God of black technology

After returning to the dormitory from Professor Witten's office, Wang Yun put down the suitcase in his hand and took a shower without resting.Then I sat in my seat and began to meditate slowly. Regarding the NS equation, generally the right end of the equation has done various theories and analyzes based on the actual situation, but the core velocity gradient tensor on the left end of the equation seems to have not yet How many people study.

In this case, would it be better to do the velocity gradient tensor on the left side of the equation?Wang Yun secretly figured out that the original NS equation is a description in the Euler coordinate system.

Well...it involves mathematics and physics, which is a very difficult thing.

It is necessary to start from both physics and mathematics at the same time. After Wang Yun was silent for a while, forget it.Still don't think too much, just want to sleep to adjust the jet lag.

When I woke up, it was already the next day.

After getting up and washing up, he walked outside the dormitory.The students coming and going seemed to be in a hurry. Wang Yun took a walk on the Princeton campus taking in the fresh air.

It has been about a semester since I came to Princeton, but I really don’t have much time to really visit Princeton.Especially on such a day of enjoying the sunshine casually, Wang Yun walked to the side lawn, enjoying the sunshine, while looking at the silent faces of the students.With a slight smile, it seems that Princeton is still the Princeton with a strong academic atmosphere.

Sitting quietly on the lawn like this, after a while, Assistant Robert found him somehow.

Seeing Wang Yun lying on the lawn, squinting his eyes and enjoying himself.Assistant Robert felt angry and funny, and he was angry because he came out of Professor Witten's office.When they arrived at the door of his dormitory, they did not find him.After visiting most of Princeton's campus, I realized that this guy was hiding in a corner enjoying the sunshine.

The same is true for the reason that Robert Assistant is funny.

Unexpectedly, Wang Yun would secretly enjoy the afternoon. He thought that Wang Yun had nothing to do except research.

"Wang!" Assistant Robert waved at Wang Yun, who slowly opened his eyes and looked at Assistant Robert.Wei Wei was taken aback, stood up and smiled and said to him, "Mr. Assistant, what do you want from me?"

"Of course." Robert blinked at Wang Yun, his deep blue pupils showed a strange look, "Wang, I thought you wouldn't rest? I didn't expect that you would still secretly rest here. It took me a while to find it."

"Oh." When Wang Yun heard Assistant Robert say that, tomorrow will come immediately. It is probably not Assistant Robert who is looking for him, but Professor Witten who is looking for him. It seems that there must be something to do.

"You're right." Assistant Robert shrugged his shoulders. "It's not that I'm looking for you, but Professor Witten is looking for you. He probably wants to ask about the NS equation."

"Huh?" Wang Yun raised his eyebrows, unexpectedly Professor Witten was quite interested in this.

Walking to the side of Assistant Robert, Wang Yun said with a smile, "Okay, let's go now." As he walked, he asked, "Why is Professor Witten suddenly interested in this?"

"Hmm." Assistant Robert smiled, "It can't be said that the professor is interested in the NS equation, it should be that he is interested in how you want to solve it. It should be to ask if you have any ideas, after all NS equations are originally a difficult point in physics equations."

Wang Yun nodded to express his understanding of Professor Witten's idea. The NS equation can be said to be an extremely difficult breakthrough point in physics equations.Not to mention him, many famous physicists and mathematicians have not broken through this problem. It is understandable for Professor Witten to worry that he will not be able to break through this problem.

Walking all the way to the office, pushing the door open, Professor Witten is wearing glasses and seems to be concentrating on researching something.Assistant Robert whispered in Wang Yun's ear, "The professor is studying the Hilbert space, and he hopes to find some clues about the Hilbert-Polya conjecture."

Wang Yun nodded to express his understanding. Hilbert space is a generalization of Euclidean space, which provides an effective way of expressing Fourier series and Fourier transform based on polynomial representation on any orthogonal system, not only functional One of the core concepts of the field of analysis, as well as one of the core concepts of formulaic mathematics and quantum mechanics.

If some clues can be found from the Hilbert space, then the Hilbert-Polya conjecture will be much simpler.In the hands of his tutor, Professor Witten, it is not difficult to achieve phased results on this topic, but it is somewhat difficult to solve this conjecture.

Professor Witten quietly studied the Hilbert space, while Wang Yun stood aside without moving or speaking.He just stood quietly and looked at the professor's research draft.

