the supervision of Shing-Tung Yau.

Some similar and influential work in the Riemannian setting was done in 1989 and 1990 by Michael Anderson, Shigetoshi Bando, Atsushi Kasue, and Hiraku Nakajima.

The case of Kähler surfaces was revisited by Tian in 1990, giving a complete resolution of the Kähler-Einstein problem in that context.

The main technique was to study the possible geometric degenerations of a sequence of Kähler-Einstein metrics, as detectable by the Gromov–Hausdorff convergence.

Tian adapted many of the technical innovations of Karen Uhlenbeck, as developed for Yang-Mills connections, to the setting of Kähler metrics.

He was a professor of mathematics at the Massachusetts Institute of Technology from 1995 to 2006 (holding the chair of Simons Professor of Mathematics from 1996).

Tian's most renowned contribution to the Kähler-Einstein problem came in 1997.

In 1998, he was appointed as a Cheung Kong Scholar professor at Peking University.

Later his appointment was changed to Cheung Kong Scholar chair professorship.

His employment at Princeton started from 2003, and was later appointed the Higgins Professor of Mathematics.

Starting 2005, he has been the director of the Beijing International Center for Mathematical Research (BICMR); from 2013 to 2017 he was the Dean of School of Mathematical Sciences at Peking University.

He and John Milnor are Senior Scholars of the Clay Mathematics Institute (CMI).

In 2010, he became scientific consultant for the International Center for Theoretical Physics in Trieste, Italy.

Tian has served on many committees, including for the Abel Prize and the Leroy P. Steele Prize.

He is a member of the editorial boards of many journals, including Advances in Mathematics and the Journal of Geometric Analysis.

In the past he has been on the editorial boards of Annals of Mathematics and the Journal of the American Mathematical Society.

Among his awards and honors:

In 2011, Tian became director of the Sino-French Research Program in Mathematics at the Centre national de la recherche scientifique (CNRS) in Paris.

Since at least 2013 he has been heavily involved in Chinese politics, serving as the Vice Chairman of the China Democratic League, the second most populous political party in China.

Tian is well-known for his contributions to Kähler geometry, and in particular to the study of Kähler-Einstein metrics.

Shing-Tung Yau, in his renowned resolution of the Calabi conjecture, had settled the case of closed Kähler manifolds with nonpositive first Chern class.

His work in applying the method of continuity showed that

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control of the Kähler potentials would suffice to prove existence of Kähler-Einstein metrics on closed Kähler manifolds with positive first Chern class, also known as "Fano manifolds."

Tian and Yau extended Yau's analysis of the Calabi conjecture to noncompact settings, where they obtained partial results.

They also extended their work to allow orbifold singularities.

Tian introduced the "α-invariant," which is essentially the optimal constant in the Moser-Trudinger inequality when applied to Kähler potentials with a supremal value of 0.

He showed that if the α-invariant is sufficiently large (i.e. if a sufficiently strong Moser-Trudinger inequality holds), then

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control in Yau's method of continuity could be achieved.

This was applied to demonstrate new examples of Kähler-Einstein surfaces.

From 2017 to 2019 he served as the Vice President of Peking University.

Tian was born in Nanjing, Jiangsu, China.

As of 2020, he is the Vice Chairman of the China Democratic League and the President of the Chinese Mathematical Society.