From Almighty Scholar to Chief Scientist

Chapter 288 Integral Hodge Conjecture
Lin Xiao probably didn't expect that such an unintentional video would make Asmail think so much.

At the beginning, he didn't pay attention to this video at all. Anyway, there is no key thing leaked in it. At most, he can see a servo motor. If others know it, they will know it. It also happens to let the outside world guess their current progress. Lest the outside world think that they can't do without Shan Tianbo.

As a result, he originally wanted to let the outsiders know that they had made progress, but unexpectedly, under the reasoning of a great cleverness, Asmail completely turned in the opposite direction.

If Lin Xiao knew about it, he would probably be speechless about it.

Of course, no matter what, whether they can understand or not has no effect on the normal progress of the X-ray project. Lin Xiao has never played tricks with them, just like he has never covered their ups and downs. Technology, after a breakthrough is made, it is directly publicized.

For Lin Xiao, any other tricks are just small ways, and directly building their lithography machines is the way and conspiracy.

So, just like that, time passed quickly.

Regarding the matter of Lin Xiao's drawing, the heat quickly passed. For everyone, this matter is just an anecdote, and the last hot search is a big deal.

However, the influence of Lin Xiao's two papers has grown, especially his theory of electronic topological bonding, which has attracted more and more research from relevant scholars, including scientists who previously studied Lin's bonding mechanism Ladies and gentlemen, many people have put their minds into the research of electron topological bonding theory. After all, Lin’s bonding mechanism is only a appearance of electronic topological bonding theory, and the latter is the essence, so naturally there are more Many people are willing to invest time to study this thing.

Of course, there are many people who continue to study Lin's bonding mechanism, and even many people have joined in the research of Lin's bonding mechanism. Once the mechanism is worked out, it will be a thesis of the first district, so no one is not excited about such a treasure.

Of course, the theory of electronic topological bonding is very meaningful to the academic community, and now the proof of Lin’s conjecture is also very meaningful to the mathematical community. Of course, since Lin Xiaofa has basically obtained mathematical The recognition of the world, the significance of this paper being published now is that people can cite this paper.

It could not be published before because this key paper has not been published, and they cannot cite it, and they cannot cite it. Then they will not be able to use the conclusion that "all functions are layered".

As for why Lin Xiao can use it in the theory of electronic topological bonding, it is because he simplified the entire proof process to a dozen pages and put it into this paper, so it was used.

Although there are suspicions of copying himself, but with Lin Xiao's reputation and the significance of his two papers, the academic circles will only think that Lin Xiao is eager to publish these two papers, and will not care too much. They even have to thank Lin Xiao for publishing the two papers as soon as possible, so that the academic community can invest time in research as soon as possible.

For example, those scholars who are eager to quote, such as Zheng Ronger's parents.

"Professor Lin, thank you very much. Our paper has been sent to "Science" and has entered the peer review process. Basically, it should be ready for publication."

Hearing Zheng Cheng's voice from the opposite side, Lin Xiao said with a smile: "That's good, congratulations to you first."

"Hey, what's there to congratulate? I still have to congratulate you, Professor Lin. Two papers published in the world's top journals in the same period, we are really envious."

Lin Xiao laughed, "It's nothing, it's just a coincidence that we got together."

"Well, next time when we go back to Beijing, we must treat you to a meal. Don't refuse Professor Lin then."

"No problem at all."

After saying a few more polite words, Lin Xiao hung up the phone, and then turned his attention back to the draft paper on the desk.

Now, about half a month has passed, and his research on Hodge's conjecture has become more in-depth. Of course, he can't say that he can completely solve the problem, but at least he is more clear about what problem he wants to solve.

"If Eq. 4 and Eq. 1 of §2 are algebraic, their motives on C will form a semisimple Abelian category with tensor products, and be the representation category of some reservationized group scheme..."

"Speaking of which, the relationship between Hodge's conjecture and motive theory is very close..."

Lin Xiao pinched his chin, lost in thought.

The motive theory is an idea proposed by Grothendieck at the age of 32. Its purpose is to find a unified theory, which serves as a pathway between algebraic geometry and various cohomology theories, and makes it the Motivation behind coherent tools.

Cohomology is an extremely difficult knowledge point in the mathematics world. As a theory related to a large number of difficult areas in mathematics such as algebraic topology, algebraic geometry, and representation theory, it plays a very important role. However, there are many categories of cohomology , such as singular cohomology, Durham cohomology, etc., and Grothendieck's motivation theory is a universal cohomology theory that tries to unify these different cohomology theories.

This is quite in line with Grothendieck's attempt to unify many mathematical theories with algebraic geometry, and then realize the vision of the Langlands program.

It is precisely because of this that finding such a theory is also called the dream of the mathematics emperor.

Thinking of this mathematician who passed away only eight years ago, Lin Xiao couldn't help but sigh in his heart. It's a pity that he missed communicating with this great man in mathematics.

If you insist on ranking all mathematicians, Grothendieck can definitely be ranked first.

Just look at his title of Mathematics Emperor. His achievements in mathematics are even inferior to that of Lin Xiao today.

Of course, after all, Lin Xiao has only been active for a few years now, and it's not that he has devoted all his time to the research of mathematics. Now he is only half a point inferior, and he is already considered extremely excellent.

Afterwards, he stopped thinking about it, Grothendieck had passed away, and he still had a lot of energy to continue researching.

