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Chinese Mathematicians Xiuxiong Chen and Bing Wang (SGY ’98) Have Made a Major Breakthrough in the Area of Differential Geometry



Xinhua News Agency reported, Xiuxiong Chen and Bing Wang (SGY ’98), professors at the University of Science and Technology of China (USTC), have successfully proved the “Hamilton-Tianconjectureand “partial--conjecture” which are two core conjectures that the international mathematics community had not been able to solve for the last two decades. A few days ago, the Journal of Differential Geometry, a top international mathematical journal, published the achievements. The length of the paper is more than 120 pages, and it took 11 years from writing to publishing.

The Alumni Innovation Fund of USTC congratulated Xiuxiong Chen and Bing Wang’s achievements.

  Starting from 2016, the Alumni Fund has supported the development of the School of Mathematics of USTC through the Key Discipline Development Fund. From 2018, the Fund increased its support to the International Institute of Geometry and Physics. It's a great honor that the Fund have supported Wang and other top mathematics talents at USTC. We are proud that the alumni foundation gives support to the talented scholars when they were young, rather than when they are already famous worldwide. The Fund supported or awarded a large number of talented scholars, such as Jianwei Pan (Alumni Fund Chair Professor), Jiang He (SGY’05, Moruo Guo Scholarship) and Yuan Cao (SGY’10, Moruo Guo Scholarship, Overseas Exchanging Scholarship).

  Differential geometry originated in the 17th century, mainly usingcalculus to research on geometric character in space, which has huge value in physics, astronomy and engineering. “Ricci Flow,” which originated in the 1980s, is a research tool using differential geometry to describe spatial evolution.

“As large as the expansion of the universe, as small as the expansion or contraction due to temperature changes, many natural phenomena can be attributed to the evolution of space.” Professor Bing Wang analogizes that as we inflate a balloon and the balloon expands, we can use “Ricci Flow” to research its spatial evolution, eventually getting a result in perfect agreement with observed reality.

  Xiuxiong Chen and Bing Wang’s team persistently research on the convergence of “Ricci Flow” in differential geometry.  Using new thoughts and new methods they became the first to prove the Hamilton-Tianconjectureand the “partial--conjecture,” two core unsolved conjectures that arose in the past two decades.

The research required 5 years of effort, and the paper is more than 120 pa

ges. Bing Wang says it is like writing a novel, “the difference is that it depends on logical deduction rather than a storyline.”

  It is worth mentioning that it took 6 more years from submitting the paper to publishing since it is a long paper and takes a long time to review. However, this period of publishing is not rare in the mathematics community since reviewers need enough time to learn about new concepts and new methods.

  Reviewers of the Journal of Differential Geometry commented that this paper isasignificant progress in the area of geometry analysis which will inspire much related research.

  Simon Donaldson, recipient of the Fields Medal, the highest prize in Mathematics, praised that this work is a ”major breakthrough in the area of geometry in recent years.”

 

 

 

Translated by Haoyu Yang