Probably at the beginning of the year that little while, Lu Zhou also not Chen Yang the time of the Yanda (Yanshan University) math center digging, this Professor Chen is then studying the Hodge conjecture. 大概是在年初那会儿,陆舟还没有将陈阳从燕大数学中心挖来的时候,这位陈教授便在研究霍奇猜想了。 Lu Zhou still remembers, at that time he studied oneself ultra elliptic curve analytic method on the blackboard, and used a very ingenious method, this originally for mathematical instrument of standard Riemann hypothesis design, after the improvement, utilized in directly to the non- strange duplicate/restores algebraic manifold algebraic topology, in the research of Geometry connection issue and polynomial equation of its definition subvariety indicated. 陆舟还记得,当时他在黑板上研究自己的超椭圆曲线分析法,并且用了一种非常巧妙的方法,将这个原本为准黎曼猜想设计的数学工具,改进之后直接运用在了对非奇异复代数簇的代数拓扑,以及其定义子簇的多项式方程所表述的几何关联问题的研究上。 Initially also because of this attractive operation, making Lu Zhou move loved heart, dug Jinling from the Yanda (Yanshan University) math center him. 当初也正是因为这一手漂亮的操作,让陆舟不禁动了爱才之心,将他从燕大数学中心挖到了金陵这边来。 Now has passed nearly for a year, the topic about Hodge conjecture still did not have the slight progress, in addition has been busy at the algebra Geometry unification theory a while ago the matter, Lu Zhou quickly this matter forgetting. 现在已经过去快一年了,关于霍奇猜想的课题仍然没有丝毫的进展,再加上前段时间一直在忙代数几何统一理论的事情,以至于陆舟都快把这件事给忘了。 „Walked, goes to my office to say.” “走,去我办公室说。” Led Chen Yang to come to own office, Lu Zhou went to the corner to help him drag a blank slate personally, and handed in own symbol pen his hand. 带着陈阳来到了自己的办公室,陆舟亲自去墙角帮他拖来了一张白板,并且将自己的记号笔递到了他的手上。 Not the time waste in the smalltalk, after receiving the pen, stands before blank slate Chen Yang thought deeply about the moment, first drew a circle in the blank slate conveniently, then marked S in side, and wrote down one line of expressions. 没有将时间浪费在客套上,接过了笔之后,站在白板前的陈阳思索了片刻,首先在白板上随手画了个圆,然后在旁边标记了s,并写下了一行表达式。 „...... Regarding compact boundless surface S, its gauss curvature k can conduct General points in the entire surface.” “……对于紧致无边的曲面s,其gauss曲率k可以在整个曲面上进行积分。” Writes, Chen Yang while continues to say. 一边写着,陈阳一边继续说道。 „What is well-known, a surface not necessarily only contains measuring, therefore I attempted to conduct the replacement to measuring of S. After replacing measuring, corresponding gauss curvature k will also change similarly, but the General points value actually has nothing to do with measuring of surface, but only counts x (s ) to be related with the euler characteristics of surface, uses this nature, we can” “众所周知的是,一个曲面不一定只容有一个度量,所以我尝试对s的度量进行了更换。在更换了度量之后,相应的gauss曲率k同样也会发生改变,但积分值却与曲面的度量无关,而只与曲面的euler示性数x(s)有关,利用这一性质,我们可以” Looks at the mathematical formula in blank slate, the Lu Zhou eyebrow lifted gently, said interestingly. 看着白板上的算式,陆舟眉毛轻轻抬了下,饶有兴趣地说道。 „Gauss-bon formula?” “gauss-bon公式？” The pen in hand stops, Chen Yangdian under said. 手中的笔停住,陈阳点了下头说道。 „.” “正是。” Then, he wrote the gauss-bon formula. 说罢,他将gauss-bon公式写了上去。 Sees one that this adds the finishing touch, the look that on the face of Lu Zhou is interested is even more strong. 看到这画龙点睛的一笔,陆舟的脸上感兴趣的神色愈发浓烈了。 In fact, he had guessed correctly probably, Chen Yang was the plan does do. 事实上,他大概已经猜到,陈阳是打算干什么了。 According to the higher-dimensional Riemannian manifold m nature, the gauss curvature can promote is the sectional curvature, its value can by the tensor decision of Riemannian curvature. As for its integrand, then very complex algebraic expression comprised of the curvature tensor is the gauss-bon integrand. 根据高维黎曼流形m的性质,gauss曲率可以推广为截面曲率,它的值可以由黎曼曲率的张量决定。至于其被积函数,则是由曲率张量组成的很复杂的代数式即gauss-bon被积函数。 As for it General points in entire manifold, is counted x ( m ) to decide by the euler characteristics of this manifold. 至于其在整个流形上的积分,则是由这个流形的euler示性数x(m)所决定。 Using these natures, then can promote the hodge theory to the complete non- tight manifold. 利用这些性质,便能够将hodge理论推广到完备非紧流形中。 