Great Country Academician

Chapter 317 NS Equation——The Light of Inspiration

Hearing this, Xu Chuan glanced at Cai Peng in surprise.

This ex-senior can get a further study at Princeton in the Department of Mathematics of Nantah University.

Although Nantah currently has him, a Fields Medal winner, the Mathematics Department has improved a lot. But to be honest, there is still a clear gap between the strength of the mathematics department and those universities with top mathematics departments.

Not to mention Princeton, Paris Normal University and other international top universities, but domestic Peking University, Shuimu University, Fudan University, Nankai University, etc. Nankai University can’t compare with it.

After all, the strength of a school or a department is not just based on the top one or two individuals, these famous schools have quite deep foundations.

As for Nanjing University, apart from him, there are almost no professors in the Department of Mathematics who are internationally famous.

Professor Zhou Hai's strength can be ranked in the upper middle class domestically, but let's forget it internationally.

In the recent international mathematics conferences, there are no professors from Nantah University who can give reports on it.

The Department of Mathematics of Nantah University was considered second-rate in China before him, and in this environment, it is very good to be able to obtain advanced studies in the Department of Mathematics of Princeton on your own.

And he remembered that Senior Brother Cai's talent in mathematics didn't seem to be very good in the past. He didn't expect that he would find the right path in the second opening of a graduation thesis.

Misfortune and fortune depend on each other, it is true.

After thinking for a while, Xu Chuan said, "I really haven't made up my mind about bringing students next year."

"However, since you have received a postgraduate degree from Princeton, it means that your talent and ability in mathematics have indeed improved a lot compared to before."

"Well, I'll give you a test paper, and you do it. If it meets my standards and requirements, I can consider it."

To be honest, he really didn't think about recruiting students this year.

However, taking students is also what he should do. After all, he is still holding the position of professor at Nantah University, so he has to accept two or three students every year.

Of course, the most important thing is that this senior brother Cai Peng has obtained the qualification for further study in Princeton, and he has indeed met the threshold requirements for recruiting students.

If the threshold is not met, he will not accept it.

Mathematics is a subject that requires both talent and hard work. It is impossible to dawdle in this subject, especially under his command.

Hearing this, Cai Peng immediately swallowed nervously.

This big guy came up with the question himself, can he pass it?

Even if it is not difficult in his eyes, the problem posed by the big cow of the Philippine award level, but if it is put on a small scum like him, I am afraid that it may not be possible to solve it.

Before he came here, he knew that the graduation thesis written by this boss for the two students was to solve a world-class conjecture problem. Gu Bing and Amelia are still fighting for it.

According to this standard, Princeton is the top of the top.

Suddenly, he suddenly wanted to go to Princeton for further study.

Scared. Scared.

This big guy is really hanging.

When he was a freshman, he killed his graduate thesis + doctoral study goal. If this falls into his hands, will he really have a chance to complete his graduation goal and go on to further study?

After learning about Cai Peng's new learning direction and reading his thesis, Xu Chuan took out a pen and paper from the drawer, thought for a while and began to write the topic.

In about ten minutes, he wrote five questions on two pages of manuscript paper.

After handing it to Cai Peng, Xu Chuan smiled and said, "I'll give you three days for the five questions. If you have the ability to finish it ahead of time, you can also hand it in to me in advance."

Five questions, his minimum requirement is to do three.

Doctoral students can be said to have completed the accumulation of knowledge, and doctoral students have entered the stage of knowledge creation.

For students at this stage, his requirements are not low.

If you are not talented enough, it is not very interesting to follow him forcefully, because it is difficult to keep up with his rhythm when explaining problems or teaching.

Cai Peng took the manuscript paper solemnly, nodded seriously, and said, "I will work hard!"

Xu Chuan said with a smile: "There is no need to have too much psychological pressure."

On the side, Zhou Hai said, "You go back and do your homework first, and I'll chat with Professor Xu."

Cai Peng responded and quickly left the office after saying hello.

It took three days for the five questions, and he didn't know if he could complete the questions at the level of this big guy. It seemed that he would have to stay up late.

After Cai Peng left, Zhou Hai took a sip of warm tea from his teacup and said, "If you have no plans to bring students next year, there is no need to force it. It would be nice to let him study at Princeton, and it will not delay you or both." he."

Xu Chuan smiled and said, "It doesn't take much energy to take care of students."

