Nov 012012
 

28 日, Xiu-Xiong Chen(陈秀雄), Simon Donaldson, Song Sun(孙崧, 很年轻, 曾在科大少年班就读) 在 arxiv 上传了一篇文章 “Kähler-Einstein metrics and stability“, 给出了一个证明 K-稳定的 Fano 流形容许 Kähler-Einstein 度量(Yau-Tian-Donaldson conjecture)的轮廓, 工具是 Donaldson 新发展的连续性方法:
“We annnounce a proof of the fact that a K-stable Fano manifold admits a Kähler-Einstein metric and give a brief outline of the proof.”

田刚 25 日在 Stony Brook 庆祝 Lawson 70 寿辰的会议上宣布证明了 K 稳定性猜想, 方法好像与 Donaldson 不太一样. 11月1日下午2:00-3:00, 田刚又在北京国际数学研究中心重复了这个报告.

孙崧, 安徽省安庆市怀宁县金拱人. 2000 年中考, 他以怀宁县第一名, 进入怀宁县最好的中学——安徽省怀宁中学.

2002年, 安徽省怀宁中学读高二的孙崧获得全国高中学生化学竞赛二等奖.  同年他参加高考, 成为怀宁县考进科大少年班的第一人.

进入中科大后, 良好的学习氛围给了他扎实的数理基础和良好的科研素养. 在他的不懈努力下, 于 2006 年拿到全额奖学金进入美国威斯康星大学数学系追随陈秀雄教授. 现为纽约州立大学石溪分校助理教授.

陈秀雄 1982 年高考就以全省前 100 名, 全市第 1 名的优异成绩被中国科技大学数学系录取, 并于 1987 年毕业. 接着, 他到中国科学院研究生院师从彭家贵教授. 1989 年由国家保送去美国宾夕法尼亚大学攻读博士和博士后, 并获美国国家科学基金资助. 1994 年获美国宾州大学博士学位. 他是著名几何学家卡拉比教授的最后一位博士.

 Posted by at 7:03 pm
Sep 042012
 

Shinichi Mochizuki has released his long-rumored proof of the abc conjecture, in a paper called Inter-universal Teichmuller theory IV: log-volume computations and set-theoretic foundations.

If true, the proof would be one of the most astounding achievements of mathematics of the 21st century.

The homepage of  Professor Shinichi Mochizuki is here.

Excited, but caution

Terence Tao’s comment(from his blog): It’s still far too early to judge whether this proof is likely to be correct or not (the entire argument encompasses \(500\) pages of argument, mostly in the area of anabelian geometry, which very few mathematicians are expert in, to the extent that we still do not even have a full outline of the proof strategy yet). For those that are interested, the Polymath wiki page on the ABC conjecture has collected most of the links to that discussion, and to various background materials.

Jun 072012
 

Please  refer to  Low Dimensional Topology blog.

virtually Haken conjecture   states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is virtually Haken.

Virtual Haken 猜想  设\(M\) 为紧致的可定向的不可约的基本群无限的\(3\)-流形, 则\(M\)有一个\(Haken\) 流形的有限覆盖.

这个猜想通常归于Friedhelm Waldhausen \(1968\)年的一篇文章, 尽管他没有正式的陈述过这个猜想.

\(3\)-流形的有限覆盖一直是\(3\)-流形拓扑理论中重要但进展缓慢的课题.

Ian Agol (UC Berkeley) announced a proof  of  the  Wise’s  Conjecture  on March 12, 2012  when he was speaking  in a  seminar lecture  at  the Institut  Henri Poincaré.  In  particular, this implies  the Virtually Haken Conjecture.  His proof is based on joint work with Daniel Groves (UI Chicago) and Jason Manning (SUNY Buffalo).  It makes heavy use of the work of Dani Wise (McGill) on the Virtually Fibred Conjecture, as well as the proof of the Surface Subgroup Conjecture by Jeremy Kahn (Brown) and Vlad Markovic (Caltech). The Proof was subsequently outlined in three lectures March 26 and 28th at the Workshop on Immersed Surfaces in \(3\)-Manifolds at the Institut Henri Poincaré. A preprint of the claimed proof  has been posted on the ArXiv , pdf .

Jun 072012
 

Terence Tao(陶哲轩)\(1\)月\(31\)日, 提交了一篇论文 “Every odd number greater than 1 is the sum of at most five primes“. 这篇文章的主要结果, 正如标题展示的, 每个奇数可以表示为不超过\(5\)个质数之和. 显然, 这个结果和 Goldbach’s conjecture(哥德巴赫猜想)有关, 把奇数情形的哥德巴赫猜想, 即弱哥德巴赫猜想(Goldbach’s weak conjecture)推进了一步, 也改进了 Ramare 的结论: 每个偶数可以表示为不超过\(6\)个质数的和.

Tao 的论文, 有 \(44\) 页, 这里是pdf . 所采用的工具, 是哈代和立特伍德所创造的圆法(Hardy–Littlewood circle method), 结合了一些另外的技巧.

次日, Tao 在他的博客 之中, 写了一篇日志 描述了证明的大概轮廓.

这个事情最近上了新闻. 这是意料当中的情事! 这篇论文已提交学术刊物, 专家们正在审查. 英国《自然》杂志网站\(5\)月\(14\)日报道说, 陶哲轩在研究“弱哥德巴赫猜想”上取得突破, 有望最终解决这个世纪难题, 详细的报道在这个Mathematicians come closer to solving Goldbach’s weak conjecture.