Chapter 317 NS Equation - That Light of Inspiration
Hearing this, Xu Chuan glanced at Cai Peng in surprise.
It is possible for this former senior to study in the Mathematics Department of NTU and get further education at Princeton.
Although NTU currently has him as a Fields Medal winner, the apparent strength of 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 colleges with top mathematics departments.
Not to mention top international universities such as Princeton and Paris Normal University, even domestic universities such as Peking University, Shuimu, Fudan and Nankai University are incomparable to Nankai University.
After all, the strength of a school or department is not just determined by the top one or two people. The foundation of these prestigious schools is quite profound.
As for NTU, aside from him, it can be said that almost none of the professors in the Department of Mathematics are internationally famous.
Professor Zhou Hai's strength can still be ranked in the upper-middle level domestically, but internationally, forget it.
In these recent international mathematics conferences, NTU’s professors have not been able to give reports at these conferences, which is a sign of performance.
The Mathematics Department of NTU could be said to be second-rate in the country before him, and in this kind of environment, he could still get advanced studies in Princeton Mathematics Department on his own, which is very good.
Moreover, he remembered that Senior Brother Cai didn't seem to have very good talent in mathematics before. Unexpectedly, he found the right path after a second proposal of the graduation thesis.
It is true that good and evil depend on each other.
After thinking for a while, Xu Chuan said: "I really haven't decided yet about taking care of students next year."
"But since you have received further education from Princeton, it means that your talent and ability in mathematics have indeed improved a lot than before."
"Let's do this. I will publish a test paper and you will do it. If it meets my standards and requirements, I can consider it."
To be honest, he really hasn't thought about recruiting students this year.
But taking care of students is what he should do. After all, he still holds the position of full professor at Nanjing University, so he must accept two or three students every year.
Of course, the most important thing is that Senior Brother Cai Peng has obtained the qualification for further study at Princeton and has indeed met the threshold conditions for recruiting students.
If the threshold is not reached, he will not accept it.
Mathematics is a subject that requires both talent and hard work. It is impossible to just dawdle in this subject, especially under him.
Hearing this, Cai Peng suddenly swallowed nervously.
This big boss personally gave the question, can he pass it?
Even if it is not difficult in his eyes, if it is a question asked by a Philippine Award-level expert, if it is put to a little scum like him, I am afraid that he may not be able to solve it even if he thinks hard.
Before he came here, he knew that the graduation thesis given by this boss to two students solved a world-class conjecture problem. Gu Bing and Amelia are still struggling with this problem.
By this standard, Princeton is the best among the best.
Suddenly, he suddenly wanted to go to Princeton for further study.
Scared. Scared.
This boss is really awesome.
When he was a freshman, he completed his graduate thesis + doctoral study goal. If this fell into his hands, would 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 papers, Xu Chuan took out a pen and paper from the drawer, thought about it and started writing 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: "Five questions, give you three days. If you are able to finish them in advance, you can also submit the papers to me in advance."
There are five questions, and his minimum requirement is to solve three.
Doctoral students can be said to have completed the accumulation of knowledge, and doctoral students' advanced studies have entered the stage of creating knowledge.
For students at this stage, his requirements are not low.
If you are not talented enough, there is no point in following him forcefully, because it will be difficult to keep up with his rhythm when explaining problems or teaching.
Cai Peng solemnly took the manuscript paper, nodded seriously, and said: "I will work hard!"
Xu Chuan smiled and said: "There is no need to put too much psychological pressure."
On the side, Zhou Hai said: "You go back and do your homework first, and I'll have a chat with Professor Xu."
Cai Peng responded, said hello and quickly left the office.
It took three days for five questions to be asked. He didn't know if he could complete the questions given by this boss at his level. It seemed that he would have to stay up all night to make him nervous.
After Cai Peng left, Zhou Hai picked up the tea cup and took a sip of warm tea. He said, "If you don't have any plans to bring students next year, there's no need to force him. It's also good to let him study at Princeton. If it doesn't delay, you won't. Him.”
