John He
每次谈到丹尼斯·帕内尔·苏利文（Dennis Sullivan），我导师都是一种特别的语气。他们是Princetong读研究生时的同学，同一个导师。我做完博士论文，我导师就安排我去Dennis Sullivan，还有Thurston那里做报告。
苏利文（1941年2月12日－），美国数学家。他在拓扑学（代数拓扑及几何拓扑）以及动力系统理论方面的研究颇有建树，是纽约市立大学研究生院的阿尔伯特·爱因斯坦讲座教授，也是纽约州立大学石溪分校的教授，2010年获数学沃尔夫奖，2022年获阿贝尔奖。
沙利文大学开始是在莱斯大学学化学工程，但在遇到一个特别有启发性的数学定理后，在第二年将专业转为数学。 那个定理是单值化定理（Uniformization theorem）的一个特例，用他自己的话来说：
像气球一样的任何拓扑学表面，无论是什么形状——香蕉或米开朗基罗的大卫雕像——都可以放在一个完美的圆形球体上，使得在每个点上，其所需的拉伸或挤压在其所有方向都是相同的。 （Any surface topologically like a balloon, and no matter what shape—a banana or the statue of David by Michelangelo—could be placed on to a perfectly round sphere so that the stretching or squeezing required at each and every point is the same in all directions at each such point.[4]
他于 1963 年获得莱斯大学文学学士学位。 1966 年，他在威廉·布劳德 (William Browder) 的指导下，他凭论文“三角剖分同伦等价”获得普林斯顿大学哲学博士学位。
关于Thurston，他对于解决上世纪的三大数学问题之一，Poincare猜想，打下了基础。Thurston conjecture解决了，可以包括Poincare猜想的许多问题。Thurston是我们讨论班的老大。另一位主力是Hamilton，办公室和我的办公室隔3米的距离，经常在讨论班一起学习（我们学他相对比较多)。走完最后一步的是俄罗斯的Perelman，证明了Thurston猜想。Perelman认为Hamilton做的贡献最大。
Perelman辞职不干，拿奖的时候，找不到人。后来，他Fields奖也不要了，百万美元的millenium奖也不要了（这个是2000年世纪初设的10几个millenium problems，解决一个可以得百万大奖，目前好像只解决了这一个）。
Princeton还有一大牛人，Andrew Wiles，解决了Fermat大定理---3大数学问题的另一个。现在还剩下一个，Riemann猜测，目前还没有解决。
几何化猜想（英語：Geometrization conjecture）指的是任取一个紧致（可能带边）的三维流形尽量作连通和以使其成为尽可能简单的三维流形的连通和，对于带边流形可能还需要沿着一些圆盘继续切割，有唯一的方法沿着一些环面割开得到尽可能简单的若干小块，这些小块均为八种标准几何结构之一。八种标准几何结构均为完备的黎曼度量，这些几何结构在某种意义上是比较“好”的，例如体积有限、“直线”都可无限延伸等等。该猜想由威廉·瑟斯顿提出。
In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected Riemann surface can be given one of three geometries (Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by William Thurston (1982), and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture.
Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture. Thurston announced a proof in the 1980s and since then several complete proofs have appeared in print.
Grigori Perelman announced a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery in two papers posted at the arxiv.org preprint server. Perelman's papers were studied by several independent groups that produced books and online manuscripts filling in the complete details of his arguments. Verification was essentially complete in time for Perelman to be awarded the 2006 Fields Medal for his work, and in 2010 the Clay Mathematics Institute awarded him its 1 million USD prize for solving the Poincare conjecture, though Perelman declined to accept either award.
The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.