He lowered his head again and looked at the thing in front of him. If Hodge's conjecture is related to the Motive theory, then maybe he can start with it.

His eyes moved slightly, and then he continued to write on the draft paper.

[H2p(X, Q) ∩ Hp, p(X) = H2p(X, Q) ∩ F p H2p(X, C)]

【…】

Time passed quietly, from the beginning of March, the days gradually came to the end of March.

During this period of time, Lin Xiao basically lived in seclusion. Except for occasionally caring about the progress of the X-ray project, the rest of the time he basically devoted himself to the research of Hodge's conjecture.

But obviously, Hodge's conjecture can be classified as a millennium problem, and even Lin Xiao has no way to solve it for the time being.

On March 3, in Lin Xiao's house.

"Well, what a hassle."

Putting down the pen, Lin Xiao scratched his hair, showing a somewhat helpless expression.

"Hodge, Hodge, why did you come up with this kind of problem? Can't you make it easier?"

However, it is clear that the difficulty of this kind of problem will not depend on human will. After all, this kind of thing involves the truth of the universe.

Of course, although helpless, there is no pity. After all, Lin Xiao’s research on Hodge’s conjecture is just to pass the time. If the millennium problems are really so easy to solve, then they are not millennium problems. It's a difficult problem. Lin Xiao spent several months trying to solve Goldbach's conjecture.

At this moment, Lin Xiao's cell phone rang suddenly.

He took a look and saw that it was a call from Russia.

Russia?
Lin Xiao was taken aback for a moment, and then suddenly realized that there was a high probability that it was a call from the current International Congress of Mathematicians.

Like the original International Congress of Mathematicians held in Rio de Janeiro, Brazil, the host country will set up a conference committee and then be responsible for various matters.

Therefore, this International Congress of Mathematicians is also organized by the Institute of Mathematics of the Russian Academy of Sciences.

After the call was connected, a voice came from the opposite side: "This is the Committee of the International Congress of Mathematicians, is this Professor Lin Xiao?"

"It's me." Lin Xiao responded.

"Professor Lin Xiao, hello!" The voice on the other side became more respectful: "That's right, it is less than four months before the convening of this International Congress of Mathematicians. According to previous regulations, you, as the speaker People, you need to submit the report three months in advance, and now there are still [-] days before the deadline for submitting the report, when do you plan to submit it?"

"Well, it will probably take less than a week. I'm basically ready."

"Okay, that's great, we're all looking forward to your report."

"Ah."

"Then I won't bother you, goodbye."

After hanging up the phone, Lin Xiao shook his head, the deadline is coming, his deadline.

Of course, he has already made preparations. Since there is no clue about Hodge's conjecture, there is no need to be obsessed with Hodge's conjecture. Just prepare and put the proof of Lin's conjecture on it.

Before that, he was almost ready to prepare a report paper on Lin's conjecture, and he could send it if he added any supplements.

Of course, people procrastinate more or less, so let's wait until the seven days he just said.

I believe that deadline will give him more productivity.

Then, putting down his phone, he turned his attention to the formula on the draft paper again.

"However, the direction of the Motive theory is definitely possible. The only problem is, how to come up with this universal cohomology theory?"

He touched his chin.

Cohomology theory is an important tool he used to study Hodge's conjecture. If Motive theory can be confirmed, it will be very helpful to solve Hodge's conjecture.

"Well, but it is not necessary to come up with this universal cohomology theory. If I can express the current Hodge conjecture in the form of an integral, then using the cohomology can explain this characteristic in a differential form, then the distance Solving Hodge's conjecture is very close."

"But how to do it?"

Lin Xiao fell into thinking again.

The integral Hodge conjecture has long been proposed by predecessors, and two forms have been proposed accordingly, but without exception, these two forms have been proved to be wrong.

And until now, people are still looking for ways to express Hodge's conjecture in the form of integrals.

Once Hodge's conjecture can be represented by integral...

Lin Xiao's mind flashed through the five-element mathematical formulas obtained from the bug in the system before. Among them, there are two formulas that he thought were strange at the beginning, which can be completely substituted into Hodge's conjecture in integral form, and this is also It will be of great help to him to prove Hodge's conjecture.

However, after thinking for a long time, Lin Xiao finally sighed helplessly.

Hey, can't think of anything.

I understand the truth, but it is not that simple to make it.

Shaking his head, he looked at the time, he still has a class this afternoon, and now he can prepare to go to Beijing University.

So he packed up all kinds of things, and he went to Beijing University.

……

In the afternoon, Lin Xiao's class started on time.

"Everyone, do you want me to draw pictures today?"

When he came to class, Lin Xiao showed a smile.

"do not want!"

In the classroom, all the students in his class were wailing.

At the beginning of this month, Lin Xiao's random drawing, and then the topic that combined algebraic geometry and number theory, really tortured them.

In the end, there are very few that are actually made, and they can be counted on one hand.

So the few students who could count with one hand were awarded two normal points, and for the remaining students who failed to do it, Lin Xiao mercilessly deducted two normal points from them.

So these students almost didn't have PTSD about drawing pictures.

Seeing their appearance, Lin Xiao smiled: "Are you scared?"

"afraid!"

"No, you guys."

Lin Xiao shook his head with a smile, and then said: "Okay, I won't tease you, this class, let's talk about o-adic theory."

"p-adic is the content of algebraic number theory. We have also discussed it before. There is a very close relationship between algebraic number theory and algebraic geometry..."

(End of this chapter)