These profound mathematical significances, are obtained by Professor Shiing-Shen Chern, is in the famous gauss-bon- Chen Gongshi mathematical connotation. 这些深刻的数学意义,是由陈省身教授得到的,也就是著名的gauss–bon–陈公式中的数学内涵。 The l2 cohomology method of recombination Sir Attia , to continue along this mentality, cannot do a good job in also really can come out to the card this suspicion. 再结合阿提亚爵士的l2上同调方法,沿着这条思路继续走下去,搞不好还真能把这个猜想给证出来。 Naturally, how should show specifically, but also needs profoundly to study and that's the end. 当然,具体该如何证明,还需要深入研究一下就是了。 Thinks of here, Lu Zhou applause nod. 想到这里,陆舟赞许地点头。 Second. 秒啊。 Really is wonderful. 实在是妙。 When does not know, Chen Yang back has stood a person. 不知何时,陈阳的背后已经站了一圈人。 When he just started the blackboard writing, the person in office then noticed here. 早在他刚刚开始板书的时候,办公室里的人便注意到了这边。 Is staring at the mathematical formula in blank slate, the Ji Mo two illumination, excited low voice said: „This, is in the legend” 盯着白板上的算式,季默两眼发光,激动的小声说道:“这,难道就是传说中的” Saw the Junior Brother speech also only to say half, what Changwen frowns, said in a low voice: „Is anything, do not keep guessing.” 见自己师弟说话又只说了一半,何昌文皱了下眉头,低声道:“到底是啥,别卖关子。” Ji Mo looked at his one eyes strangely. 季默奇怪地看了他一眼。 „Hodge conjecture! Clearly.” “霍奇猜想啊！很明显嘛。” what Changwen: „......” 何昌文:“……” Where this special was obvious?! 这特么哪里明显了？！ However is careful looks, probably truly is this. 不过仔细一看,好像确实是这样。 Thinks of here, what Changwen comforted oneself one in the heart. 想到这里,何昌文不禁在心中安慰了自己一句。 Un, if looks earnestly, he should also be able to look. 嗯,如果认真看的话,他应该也是能看出来的。 The pen in blank slate stopped, Chen Yang is lost in thought. 白板上的笔停下了,陈阳陷入了沉思。 Obviously, this mentality he only arrived at half, how behind should walk did not have very good idea. 显然,这条思路他只走到了一半,后面该怎么走还没有很好的想法。 Does not know the office when comes, stands continuously silent Professor Perelman, suddenly says. 不知何时来的办公室,站在旁边一直沉默不语的佩雷尔曼教授,忽然开口说道。 „This mentality seems like Interesting.” “这条思路看起来有点意思。” Then looked to Professor Perelman, Chen Yang gawked slightly, some accidents/surprises said. 回头看向了佩雷尔曼教授,陈阳微微愣了下,有些意外地说道。 „When do you come?” “您是什么时候过来的？” „Probably when you write about half...... I am looked for Professor land, has not thought that here also has the unexpected benefit,” stopped, Perelman continued, „...... can use to start writing to me?” “大概在你写到一半的时候……本来我是来找陆教授的,没想到在这里还有意外收获,”停顿了一下,佩雷尔曼继续说,“……可以给我用下笔吗？” No hesitation, Chen Yang let the symbol pen in hand decisively. 没有任何的犹豫,陈阳果断将手中的记号笔让了出来。 Took the pen from the hand of Professor Chen, stood Perelman before blank slate pondered the moment, later emptied several lines under his mathematical formula, continued to write. 从陈教授的手中接过了笔,站在白板前的佩雷尔曼沉思了片刻,随后在他的算式下面空了几行,继续写了起来。 „Since there is a ready-made algebra Geometry unification theory to utilize, the type ( 3 ) proof I abbreviated.” “既然有现成的代数几何统一理论可以运用,式的证明我就省略了。” „...... My suggestion is, regarding the proof of later part, we can promote the tight manifold m issue to its universal covering manifold, obtains complete non- tight manifold m.” “……我的建议是,对于之后部分的证明,我们可以将紧流形m问题提升到它的通用复盖流形上,得到完备非紧流形m。” „According to Attia's theorem, if we can under the condition of sectional curvature show that except for middle l2 homology group other is zero......” “根据阿提亚的定理,如果我们能在截面曲率的条件下证明除了中间的l2同调群其余都为零……” Saying, the pen in his hand shook gently, wrote down one line of succinct and exquisite mathematical formulas quickly. 说着,他手中的笔轻轻抖了一下,很快写下了一行简洁而优美的算式。 【When h ^ n ( m ) 6 ≠ \ { 0 }, works as q ≠ n, h ^ q ( m ) = \ { 0 }】 【h^n(m)6≠\,且当q≠n时,h^q(m)=\】 Sees this line of mathematical formulas the instance, Chen Yang pupil contracts slightly. 看到这行算式的瞬间,陈阳的瞳孔微微收缩。 The expression on face appeared a clear(ly) to become aware instantaneously, he constrained the exciting tone to say. 脸上的表情瞬间浮现了一丝明悟,他压抑着激动的语气说道。 „...... We can obtain the proof of Hodge conjecture!” “……我们就能得到霍奇猜想的证明！” Then the issue came. 那么问题来了。 How should show, under the condition of sectional curvature, except for middle l2 homology group other is zero? 