nLab Gang Tian

Gang Tian is a Chinese-American differential geometer. With Yongbin Ruan, he is one of the pioneers of differential geometric formalization of quantum cohomology.

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Selected writings

Introducing a mathematical definition of quantum cohomology rings:

• Yongbin Ruan, Gang Tian, A mathematical theory of quantum cohomology, Mathematical Research Letters 1 2 (1994) 269-278 [doi:10.4310/MRL.1994.v1.n2.a15, pdf]

• Bernd Siebert, Gang Tian, On Quantum Cohomology Rings of Fano Manifolds and a Formula of Vafa and Intriligator, Asian Journal of Mathematics 1 4 (1997) 679 – 695 [arXiv:alg-geom/9403010, doi:10.4310/AJM.1997.v1.n4.a2]

Related work on technique of virtual classes

• Jun Li, Gang Tian, Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998) 119-174 doi

• Yongbin Ruan, Gang Tian, A mathematical theory of quantum cohomology, J. Diff. Geometry 42 2 (1995) 259-367 [doi:10.4310/jdg/1214457234]

On Uhlenbeck's singularity theorem in higher dimensions:

• Terence Tao, Gang Tian, A singularity removal theorem for Yang-Mills fields in higher dimensions (2002) [arXiv:math/0209352]

On D=8 Seiberg-Witten theory:

• Yi-hong Gao and Gang Tian, Instantons and the monopole-like equations in eight dimensions (2000) [arXiv:hep-th/0004167, DOI:10.1088/1126-6708/2000/05/036]

On special holonomy:

• Jeff Cheeger, Gang Tian, Anti-self-duality of curvature and degeneration of metrics with special holonomy, Commun. Math. Phys. 255, 391–417 (2005) doi
• Paolo de Bartolomeis, Gang Tian, Stability of complex vector bundles, J. Diff. Geometry 43:2 (1996) pdf

On Ricci flow and (the proof of) the Poincaré conjecture:

• John W. Morgan, Gang Tian: Ricci Flow and the Poincaré Conjecture, Clay Mathematics Monographs 3 (2007) [arXiv:math/0607607, webpage, pdf]

category: people