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. If he can get the Princeton application, he has met the minimum standard. As for the five questions, if he can do three of them, I will consider it. If he can't do it, Then go to Princeton.”
"If you can't keep up with the rhythm, if you follow me to learn mathematics, you won't learn anything."
Zhou Hai nodded and said: "It depends on him. I can only help build a bridge."
After a pause, he smiled again: "But speaking of which, all the students I have who have some relationship with you seem to have enlightened themselves. Liu Jiaxin also used to study normally, but then took off directly."
Xu Chuan said with a smile: "Senior Jiaxin is different from Cai Peng. Her talents are actually very powerful, but making money part-time takes up too much of her time. After solving the difficulties in life, her talents It just broke out. He helped me solve a modeling problem before.”
"As for Cai Peng, I'm not sure. Maybe it's like you said, after changing the field of study, he is like a duck in water."
Zhou Hai thought for a while and said with a smile: "Maybe it is what you said. It seems that I will pay more attention to those students who live in poverty in the future."
Xu Chuan smiled and said: "Actually, the school's stipends and bonuses are enough for a college student, but senior Jiaxin has a younger sister who is also studying, and her parents are gone, so it is difficult to make money."
For 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. They will not engage in all kinds of crooked ways like elementary schools. (PS: So college entrance examination students, please work hard!)
After chatting with Zhou Hai for a while, Professor Zhou left, and Xu Chuan also picked up a mathematics book from his desk.
He had a math class today. He had originally planned to let Gu Bing or Amelia take over, but now he suddenly became interested, and since he still had time, he just went to class by himself.
In the large classroom, the students who were waiting for class were stunned for a moment when they saw Xu Chuan, and then they burst into joy. The boss actually came to class in person again. He had stopped for a while before.
Xu Chuan didn't pay much attention to the reactions of these students. He had been taking courses at NTU for a while and was considered a semi-regular 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 general language. Please turn the textbook to page 32. I hope you have previewed it before."
As soon as these words came out, many students in the large classroom suddenly panicked. "It's over. Kaishen is giving the lecture today. I definitely didn't preview enough! I only saw the Abel group layer on the topological space."
"Fuck! After all, you got there in the preview. I haven't even finished reading the algebraic varieties."
"It's over, it's over. This big guy lectures faster than flipping through books. He's dead this time. He'll fail the final algebra again."
"Who will save me!"
There was a cry in the classroom.
After taking some classes with Xu Chuan, students from Nanjing University and even some students from other schools all know that this expert lectures as fast as a rocket.
If you don't pay attention, you will go straight to the sky with a 'biu'.
In this boss's class, picking up a pen and being confused for the whole class is not a story, this can really happen!
On the podium, Xu Chuan didn't care whether these people had previewed the class. He opened the textbook and started class.
"Regarding Grothendieck's schematic language, we have discussed it a long time ago, and we have also understood the most basic definitions and properties of morphisms and condensates."
"Although we have already given some concepts in terms of algebraic varieties, it is more convenient to discuss them in the language of outlines. For example, abstract algebraic varieties are actually finite outlines of integers over algebraic closed fields, and such as Cartier divisors and reversible layers. ”
"."
In class, Xu Chuan first briefly reviewed the basic content, and then cut into the main text.
The calculations on the blackboard continued to appear and disappear as he explained and time passed, and the content of the class also extended from Grothendieck's schematic language at the beginning to the use of schematics and cohomology to study curves.
In the large classroom, many students were already struggling and confused, while some of the smarter ones had given up on listening to the lectures, 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 pace of this master's class, you can't miss it.
Take a photo first, then play it back and study it slowly when you go back.
The first one was followed by the second. Soon, most of the students in the classroom started taking pictures with their mobile phones.
“.That’s it for today’s class.”
After writing the last calculation on the blackboard, Xu Chuan threw the chalk in his hand to the podium, turned around and said with a smile: "There is still a little time left. If students have any questions, they can ask them now."
