21 Facts About Tian Gang

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

Tian Gang is known for contributions to the mathematical fields of Kahler geometry, Gromov-Witten theory, and geometric analysis.

Tian Gang graduated from Nanjing University in 1982, and received a master's degree from Peking University in 1984.

Tian Gang was a professor of mathematics at the Massachusetts Institute of Technology from 1995 to 2006.

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

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

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

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

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

However, certain incorrect statements in Tian Gang's work, owing to the highly technical nature of the paper, went unnoticed until after its publication.

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

Tian Gang published a proof of the conjecture in the same year, although Chen, Donaldson, and Sun have accused Tian Gang of academic and mathematical misconduct over his paper.

In one of his first articles, Tian Gang studied the space of Calabi-Yau metrics on a Kahler manifold.

Tian Gang showed that any infinitesimal deformation of Calabi-Yau structure can be 'integrated' to a one-parameter family of Calabi-Yau metrics; this proves that the "moduli space" of Calabi-Yau metrics on the given manifold has the structure of a smooth manifold.

Tian Gang showed that a certain rescaling of this sequence will necessarily converge in the topology to the original Kahler metric.

Ruan and Tian Gang's results are in a somewhat more general setting.

Li and Tian Gang then adapted their algebro-geometric work back to the analytic setting in symplectic manifolds, extending the earlier work of Ruan and Tian Gang.

Tian and Gang Liu made use of this work to prove the well-known Arnold conjecture on the number of fixed points of Hamiltonian diffeomorphisms.

In collaboration with John Morgan, Tian Gang published an exposition of Perelman's papers in 2007, filling in many of the details.

Morgan and Tian Gang's exposition is the only of the three to deal with Perelman's third paper, which is irrelevant for analysis of the geometrization conjecture but uses curve-shortening flow to provide a simpler argument for the special case of the Poincare conjecture.

In collaboration with Natasa Sesum, Tian Gang published an exposition of Perelman's work on the Ricci flow of Kahler manifolds, which Perelman did not publish in any form.