Hearing this, Xu Chuan glanced at Cai Peng with some surprise.

To be able to get a Princeton degree in the Department of Mathematics of NTU, this former senior brother can.

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

Not to mention the international top such as Princeton and Paris Normal University, but also Peking University, Shuimu, Fudan University, and Nankai University in China, which cannot be compared.

After all, the strength of a school and a department is not only based on the top one or two people, but the foundation of these famous schools is still quite deep.

And NTU, aside from him, is a professor in the Department of Mathematics, which can be said to be almost not internationally famous.

Professor Zhou Hai's strength can still be ranked in the middle and upper echelons in China, but in the world, forget it.

In the recent International Mathematical Conferences, there are no professors at NTU who can give presentations on them.

The Department of Mathematics at NTU could be said to be the second-rate in China before him, and in this environment, it is very good to be able to get a further study in the Department of Mathematics at Princeton on his own.

And he remembered that this Senior Brother Cai's talent in mathematics didn't seem to be very good before, but he didn't expect that the second opening of a graduation thesis would hit the right path.

Blessings and misfortunes depend on each other, this is indeed true.

After thinking about it, Xu Chuan said: "I really haven't thought about it for the time being, I really haven't thought about it for the time being." ”

"But now that you've got a Princeton degree, it means that your talent and ability in mathematics have indeed improved a lot compared to before."

"In this way, I will produce a test paper, you will do it, if it can meet my standards and requirements, I can consider it."

Accepting students or something, to be honest, he really didn't think about it this year.

However, taking students is also what he should do, after all, he still has the position of full professor of Nanda, 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 at Princeton, and he has indeed met the threshold conditions for him to recruit students.

If he doesn't reach the threshold, he won't take it.

Mathematics is a subject that requires both talent and effort, and it is impossible to mess around in this subject, especially under him.

Hearing this, Cai Peng immediately swallowed nervously.

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

The title of the Philippine Award-level bull, even if it is not difficult in his eyes, but if it is put on a small scum like him, I am afraid that he may not be able to make it if he wants to break his head.

Before he came, he understood that the graduation thesis that this big guy gave to the two students was a world-class conjecture problem, and Gu Bing and Amelia were still struggling for it.

This standard is the top of the top in Princeton.

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

I'm scared, I'm afraid.

This big guy is really hanging.

In his freshman year, 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 further his studies?

After learning about Cai Peng's new study direction, and looking at his paper again, Xu Chuan took out a pen and paper from the drawer, thought about it 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 said with a smile: "Five questions, give you three days." If you are able to finish it in advance, you can also submit it to me in advance. ”

Of the five questions, his minimum requirement is to make three.

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

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

If you don't have enough talent, it's not interesting to force your way up with him, because it's hard to keep up with him when you're explaining a problem or giving a lesson.

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

Xu Chuan smiled: "There is no need to have too much psychological pressure. ”

On the side, Zhou Hai said, "You go back first and do the questions well, and I'll talk to Professor Xu." ”

Cai Peng answered, said hello and quickly left the office.

Five questions for three days, with the level of this big guy, he doesn't know if he can complete it, it seems that he has to stay up all night to burst his liver.

Cai Peng left, Zhou Hai took a sip of warm tea from the teacup, and said, "If you don't have a plan to take students next year, there's no need to force it." It's also good to let him go to Princeton to study, and it won't delay you or him. ”

Xu Chuan smiled and said, "It doesn't take much energy to take students or something." ”

"And to be honest, my requirements are not low, and he can get Princeton's application, which is also the minimum standard. As for the five questions, if he can make three, I will consider it. If you can't do it, go to Princeton. ”

"I can't keep up with the rhythm and follow me to learn math, but I can'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 which, the students under me who have something to do with you all seem to have enlightened themselves, and so does Liu Jiaxin, who used to study in general, and took off directly later." ”

Xu Chuan said with a smile: "Senior Sister Jiaxin is not quite the same as Cai Peng, her own talent is actually very powerful, but it takes too much of her time to make money part-time." After solving the difficulties of life, her talent exploded. Helped me solve a modeling problem before. ”

"As for Cai Peng's side, I don't know very well. Perhaps, as you said, after changing your field of study, you are like a fish in water. ”

Zhou Hai thought for a while and said with a smile: "Maybe it's really what you said, it seems that I will pay more attention to those students who live poorer lives in the future." ”

Xu Chuan said with a smile: "Actually, the school's grants and bonuses are enough for a college student, but there is a younger sister on Jiaxin's side who is also studying, and her parents are gone, so it is very difficult to make money." ”

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

Moreover, if there are poor students in the school, they can basically receive it as long as they are confirmed, and they will not engage in all kinds of crooked and evil ways like in primary schools. (PS: So college entrance examination candidates should come on!) ）

After chatting with Zhou Hai for a while, Professor Zhou left, and Xu Chuan also 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 care of it, but this time he suddenly became interested, and he had time, so he simply went to it himself.

In the big classroom, the students who were waiting for class were stunned for a moment when they saw Xu Chuan, and then the joy broke out wildly, this big guy actually came to class in person again, and they had stopped for a while.

Xu Chuan didn't pay much attention to the reactions of these students, he had also been holding classes at NTU for a while, and he was a semi-fixed NPC, and the enthusiasm of these 'players' had long passed.