"And to be honest, my requirements are not low. He can get the Princeton application, but he has met the minimum standard. As for the five questions, if he can solve three of them, I will consider them. If he can't, Then go to Princeton."

"If you can't keep up with the rhythm, follow me to learn mathematics, but you won't learn anything."

Zhou Hai nodded and said, "It's up to him, I can only help build a bridge."

After a pause, he smiled again: "But speaking of it, the students under me who have something to do with you all seem to be enlightened, and so is Liu Jiaxin, who used to be a mediocre student, but then took off directly."

Xu Chuan said with a smile: "Senior Jiaxin is not the same as Cai Peng. Her own talent is actually very powerful, but it takes her too much time to make money from part-time jobs. After solving the difficulties in life, her talent It exploded. It also helped me solve a modeling problem before."

"As for Cai Peng, I'm not too sure. Maybe it's just like what you said, after changing the field of study, I feel like a fish in water."

Zhou Hai thought for a while, then smiled and said, "Maybe it's really what you said, it seems that I will pay more attention to those students who live in poverty in the future."

Xu Chuan said with a smile: "Actually, the school's bursaries and bonuses are enough for a college student. It's just that senior sister Jiaxin has a younger sister who is also studying, and her parents are gone, so it is very difficult to make money."

For 985-level colleges and universities, the amount of grants and scholarships is still very good, basically enough for poor students to complete their studies.

And if there are poor students in the school, basically as long as they prove it, they can receive it, and they will not engage in all kinds of crooked ways like in elementary schools. (PS: So college entrance examination candidates have to work hard!)

After chatting with Zhou Hai for a while, Professor Zhou left, and Xu Chuan picked up a math book from his desk.

He had a math class today, and he originally planned to let Gu Bing or Amelia take over, but now he suddenly became interested, and since he had time, he simply went to it by himself.

In the big classroom, the students who were waiting for the class were stunned for a moment when they saw Xu Chuan, and then they burst out with joy. This big guy actually came to class again in person, and he stopped for a while before.

Xu Chuan didn't pay too much attention to the reactions of these students. He had been teaching at Nantah University for a while, and he was considered a semi-permanent NPC. The enthusiasm of these 'players' had long since passed.

After trying the headset, Xu Chuan said, "Students, today we are going to talk about Grothendieck's outline language. Please turn to page 32 of the textbook. I hope you have previewed it before."

As soon as these words came out, many students in the big classroom panicked.

"It's over. Today is Chuan Shen's lecture in person. I must have not previewed enough content! I only saw the Abel group layer on the topological space."

"Damn! You've still previewed there, I haven't even finished the algebraic variety."

"It's over, it's over, this boss can teach lectures faster than flipping through books, this time he's dead, and the final algebra has to fail again."

"Who will save me!"

There was howling in the classroom.

After Xu Chuan took some classes, the students of Nantah University and even some students who came to take classes from other schools almost knew that the speed of this big cow's lectures was as fast as riding a rocket.

If you don't pay attention, you will go directly to the sky with a 'biu'.

In the class of this big guy, picking up a pen and forcing the whole class is not a story, it can happen for real!

On the podium, Xu Chuan didn't care whether these people had previewed or not. He opened the textbook and started class.

". Regarding Grothendieck's profile language, we have discussed it a long time ago, and we have also learned about the most basic definitions and properties of profiles in morphisms and cohesive layers."

"Although we have given some concepts in the form of algebraic varieties, it is more convenient to discuss them in the language of profiles. For example, abstract algebraic varieties are actually finite profiles of algebraic closed fields, and Cartier divisors and reversible layers. "

"."

In class, Xu Chuan first briefly reviewed the basic content, and then cut into the main text.

The calculation formulas on the blackboard are constantly appearing and erasing with his explanation and the passage of time, and the content of the class has also extended from Grothendieck's outline language at the beginning to the use of outlines and cohomology to study curves.

In the large classroom, many students have already started to struggle and feel confused, while some more clever ones have given up on listening to the class, took out their mobile phones from their pockets* and started staring at the podium to take pictures.

Even if you can't keep up with the rhythm of this big guy's class, you can't miss it.

First take a picture, and then go back and slowly play back the research.

As soon as there was the first one, there was the second soon, and most of the students in the classroom started to hold up their mobile phones to take pictures.

"... This is the end of today's class."

After writing the last formula on the blackboard, Xu Chuan threw the chalk in his hand on the podium, turned around and said with a smile: "There is still a little time left, if you have any questions, you can ask them now."

