From Almighty Scholar to Chief Scientist

Chapter 290
A week passed quickly.

In Lin Xiao's room, he was still working on his work.

According to the exchange with Peter Schultz that day, Lin Xiao's thinking also got many different perspectives.

It's like writing. When you get a topic in hand, the content written by different people will be very different, no matter the angle of entry or the thoughts that the article wants to express, it will be very different.

The same goes for math problems.

Even if it is a question under that kind of exam-oriented education, there may be many different solutions, let alone a world-class question like Hodge's conjecture.

Therefore, Peter Schultz's different views also broadened Lin Xiao's thinking.

But it also made him gain a lot.

Until now.

[Assume (X, A) is a space pair, G is an arbitrary commutative group, denote that C(X, A) represents the singular chain complex of (X, A), and is a complete space composed of the closed p form of the differential manifold M For the subvariant space composed of proper p forms, it is the Motive motivation cohomology group. 】

【HdR(M)≌R^n...】

Looking at the final definition of motivational cohomology on the draft paper, a smile appeared on Lin Xiao's face.

Motive cohomology is the key to figure out the integral Hodge conjecture, and now, he finally got it done.

Of course, what he created is not the kind of universal cohomology pursued by motivation theory. Universal cohomology is an encapsulation of all cohomology sets, and his current motivational cohomology is only in line with Motive motivation theory. relevant.

However, it already has the rudimentary form of motivational theory—because of this motivational cohomology, it has communicated various cohomology theories such as singular cohomology and Durham cohomology, but it is only limited to these types for the time being. The real omnipotence, or in other words, the universal cohomology.

As for the real motivation theory, Lin Xiao faintly felt that perhaps more development was needed.

"In this way, I should call it Lin's motivational coherence for the time being?"

Smiling slightly, Lin Xiao picked up the pen and added the word "Lin's" in front of the name of the homology of the motive.

Nodding in satisfaction, he put down his pen.

It is one step closer to let the word "Lin's" spread all over the mathematics world.

I just hope that future students will not blame him.

But in retrospect, the multidimensional field theory in the physics world has probably caused headaches for many students. It is said that some university textbooks have already included part of the multidimensional field theory, especially those students who study particle physics. After all, the Standard Model under the multidimensional field theory has replaced the previous Standard Model, and the Standard Model under the multidimensional field theory has higher and higher requirements for mathematics, which of course hurts those physics students.

Of course, these have nothing to do with Lin Xiao.

Bring your attention back to your eyes, and with Lin's motivational coherence, it is basically enough.

"Then the next step is to figure out the Hodge conjecture in the integral form."

The corner of Lin Xiao's mouth curled up. With Lin's motivational coherence, he could complete this step with his eyes closed.

So he picked up his pen again and began to write.

"Firstly, Lin's motivational cohomology is expressed as a differential form..."

【ω=dα+δβ+γ】

[(α, β)=∫αΛ*β]

【…】

Until ten minutes passed.

"To sum up, the Hodge conjecture in the integral form should be like this: Let X be a projective complex manifold, and then each cohomology class H^2k(X, Z)∩H^k, k(X) is the sum of the torsional and cohomological classes of algebraic rings with integral coefficients on X."

"Finally, it's done."

Looking at himself after a lot of mathematical formula calculations, and finally simplified the form of Hodge's conjecture, Lin Xiao showed a brighter smile than before.

"Hodge's conjecture in integral form, it turns out to be like this."

"It seems that it is indeed easier to understand than the previous form."

Lin Xiao touched his chin.

The reason why Hodge’s conjecture is converted into this integral form is naturally because the original form is too difficult to understand. Mathematics is the process of simplifying complex things, making complex things into simple things, and finally solving this problem is this process.

In a word, it is to pull those difficult problems to the same level as myself, and then use my rich experience to solve them.

"Well... Next, it's time to prove Hodge's conjecture in integral form."

By proving the Hodge conjecture in integral form, the final Hodge conjecture can be proved.

One of the Seven Millennium Problems...

Even Lin Xiao couldn't help but look forward to it at this time.

