Power, Simplicity and Beauty
Advances in Mathematics
On Mar 10, Ciprian Manolescu posted a preprint on ArXiv proving that the Triangulation Conjecture is false: Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture 当然, Ciprian Manolescu 的论证还需要经过检验, 目前还不能肯定完全正确. Ciprian …
Ciprian Manolescu refutes the triangulation conjecture Read MoreGang Tian(田刚) has just uploaded to the arXiv his paper “K-stability and Kähler-Einstein metrics“(Nov 20, 2012). The motivation of this paper is: “In this paper, we prove that if a Fano …
Gang Tian has just uploaded to the arXiv his proof of the fact that a K-stable Fano manifold admits a Kähler-Einstein metric Read More28 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 …
Two proofs for the Yau-Tian-Donaldson conjecture have been announced independently Read MoreShinichi 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 …
Shinichi Mochizuki has released his proof of the abc conjecture Read MorePlease 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, …
Ian Agol announced a proof of virtual haken conjecture on March 12, 2012 Read MoreTerence 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 …
Terence Tao come closer to solving Goldbach’s weak conjecture Read More