After a while, Professor Witten raised his head, looked at Wang Yun, raised his glasses with his hand, and said with a smile, "Wang, are you here?"

"Professor." Wang Yun smiled, "I've been here for a while, and I see that you are fascinated by your research, so I won't bother you."

"What's the result of your research?"

"Not very ideal." Professor Witten shook his head, looked at Wang Yun and asked, "Wang, do you have any thoughts on Hilbert space?"

"Hmm." Wang Yun was silent for a while, "If it's a pure Hilbert space, I think the strong convergence problem is worth a try."

"Oh?" Professor Witten became interested, "Wang, it seems that you still have some research on Hilbert space, which is one of the core theories in the functional field and quantum mechanics. If you have some knowledge about Hilbert space I understand, I think it will be of great help to you in quantum mechanics in the future."

"Especially, you should not only want to learn some mathematics, but also want to understand the aspect of quantum physics, right?"

"Professor, you are right." Wang Yun said with a polite smile, "If I don't learn your theory, I always feel a little bit unwilling."

Professor Witten handed Wang Yun his pen and jokingly said, "If you can learn my M theory, I promise to give you my most beloved pen."

Wang Yun smiled knowingly. Wang Yun, who has seen a beautiful mind, naturally knows what is going on with this practice of giving away pens.Although Princeton has long clarified that the plot of giving away the pen is only a fictional movie, it still cannot stand people's discussion.Gradually, Princeton also fashioned such an approach.Of course, not as shocking as the movie scene.

But it's just a private exchange of pens!

"Thank you, Professor." Wang Yun took a pen and began to write down the first line of numbers on the draft paper——

[Define PΓv as the metric projection from v to Γ, and set w*=PΓv, w*=(x*, y*). Similarly, define PCv1 as the metric projection from v1 to C, and PQv2 from v2 to Q, let x *=PCv1,y*=PQv2

Suppose H1, H2, H3, A, B, A*, B*, Ui,, G, G* are the same as above, then w*=(x*, y*)∈H1×H2 is a solution to the generalized split equation problem If and only for any given ρn, i>0①

...]

Professor Witten raised his eyebrows. It seems that Wang Yun still has some understanding of Hilbert space.

When Wang Yun stopped writing and looked at Professor Witten, he smiled embarrassedly, "That's all I know about the strong convergence theorem, Professor, did you ask me to come because of the Hilbert space? ?”

"That's not true." Professor Witten put away his pen, looked at Wang Yun and said silently, "Wang, what do you think about the NS equation?"

"I don't have any idea yet, but the NS equation was originally described in the Euler coordinate system. Although it is a nonlinear partial differential equation, I want to start with the Euler coordinates and combine them with Lagrange coordinates to see if I can find some clue."

Professor Witten said with a smile, "So, you want to go to the Institute for Advanced Study in Princeton because you want to talk to those professors of theoretical physics?"

"Almost." Wang Yun answered Professor Witten's question straightforwardly, "Professor, I think you have something else to do?"

"Wang." Professor Witten suddenly became serious, "You are the most talented student I have ever seen, bar none."

Wang Yun looked at the professor and told him intuitively that Professor Witten must have something to tell him, and it was a very important thing.

"My M theory still has some flaws in the end." Professor Witten stared at Wang Yun, "It is my life's work. If possible, I would like to complete M theory in your hands. Wang, I see a glimmer of possibility in you .”

After pondering, Professor Witten continued, "That is a grand proposition, the unified field theory, the unified gauge field theory that Einstein wanted to make in his later years, maybe in my lifetime, I can see it in your hands end."

ummmmm...

Wang Yun didn't know what to say for a moment. He didn't have a deep understanding of quantum physics at all, and he didn't even dare to think about such things as unified field theory.

Naturally, he would not say such words to his mentor.I can only think about it in my heart, since the mentor has such high expectations for him, how can he live up to the expectations of his mentor.

"Wang, if you are free tomorrow, you can come to the office." Professor Witten thought for a while, and said in a relaxed tone, "Maybe I shouldn't tell you these things so early now, after all, for you , It’s still too early. However, if you continue to follow the current academic path, I believe that one day, I will see that you have your own opinions on the unified field theory. I am very optimistic, you are a Someone who can surpass me."

"Thank you, Professor." Wang Yun thought for a while, and he had nothing to do tomorrow, "I will definitely come to your office tomorrow."