This is another truth in the universe, how can Lin Xiao not look forward to it?
Moreover, the role of Hodge's conjecture in promoting the great unification of mathematics also makes Lin Xiao very much looking forward to the rewards that will be brought to him after the proof.

Of course, he did not underestimate the integral Hodge conjecture.

The difficulty of proving the integral Hodge conjecture is at least half the level of the Millennium Problem.

That is to say, he completed the process from Hodge's conjecture to integral Hodge's conjecture, but only completed half of the work, and now there is still half of the work waiting for him to complete.

Moreover, no one knows whether it will be more difficult in the end.

However, just as Lin Xiao was about to make a move, his phone rang again, and he saw that it was from Russia again.

He rubbed his nose. The last time he called, he said the report would be submitted in a week, but now it looks like a week has passed?
After connecting the phone, the voice of the staff member from last time came from the opposite side: "This is the Organizing Committee of the International Congress of Mathematicians, is this Professor Lin?"

"it's me."

"Hello, Professor Lin! Is your report ready? Last time you said that the report will be finished in one week, so I'm here to ask you now."

Lin Xiao replied truthfully: "Uh...not yet, maybe we have to wait a week."

A helpless voice came from the opposite side: "Okay, then please hurry up."

"I know, don't worry."

Although he said so in his mouth, Lin Xiao was not sure that he could completely solve Hodge's conjecture in the remaining seven days, unless he spent truth points, but obviously, using truth points to solve Hodge's conjecture did not conform to his concept, and the system The rewards will also be greatly reduced, so there is no need for him to use this thing just to pretend to be cool at the International Congress of Mathematicians.

Of course, he didn't forget that the system rewarded him with a [A flash of inspiration] last time, but even if he used this, it was still impossible for him to prove Hodge's conjecture in just seven days.

From this point of view, the current integral Hodge conjecture can only be submitted as a phased result.

But at this moment, an idea flashed in Lin Xiao's mind, and he asked, "By the way, the Fields Medal winner will also arrange a one-hour lecture?"

The staff member on the opposite side was taken aback, apparently not expecting that Lin Xiao would ask this question.

Is Lin Xiao scheduled for the Fields Medal?

Of course, no matter what, the probability of Lin Xiao being able to win the Fields Medal can be said to be the one with the highest probability among all the mathematicians who are expected to win the Fields Medal at this International Congress of Mathematicians.

If Lin Xiao couldn't get it, the others would probably be too embarrassed to get it.

After all, this year, there are no other unsuspecting candidates.

Afterwards, the staff member smiled and said, "Yes, of course it will be arranged. After the list of Fields Medal winners is announced, a Fields lecture will be arranged."

Lin Xiao's heart moved, and then he smiled and said: "Okay, thank you for your information, I will submit the report as soon as possible."

"Well, good Professor Lin." The staff member said, "I also wish you the Fields Medal."

"Thank you."

Lin Xiao said with a smile.

Then, the phone hung up.

And Lin Xiao began to plan.

Every International Congress of Mathematicians will prepare a lecture for the winners. Of course, because the winners basically have no time to prepare the lecture content, they will basically prepare some learning process, share life experiences or stories, and this lecture , all for one hour.

Well, if Lin Xiao can win the Fields Medal, then he will have one more lecture, and in this lecture, he can talk about whatever he wants, and there is no hateful deadline.

This is equivalent to saying that in the next three months, Lin Xiao can be used to solve Hodge's conjecture, and then report his integral Hodge's conjecture at the one-hour plenary meeting, and then in Phil In this lecture, the thorough proof of Hodge's conjecture is done.

Of course, the premise is that Lin Xiao can win the Fields Medal, but his confidence in this is still relatively high.

The Fields Medal is originally an award for young scholars under the age of 40, and it is not an award like the Nobel Prize that occasionally has to consider the age of the candidate, so even from the point of view of ensuring authority, Lin Xiao will not be awarded this year. If so, it basically makes no sense.

So Lin Xiao has this confidence, he has locked a Fields lecture.

"However, there is still a lack of a report on Lin's conjecture."