Hearing this, palms suddenly rose in the classroom.
Xu Chuan picked one at random, and the other person quickly stood up.
"Professor, can you talk about the application of cohomology of Abelian group layers in topological spaces?"
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 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 It can be handled with cohomology, and in fact one can use cohomology 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 brought him new inspiration.
Xu Chuan smiled and continued to ask students to answer questions.
After being asked to ask a question, a student stood up excitedly: "Professor, can you tell us about the staged proof of the NS equation?"
Xu Chuan was stunned for a moment, shook his head and said with a smile: "Why are you always interested in this kind of thing?"
In his class, students ask this question every time during the question-and-answer session. They are either interested in Hodge's conjecture or NS equations.
Maybe this is human nature? Between knowledge and gossip, the public might be more willing to choose gossip?
Sensing that there seemed to be hope, the classroom suddenly became lively.
"Professor, tell me!"
"This also broadens our horizons and allows us to understand the vastness of mathematics."
"Yeah, let's take a look at the world of mathematics, Professor"
After thinking about it, Xu Chuan looked at the time. It was two fifty-five in the afternoon and said, "Okay, since you want to hear it, I will give you a brief explanation."
As he spoke, he picked up the chalk from the table, erased the original calculations on the blackboard, rewrote the rows of calculations, turned sideways and looked at the students in the classroom, and said:
"NS equations are special forms of diffusion and convection equations. They are all related to conservation laws and are direct mathematical responses to the most basic physical theorems."
"In the process of studying NS equations, I first collaborated with Professor Fefferman of Princeton."
"Fefferman used the Lie group with a smooth differential manifold structure to perform smooth mapping, allowing the Lie group G unitary table G to play a continuous role in the Hilbert space, thus starting our journey to study NS equations."
"Behind."
In the classroom, Xu Chuan briefly explained his process of studying NS equations, and wrote down some key steps of calculations on the blackboard with chalk.
To him, these things are just easy to come by.
For these students in the classroom, I am afraid that most of them cannot understand it well.
But it doesn't matter. On the contrary, each of these students' eyes are shining. For them, this is just listening to a story. If they can remember a little bit, they can also brag about it when they go out to dinner or chat in the future. Bragging: "I remember back then, I listened to what the God of Sichuan did."
On the podium, Xu Chuan ended the story with a smile: "For the NS equation, I have now expanded it to the point where, given a finite space, when the initial value is infinitely smooth, a smooth solution to the three-dimensional incompressible Navier-Stokes equation exists."
"There is still the last step to spread the restrictions of limited space to infinite space. This step may take a long time to study; of course, it may also appear tomorrow."
As soon as he finished speaking, someone in the classroom shouted loudly: "Professor, if you want to solve the last step, do you have any ideas? Or which direction should we start from?"
Xu Chuan smiled and said: "I'm afraid this issue is not something you should consider now. You'd better lay a solid foundation before talking."
After a pause, he continued: "But since you asked, I can still tell you."
"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 fluid micelle hypothesis, that is, the fluid particles described by the NS equation are infinitesimal in space, but in fact they are infinite relative to the molecules."
After thinking for a while, Xu Chuan spoke again: "If we want to solve this last step, maybe we can start from the mathematics of micro-element fluids? Through the study of viscous fluids"
On the podium, he stood there before he finished speaking, his brows wrinkled unnaturally.
The four words "Micro-Element Fluid" were like a ray of light in the dark night, illuminating a way forward in his mind.
Ignoring the already agitated students in the classroom, Xu Chuan quickly pulled out a piece of chalk from the podium and began to write quickly on the blackboard.
PS: The second update of 8,000 words has been delivered, and the third update is being written, so it may be late (mainly because looking up information is a bit exhausting, life is not easy, Maomao sighed.)
Also: Thank you for your monthly support, thank you, thank you very much, I will continue to update tomorrow!
(End of chapter)