Hearing this, palms were raised in the classroom.

Xu Chuan picked one at random, and the other party quickly stood up.

"Professor, can you talk about the application of cohomology of Abelian group layers on topological spaces?"

Hearing this question, Xu Chuan glanced at the students standing up, and said with a smile, "This is actually easy to understand."

"As an application, it is first proved that the arithmetic genus of the projective variety X can be calculated by the cohomology group, and the arithmetic genus of the projective variety depends on the projective embedding of X. Including flat morphisms and smooth morphisms, both of which Cohomology can be used to deal with it, and in fact cohomology can be used to better understand flatness and smoothness."

"Thank you, Professor." The boy who asked the question thanked him with thoughtful eyes and sat down. Obviously, Xu Chuan's answer gave him new inspiration.

Xu Chuan smiled and continued to point students to answer questions.

After being asked a question, a student stood up excitedly: "Professor, can you tell us about the staged proof of the NS equation?"

Xu Chuan froze for a moment, shook his head and smiled, "Why are you always interested in this kind of thing?"

In his class, every time there are students asking questions, they are either interested in the Hodge conjecture or the NS equation.

Maybe this is human nature? Knowledge and gossip, the public may be more willing to choose gossip?

Sensing that there seems to be hope, the classroom immediately joins the fun.

"Professor, tell me!"

"It's also about broadening our horizons and allowing us to understand the vastness of mathematics."

"Yeah, let's see the world of mathematics, Professor"

After thinking about it, Xu Chuan looked at the time, and at 2:55 in the afternoon, he said, "Okay, since you want to hear it, I'll tell you a brief story."

As he spoke, he picked up the chalk from the table, erased the previous calculations on the blackboard, re-wrote the calculations line by line, turned sideways to look at the students in the classroom, and said:

"The NS equation is a special form of the diffusion-convection equation. They are all related to the conservation law and are the direct mathematical reaction of the most basic physical theorems."

"In the process of my research on NS equations, I first started to cooperate with Professor Fefferman in Princeton."

"Fefferman used the Lie group with a smooth differential manifold structure to carry out smooth mapping, allowing the unitary table G of the Lie group G to perform a continuous action on the Hilbert space, thus starting our journey to study NS equations."

"later."

In the classroom, Xu Chuan briefly explained the process of his research on the NS equation, and wrote down some calculation formulas of key steps on the blackboard with chalk.

For him, these things are just easy to come by.

For these students in the classroom, I am afraid that most of them don't understand well.

But it doesn't matter. On the contrary, these students all have bright eyes. For them, this is purely listening to the story. If they can remember a little bit, they can brag about it when they go out for dinner or chatting in the future. Bragging: "I think back then, I listened to what God Chuan did."

On the podium, Xu Chuan concluded the story with a smile: "For the NS equation, so far, I have expanded to the point where a smooth solution to the three-dimensional incompressible Navier-Stokes equation exists given a finite space and when the initial value is infinitely smooth."

"Now there is still the last step, which is to spread the limitation of the limited space to the infinite space. This step may take a long time to study; of course, it may appear tomorrow."

As soon as his words fell, someone in the classroom shouted loudly: "Professor, if you want to solve the last step, do you have any ideas? Or where should we start?"

Xu Chuan smiled, and said, "I'm afraid this question is not something you should consider now. You'd better lay the foundation honestly."

After a pause, he continued, "But since you asked, I can still talk about it."

"In fact, for the NS equation, the solution may not be directly calculated. At least for now, the mathematical community may not be able to solve it."

"Because in a sense, its essence is the assumption of fluid microgroups, that is, the fluid particles described by the NS equation are infinitely small in space, but actually infinite compared to molecules."

After thinking for a while, Xu Chuan said again: "If we want to solve this last step, maybe we can start from the mathematics of microelement fluids? Through the analysis of viscous fluids."

On the podium, he stood there before he finished speaking, his brows furrowed unnaturally.

The four words 'Weiyuan Fluid' were like lights in the dark night, illuminating a way forward in his mind.

Ignoring the agitated students in the classroom, Xu Chuan quickly pulled out a piece of chalk from the podium, and began writing on the blackboard quickly.

PS: 8,000 words have been delivered for the second update, and the third update is being written, it may be late (mainly because checking information is a bit of a waste of brains, life is not easy, Maomao sighs.)

Another: Thank you for your monthly ticket support, thank you, thank you very much, and continue to explode tomorrow!