该如何证明,在截面曲率的条件下,除了中间的l2同调群其余都为零？ Talked here to stop suddenly suddenly. 对话到这里忽然戛然而止了。 After short excitement, two people fell into as if by prior agreement silent. 短暂的兴奋之后,两人不约而同地陷入了沉默。 Finally, looked as if by prior agreement to Lu Zhou. 最后,又不约而同地看向了陆舟。 Notices two people to look to oneself, Lu Zhou that from beginning to end a few words have not said blinks suddenly, said with a smile. 注意到两人看向自己,从头到尾一句话都没说的陆舟忽然眨了眨眼,笑着说道。 „I feel your ideas good......, although I have not carefully studied this topic, but the intuition told me to walk according to this road, 80% can have harvest.” “我觉得你们的想法都不错……虽然我没仔细研究过这个课题,但直觉告诉我照着这条路走下去,八成是能够有所收获的。” , He continued to say. 顿了顿,他继续说道。 „This mentality is interesting, my suggestion is, you might as well study this topic to be good together.” “这个思路非常有意思,我的建议是,你们不如一起研究这个课题好了。” Always felt that Lu Zhou as if looked at anything, has not actually explained the words. 总感觉陆舟似乎看出来了些什么,却又没有把话说明白。 Perelman frowns, asked scruple. 佩雷尔曼皱了下眉头,迟疑问道。 „Don't you participate? This is a very interesting difficult problem.” “你不参与吗？这可是个很有意思的难题。” Far more than is interesting. 何止是有意思。 The Hodge conjecture can be said as in the modern mathematics development the abstract characteristics reflects, what research is the mathematical three big bifurcation analysis, analysis situs and inner link between algebra Geometry. 霍奇猜想可以说是现代数学发展中抽象特征的集中体现,研究的是数学三大分支分析、拓扑、代数几何之间的内在联系。 As for the difficulty, as it of millennium difficult problem, is naturally without a doubt. 至于难度,作为千禧难题的它,自然是毋庸置疑的。 Those who made Perelman surprise was, Lu Zhou has not shown very strong interest unexpectedly. 令佩雷尔曼诧异的是,陆舟居然没有表现出很强烈的兴趣。 Lu Zhou: „......, although I am interested very much, but that side imcrc also one pile of things wait for me to process, perhaps recently I more time, cannot assign to the math.” 陆舟:“……虽然我很感兴趣,但imcrc那边还有一堆事情等着我去处理,恐怕最近我都没有更多的时间,能够分配到数学这边了。” Heard this news, on Perelman face showed the regrettable expression. 听到这个消息,佩雷尔曼脸上露出了遗憾的表情。 „That was really regrettable.” “那实在是太遗憾了。” „Perhaps although I cannot extract the time help, but my serious recommends Professor Chen to you,” patted Chen Yang shoulder, Lu Zhou said with a smile, „he was an outstanding scholar, about his ability, believes that you were also found, I was not many boast. In brief, words that you cooperate, I believe that certainly can solve this problem.” “虽然我恐怕抽不出时间帮忙,但我郑重的向你推荐陈教授,”拍了拍陈阳的肩膀,陆舟笑着说道,“他是一位优秀的学者,关于他的能力,相信你也是了解的,我就不多吹牛了。总之,你们合作的话,我相信一定能够解决这个问题。” Although was skeptical on this absolute view, but looked at a Professor Chen, Perelman has not said anything, but selected, approved this partner evidently. 虽然对这种绝对的说法表示怀疑,但看了一眼陈教授,佩雷尔曼也没有说什么,只是点了下头,看样子是认可了这位合作伙伴。 Two people are that words not many types, does not have too many exchanges. 两人都是那种话不多的类型,也没有太多的交流。 After Lu Zhou clears throat, looks that Perelman continues to say. 陆舟清了清嗓子之后,看着佩雷尔曼继续说道。 „Said, you do continue to remain here do not have the issue? The unification theory of algebra and Geometry has been completed.” “说起来,你继续留在这边没问题吗？代数与几何的统一理论已经完成了。” „Does not have the issue,” Perelman shakes the head, „I and mother have telephoned, she lets the matter that I am myself to handle, does not need to care about that side her. I really have the matter that wants to handle has not completed, I planned that here...... treats some time again, solved the Hodge conjecture went back again.” “没有问题,”佩雷尔曼摇了摇头,“我和母亲已经打过电话了,她让我去做自己想做的事情,不用太在意她那边。我确实还有想做的事情没有完成,我打算在这里……再待一段时间,把霍奇猜想解决了再回去。” Although very accidental/surprised Professor Perelman will choose to remain unexpectedly, but this good deed Lu Zhou will not naturally reject, immediately said with a smile. 虽然很意外佩雷尔曼教授居然会选择留下来,但这种好事陆舟自然是不会拒绝,当即笑着说道。 „You live in the original that apartment, I will help you apply to extend the period of revolution of apartment.” “那你还是住在原来那个公寓吧,我会帮你申请延长公寓的使用时间。” Perelman nods, thank. 佩雷尔曼点了点头,感谢道。 „Troubled you.” “麻烦你了。”