After trying the headset, Xu Chuan said: "Students, today we are talking about Grothendieck's general language, please turn to page 32 of the textbook, I hope you have already studied it before." ”

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

"It's over, today is Kawajin himself giving a lecture, and the content I have prepared is definitely not enough! Only the Abel group layer is seen on the topological space. ”

"! You've got there anyway, and I haven't even finished reading algebra clusters. ”

"It's over, this big guy lectures faster than turning books, this time it's dead, and the algebra at the end of the semester has to hang up again."

"Who's going to save me!"

In the classroom, there was a wail.

After Xu Chuan took some classes, the students of NTU and even some students from other schools almost knew that the speed of this bull's lecture was like riding a rocket.

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

In this big guy's class, it's not a story to pick up a pen and be stunned for a whole class, this can really happen!

On the podium, Xu Chuan didn't care whether these people had pre-studied or not, opened the textbook, and he started the class.

"We have discussed Grothendieck's generalization language for a long time, and we have also learned about the basic definitions and properties of generalizations in morphism and condensation layers."

"Although some concepts have already been given in the form of algebraic clusters, it is more convenient to discuss them in the language of generalizations, such as abstract algebraic clusters, which are actually finite generalizations on algebraic closed fields, such as Cartier dividers and reversible layers"

“.”

In class, Xu Chuan first made a brief review of the basic content, and then cut into the text.

The equations on the blackboard continue to appear and disappear with his explanations and the passage of time, and the content of the class extends from Grothendieck's general language at the beginning to the study of curves using generalizations and upper cohomology.

In the big classroom, many students have begun to struggle and be confused, and some of them have given up listening to the class, took out their mobile phones from their pockets and began to stare at the lectern to shoot.

This big guy's class, even if you can't keep up with the rhythm, can't miss it.

Take a picture first, then go back and slowly replay the study.

There was the first one, and soon there was a second, and most of the students in the classroom began to hold up their phones to take pictures.

That's all for today's lesson."

After writing the last equation on the blackboard, Xu Chuan threw the chalk in his hand onto the podium, turned around and smiled: "There is still a little time left, if you have any questions, you can raise them now." ”

Hearing this, a palm suddenly rose in the classroom.

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

"Professor, can you tell us about the application of the upper cohomology of the Abel group layer on the topological space?"

Hearing this question, Xu Chuan glanced at the student who stood up and said with a smile: "This is actually very easy to understand. ”

As an application, it is first proved that the arithmetic deficit of the projective cluster X can be calculated by the upper cohomology group, and the arithmetic deficit of the projective cluster depends on the projective embedding of X. This includes flat and smooth morphology, both of which can be dealt with with with upper cohomology, and in fact 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, it was obvious that Xu Chuan's answer had brought him new inspiration.

Xu Chuan smiled and continued to answer the students' questions.

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

Xu Chuan was stunned for a moment, shook his head and smiled: "Why are you always interested in this?" ”

In his class, every question session has students ask this kind of question, either interested in the Hodge conjecture or interested in the NS equation.

This is probably human nature? Knowledge and gossip, the public may prefer to choose gossip a little?

Sensing that there seemed to be hope, the classroom suddenly became lively.

"Professor, let's talk about it!"

"It's also about broadening our horizons and giving us a broad understanding of the breadth of mathematics."

"yes, let's look at 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, then I'll tell you a little bit about it." ”

As he spoke, he picked up the chalk from the table, erased the equation from the original blackboard, wrote a new line of equations, turned to look at the students in the classroom, and said:

"The NS equation is a special form of the diffusion convection equation, which is related to conservation laws and is a direct mathematical response to the most basic physical theorems."

"When I was working on the NS equations, I first started with Professor Feverman at Princeton."

"Fefferman used the Lie group with a smooth differential manifold structure to perform a smooth mapping, so that the Lie group G unitary table G made a continuous effect on the Hilbert space, thus starting our journey to study the NS equation."

"Back."

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

For him, these things are just a matter of handiness.

And for these students in the classroom, I'm afraid most of them don't understand it.

But it doesn't matter, on the contrary, these students are all bright-eyed, for them, this is purely listening to a story, can write down a little bit is a little, go out to dinner or chat or something in the future, and can brag: "I think back then, I listened to how the god of Kawajin was doing."

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

"Now there is still one last step left, spreading the limitations of finite space into infinite space, and this step may take a long time to study; Of course, it is also possible that it will appear tomorrow. ”

As soon as his words fell, someone in the classroom shouted, "Professor, if you want to solve the last step, do you have any ideas?" Or in which direction should I 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 hypothesis of fluid microclusters, that is, the fluid mass points depicted by the NS equation are spatially infinitesimal, but in fact infinitely relative to the molecule."

After thinking for a while, Xu Chuan re-spoke: "If you want to solve this last step, maybe you can start from the micro-element fluid mathematics?" By using the "

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

The words 'microfluid' were like a light in the night, illuminating a way forward in his mind.

Ignoring the students who were already in some commotion in the classroom, Xu Chuan quickly pulled out a piece of chalk from the podium and began to quickly write on the blackboard.

PS: The second update of 8,000 words was delivered, and the third update is being written, and it may be later (mainly because it is a bit of a waste of brains to check the information, life is not easy, and the cat sighs.) ）

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

(End of chapter)