"Professor Bourgain will come to my office tomorrow. At that time, you can ask him about functional analysis. In Banach space theory, I think there is no one who is more powerful than him. Although you There is no direct connection to the NS equations studied, but maybe there will be some inspiration."

After talking with Professor Witten, Wang Yun left the office, and the sky gradually darkened.Wang Yun walked in the campus silently, not knowing how that guy Yuan Chengde was doing with his studies.When walking through the boulevard, several students looked at him sideways.It was not cold in Princeton at this time, and Wang Yun always felt that the eyes of the group of students were a little strange.

Originally, I wanted to go back to the dormitory directly, but after thinking about it, since I have nothing to do recently, I might as well read more books.

When I walked to the library, the number of students had gradually increased.Wang Yun borrowed literature about Euler coordinates, picked a place at random, and sat down.

Just as he was about to open the book, he heard two students with their backs facing away seem to be discussing, "It's just this guy who graduated from Princeton after half a year."

"My God, is this guy's graduation thesis Kakutani's conjecture?"

"That's right, I heard that his new subject is the NS equation, and his tutor didn't get involved."

"Can he do it?"

"Who knows?"

ummmmmmm...

Well, I have already started talking about me, Wang Yun shook his head, opened the book and looked up the information carefully, and ignored the group of Princeton students.

Fortunately, although everyone looked at him with strange eyes, nothing strange happened.Probably due to the fact that Princeton has produced a large number of geniuses, Wang Yun seems very dazzling, but for those PhDs who graduated at the age of 20, it is nothing at all.

Reading Zhibo at the age of 19 is just the genius passing line of Princeton, far from the level of monsters.

Wang Yun slowly wrote the formula on the draft paper, frowning slightly while writing.He used Euler coordinates and Lagrangian coordinates to find clues. Is he right or wrong?

Just like Professor Witten using Hilbert space to find clues, no one will know whether it is right or wrong.

What is the real picture of turbulence?The system allows him to inherit the theory of his mentor, and Professor Witten hopes that he can further improve M theory and make it the real ultimate theory of physics, or even a unified field theory.This is simply... Wang Yun's heart began to be a little messed up. For Wang Yun now, it was a bit too difficult, and it even made him feel that he was under extremely heavy pressure.

Although this is not the original intention of Professor Witten, and Professor Witten's original intention is to want Wang Yun to pay attention to quantum physics.After all, any research Wang Yun is doing now has nothing to do with quantum physics.

"I saw you standing here alone in a daze from a long distance away." Luo Zhendong stood behind Wang Yun, patted his shoulder and said, "What are you thinking? Professor Witten's doctoral student?"

Raising his head, Wang Yun reluctantly smiled at Luo Zhendong, "Why are you here?" He was very puzzled. Luo Zhendong, who had a second-degree illness, was almost never seen in the library on weekdays. It is said that this guy I have a quirk, I like to study alone in the dormitory, why did I come to the library today?

"I don't want to either." Luo Zhendong shrugged his shoulders. "I was kicked out by Yuan Chengde. He was studying the Mersenne prime number distribution conjecture. I have a feeling that he wants to start with the twin prime number conjecture."

"It's pretty good." Wang Yun looked at Luo Zhendong, "If you take this as a subject, I believe the instructor is very happy to wait for him to solve it before graduating."

"Maybe, a big boss in the mathematics department can still take a fancy to him." Wang Yun's tone was very relaxed, "What about you? What subject did you choose?"

"Me?" Luo Zhendong pointed at himself, then shook his head and said, "There is no subject, and I don't know what kind of subject I should choose now. It's not like you, a boss, by the way, your subject Have you applied for the materials?"

Hearing what Luo Zhendong said, Wang Yun forgot about it.Wait, he remembered that Kakutani guessed last time that he didn't apply for the project, and he didn't submit the materials, right?How did it pass?

Seeing his confused appearance, Luo Zhendong touched the bridge of his nose, "Don't think about it, Professor Witten must have done the application for you. This time, you can apply yourself. It seems that the materials for the project application are not very good. Trouble, at worst, just ask Professor Witten's assistant."

"I heard that Professor Witten's assistant is pretty good."

"Now, I seem to be Professor Witten's assistant." Wang Yun was silent for a while, "Forget it, I'm going to Professor Witten's office tomorrow, so let's take this opportunity to ask Mr. Robert."

"You didn't choose a subject, so you are in the library—?" He looked at Luo Zhendong who was standing behind him wonderingly.