Peking University, Beijing, Jun. 14, 2010: On June 9, the 2010 Clay Mathematics Conference commenced at the Poincaré Institute in Paris, France. Academician Tian Gang, director of International Mathematics Research Center of Peking University attended the conference and gave a keynote address titled “Metric geometry and analysis of 4-manifolds”.
Clay Mathematics Conference is a significant conference in the international mathematics world, which is aimed at confirming and discussing the most recent research achievement in the mathematics field. The theme this year is to congratulate and commend Russian mathematician Grigority Perelman for his complete solution to the first of the Millennium Problems, the Poincare Conjecture, as well as investigating the future of the development of world’s mathematics. Based on his great contribution to enrich and verify Perelman’s solutions to the Poincare Conjecture and the work of the Thurston Geometrization Conjecture, Academician Tian Gang was invited by Clay Mathematics Institute as the only Chinese mathematician to give a keynote address on the conference this year.
Academician Tian Gang discussed several curvature equations on 4-manifolds and their application in topology and geometry, which is closely related to Grigority’s work, and put forward some important ways and problems in applying curvature equations and the approach of geometry analysis to the research of 4-manifiods.
Together, with the aid of Tian Gang, Perelman’s cracking job of the Poincare Conjecture gained recognition quite successfully. In 2007, Academician Tian Gang and John Morgan’s work “Ricci flow and the Poincaré conjecture” helped verify and explain several detailed questions of Perelman’s works, offer a more specific proof for the dematerialization of limited time of Ricci flow, as well as elaborate their own thoughts at the same time. James Carlson, director of Clay Mathematic Institute fully acknowledged Tian Gang’s outstanding contribution of enriching and verifing Perelman’s solutions to the Poincaré Conjecture and the work of the Thurston Geometrization Conjecture in the announcement of the first prize of Millennia Problems to Perelman.
Clay Mathematics Institute was one of the most influential math research institutes in the world, having attracted many world-renowned scholars from universities and institutes such as Harvard, Princeton, Cornell, Courant Institute, Imperial College、IHES、Institut Fourier, to attend this meeting, like Fields awards winner Michael Atiyah、William Thurston、Stephen Smale、Simon Donaldson, and Abel prize winner.
Extended Readings:
Tian Gang was born in Nanjing, currently a Professor at Peking University, director of Peking International Mathematics Research Center and professor in Princeton University. Tian Gang has solved a series of geometry and mathematical physics major issues, especially in the research of K？hler-Einstein Metrics, in which he fully resolved the complex surface case and found that the measurement and the stability of geometry are closely connected. Collaborating with others, he established the strict mathematical basis for the theory of quantum cohomology and firstly demonstrated that the quantum cohomology can be conjugated to solve the Arnold conjecture for symplectic non-degenerate case. Tian Gang also has outstanding achievements in high-dimensional gauge field theory, by which he established the deep connection between the establishment of a self-dual Yang-Mills contact with geometric scaling. In 1994, Tian Gang was awarded the "Waterman Award” by the National Foundation. In 1996, Tian Gang was awarded the “Veblen Geometry Prize" by the Mathematical Association of the United States.
Edited by: Connie Chang
Translated by: Chen Long
Source: PKU News (Chinese)
