Gang Tian
Tian Gang (田 刚) (* November 24, 1958 in Nanjing) is a Chinese mathematician who deals with differential geometry and topology.
Life
Tian graduated from Nanjing University ( bachelor's degree, 1982) and Beijing University, where in 1984 he received his diploma in mathematics. In 1988 he received his doctorate at Shing-Tung Yau at Harvard University. After that, he was at Princeton University, the State University of New York at Stony Brook and from 1991 at the Courant Institute of Mathematical Sciences of New York University. From 1995 he was at the Massachusetts Institute of Technology (MIT). Today he is at the same time mathematics professor at Princeton University and Peking University ( " Cheung Kong Scholar Professor " since 1998). He has been a visiting professor at the Institut des Hautes Études Scientifiques ( IHES ), the Institute for Advanced Study, Stanford University ( Bergmann Lecture 1994) and the Academia Sinica in Beijing.
1991 to 1993 he was Sloan Fellow. In 1994 he received the Alan Waterman Award of the National Science Foundation and the 1996 Oswald Veblen Prize -. In 2004 he became a member of the American Academy of Arts and Sciences. In 1990 he was invited speaker at the International Congress of Mathematicians (ICM ) in Kyoto ( Kähler -Einstein metrics on algebraic manifolds ) and in 2002 he gave a plenary lecture at the ICM in Beijing ( Geometry and Nonlinear Analysis).
Work
Tian initially dealt in connection to his teacher Yau with the existence of Kähler -Einstein metrics on compact complex manifolds. That is the question for such manifolds, which allow both Kähler metrics and Einstein manifolds are ( their Ricci curvature is proportional to the metric tensor, the sign of the constant of proportionality depends on the first Chern class ). Examples are important in string theory Calabi -Yau manifolds (where the first Chern class vanishes ). The existence in the case of negative first Chern class has been proven by Thierry Aubin in 1976 and for the case of vanishing Chern classes followed the existence of Yau's proof of Calabi 's conjecture (1977). In the case of positive Chern class Yau found a counter-example ( the complex projective plane with blow -up in two points ). The question of the existence of Kähler -Einstein metrics on complex surfaces with positive Chern class was then released by Tian. He also showed the stability (in the sense of geometric invariant theory by David Mumford ) of the Kähler - Einstein metric in this case ( what had been conjectured by Yau ).
The name of Tian is also connected to the Bogomolov - Tian- Todorov theorem on the smoothness ( absence of obstruction ) of the moduli space of Calabi -Yau spaces ( with Bogomolov, Andrei Todorov ).
He also studied the moduli spaces of curves in algebraic and symplectic geometry and quantum cohomology with Yongbin Ruan ( deformation of the cohomology ring of symplectic manifolds, specifically, they proved the associativity of quantum cohomology ring).
In 2006, he played an important role in the verification of the correctness of the proof of the Poincaré conjecture by Grigori Perelman. By John Morgan, he published a full version of the proof ( John Morgan, Tian " Ricci Flow and the Poincare Conjecture ", Clay Mathematics Institute 2007), which had previously been published only in Preprints of Perelman (and not with all the necessary details).
Writings
- Canonical metrics in Kähler Geometry. Birkhäuser, 2000
- John Morgan: Ricci Flow and the Poincaré Conjecture. American Mathematical Society, 2007