It was planned to be carried out at the International Congress of Mathematicians before, but since Hodge's conjecture was first, it is obvious that there is no such opportunity now.

"Doesn't this mean that I have to prepare a report on Lin's conjecture?"

A strange expression suddenly appeared on Lin Xiao's face.

Three reports in a row?

This plot is somewhat familiar.

Isn't that what the original Andrew Wiles did?

This troublesome prover of Fermat's Last Theorem gave three reports in a row, and the titles of these three reports were "Modular Forms, Elliptic Curves, and Galois Representations".

Obviously, he didn't hint in the title that he would discuss Fermat's Last Theorem, but by the end of his second lecture, people already knew his purpose, so people flocked to the third lecture .

Even though people guessed his purpose, Wiles still pretended not to know, and only proved the general situation of Taniyama Shimura's conjecture at the end of the third report, and then, as his colleagues thought of it later, pointed out that it meant Fermat’s Last Theorem is correct—despite the fact that his proof was questionable, and he didn’t actually complete it until two years later, like that joke: when Wiles said it was obvious, it took two years Years later it's really obvious.

Thinking of this, Lin Xiao couldn't help but smile, this script is good, and now it's his.

Then, he picked up his phone again and called their dean, Zhao Qi.

"Professor Lin, why do you have time to call me?"

From the opposite side came Dean Zhao's laughing voice.

Lin Xiao smiled, "Dean Zhao, I'm bringing you good news."

"Oh?" Zhao Qi's voice suddenly rose, "What good news?"

Lin Xiao smiled and said, "I'm going to put the report on Lin's conjecture in our school."

Zhao Qi was even more excited immediately: "That's great!"

No matter what, it is definitely a good thing that Lin Xiao put this report in their school.

Although the enthusiasm about Lin's conjecture has passed and the paper has been published, if Lin Xiao decides to make a report on Lin's conjecture, it will definitely attract many people.

After all, many people are still looking forward to Lin Xiao's report.

However, after being happy for a while, Zhao Qi suddenly calmed down, and then asked in a low voice: "Professor Lin, if you want to prove the report of Lin's conjecture in our school, then your report at the International Congress of Mathematicians, could it be Hodge guess?"

Now it was Lin Xiao's turn to be surprised: "How do you know?"

But when Lin Xiao said that, Zhao Qi was even more shocked, "It turned out to be true!"

Afterwards, he smiled and said: "Didn't you go to class before and exchange Hodge's conjecture with Schultz in class, and then the students spread out, saying that you proved Hodge's conjecture. Now it seems that this rumor is true It's gone."

Lin Xiao was speechless for a moment.

That's how the rumors spread.

He was obviously asking Schultz about how to prove Hodge's conjecture, how did it become that he had already proved Hodge's conjecture?
He said helplessly: "I haven't proved Hodge's conjecture yet, it's all rumored."

"Is there no proof?" Zhao Qi was taken aback, but quickly realized: "However, since you plan to give a report on Hodge's conjecture at the International Congress of Mathematicians, it should also mean that you have made great achievements, right? "

"Yes."

"Then I'm really looking forward to the news at that time." Zhao Qi said with a smile, "Unfortunately, as the dean, I don't have time to go to the International Congress of Mathematicians, otherwise I must read your report."

"You can also watch it online in the future." Lin Xiao said with a smile.

"Well." Zhao Qi said: "Then I wish you a successful proof in the end."

"Haha, then I'll borrow your auspicious words."

Lin Xiao thanked with a smile.

Then, they discussed the timing of the report on Lin's conjecture. The academic report was decided to be held at the end of June, only about a week away from the International Conference of Mathematicians that started in early July.

In this way, mathematicians from various countries can come here to listen to his report, and then go directly to Russia to participate in the International Congress of Mathematicians.

After the discussion, Lin Xiao hung up the phone, and then once again focused on the integral Hodge conjecture in front of him.

The next step is to sort out the report as soon as possible.

Of course, in order to make the three reports cohesive, he had to deal with the report submitted to the International Congress of Mathematicians in a disjointed manner.

Well, it's not bad to be a broken dog.

(End of this chapter)