God of black technology

After eating, Wang Yun, Yuan Chengde and Luo Zhendong came to the dormitory.Wang Yun and Yuan Chengde discussed twin primes together, and Luo Zhendong studied Hilbert spaces alone.

For Luo Zhendong, functional analysis is still good.The key is the quantum field theory, which he really can't figure out.After Wang Yun and Yuan Chengde finished communicating, they raised their hands and glanced at the time. It was already early morning.Standing up, he said to Yuan Chengde and Luo Zhendong, "Go to rest early, don't you have something to do tomorrow?"

Wang Yun knew just how heavy Princeton's homework was. Although the professors and teaching assistants did not assign much homework, it did not mean it was easy.On the contrary, it is precisely because professors and teaching assistants require self-study, but on Princeton's academically dense campus, ordinary students will feel extremely depressed.That's why Princeton is a revelry for geniuses and monsters.It is the nightmare of ordinary students.

After bidding farewell to the two, Wang Yun returned to his dormitory.Lying on the bed, he is going to face his mentor Professor Witten and Professor Bourgain who is visiting Princeton University tomorrow with a better mental outlook.

After waking up the next day, Wang Yun took advantage of the morning sun after washing up, and ate a meal first.Then followed Yuan Chengde and the others to take a class on functional analysis, thinking that the time was almost up, and then walked to Professor Witten's office.

First he knocked on the door lightly, and after hearing Professor Witten's affirmative voice, Wang Yun pushed the door open and entered.

Professor Witten and Professor Bourgain were sitting face to face, the assistant was standing beside them, and a small blackboard was placed in front of them.When seeing Wang Yun coming in, Professor Witten said with a smile, "It just so happened that I was talking about you with Professor Bourgain."

"Professor Bourgain is very interested in your attempt to solve the NS equation." Professor Witten looked at Wang Yun, waved his hand and said, "Wang, you have already met Professor Bourgain, right?"

"That's right." Wang Yun nodded with a smile and said, "I have met Professor Bourgain, even during the academic report meeting." Having said that, Wang Yun also knew that it was just Professor Witten being polite . Professor Witten should not forget that in the last academic report, Professor Bourgain dug his own affairs in front of him, right?

Professor Bourgain looked at Wang Yun, "Wang, you really surprised me. I didn't expect that after you solved the Kakutani conjecture, you would choose the NS equation as a doctoral research project. I thought you were still developing in differential topology. Or work on the Hilbert conjecture with your advisor."

Wang Yun said with a smile, "I originally wanted to study Hilbert's conjecture with Professor Witten, but I think that after staying in Princeton for half a year, I might be able to try to solve the NS equation. It won't be too late to study with Professor Witten."

Hearing Wang Yun's words, Professor Bourgain turned his head to look at Professor Witten and said, "Witten, old man, you really have taken in a good apprentice."

Wang Yun stood silently beside Professor Witten, without continuing to speak.Listening to them talk about quantum field theory and functional analysis, I was quite interested in listening to them.Unexpectedly, Professor Bourgain looked at Wang Yun and said with a smile, "I heard that you are good at studying nonlinear partial differential equations?"

Professor Bourgain's sudden question made Wang Yun unable to react. After a long time, he nodded dully, "It's kind of research."

"Although my research is in the field of functional analysis, I believe that your supervisor, Professor Witten, has some experience in this part. Wang, look at this—" Professor Bourgain took a pen and wrote on the small blackboard when he said this— —

[x′=f(t, x), the global existence of the solution of x(t0)=x0(2.1), where f:[t0, T]×X→X, T can take positive infinity, f is a continuous function, and record J=[t0, T] at the same time.For convenience, we make the following assumptions (a) f∈C[J×X,X]; (b) for each initial data on (t0,x0)∈J×X, the initial value problem (2.1) has a local untie.

In order to prove the main results of this part, it first involves the theorem that there is a global solution to the initial value problem (2.1) and the following two related lemmas.

Theorem A[6] Assuming that conditions (a) and (b) are both true, for (t, x)∈J×Y, there is ‖f(t,x)‖≤g(t,‖x‖), where g∈C [R+×R+, R+] is also a non-decreasing function with respect to the second variable.If the initial value problem

The maximum solution u(t, t0, u0) of u'=g(t, u), u(t0)=u2.2>0(0) exists globally on J, so for each x0∈X and ‖x0‖≤ u0, the initial value problem (2.1) has a global solution on J. ①】

Wang Yun raised his eyebrows. This is—the boundary problem of nonlinear ordinary differential equations in Banach space, right?Well, he doesn't know much about functional analysis, and it happens that Professor Bourgain is one of the masters, or in other words, the world's top batch of masters in the field of functional analysis.

"It seems that you understand it." Professor Bourgain was quite relieved, "I didn't expect you to do some research on functional analysis, so next—"

Professor Bourgain began to write on the small blackboard again, and Wang Yun was fascinated by it.The assistant next to him, Robert, took a step back. He could still understand the front, but he really couldn't understand the back. He looked at the small blackboard in a daze and didn't know what he should do.

Just looking at it like a fool, Wang Yun knew that Professor Bourgain came to have an academic exchange with his supervisor, Professor Witten. Naturally, it is impossible to give him any help in nonlinear partial differential equations, but learn more about general Function analysis is also very good.

It can broaden your horizons a lot, maybe when you will have inspiration to solve this problem?

Obviously, it's still not possible now. Professor Bourgain was still writing formulas and theories on the blackboard, and the more he wrote, the more profound and excited he became.Wang Yun went from being able to keep up with Professor Bourgain's rhythm at the beginning to being able to barely keep up with Professor Bourgain's rhythm. In the end, he had to think for a while before he could figure out what the formula on the blackboard would be tomorrow.

The top boss really deserves to be the top boss, and it is enough for Wang Yun to comprehend a simple formula.

Professor Bourgain said with a smile, "Because I'm not very familiar with nonlinear partial differential equations, so I won't make a fool of myself. I heard that Professor Witten has allowed you to go to the Institute for Advanced Study in Princeton as an assistant, and the group in the Institute of Physics over there Guys know a lot about nonlinear partial differential equations, if you have any questions you don't understand, you can ask them directly."

When talking about this, Professor Bourgain shook his head, "If you don't learn functional analysis well, I don't think Professor Witten will let you go. After all, functional analysis and quantum field theory are very closely combined. As a mathematical physics Wang, I believe it is impossible for you not to be interested in quantum field theory."

Wang Yun admitted generously, "Yes, Professor Bourgain, I am really interested in quantum field theory, and I have learned some theories about quantum field theory in private. However, it is not very mature yet, so I will Stop being ugly."

Professor Witten nodded in satisfaction. It would be crazy if the students he led didn't even know anything about quantum field theory.You know, his main achievements are concentrated in the field of quantum physics.

The so-called quantum field theory is the physical theory combining quantum mechanics, special relativity and classical field theory.Field theory refers to the distribution of a certain physical quantity in a region of space as a field in physics.Divided into steady field and unsteady field, generally speaking, the related theory is topology.

Don't look at Professor Bourgain as if he is just slick in mathematics, if he is asked to do field theory, he will naturally be slick.This is why, so many top masters who study mathematics can almost be said to be the reason for both mathematics and physics.After all, the ties between mathematics and physics run deep.

Wang Yun stood quietly behind Professor Witten, listening to the two big men talking.I wondered in my heart, what kind of mathematical model should I build for my NS equation?He just has some ideas now, but the specific ideas have not been clarified yet.

In this way, I am afraid that he will not try to solve this problem in the past two years.

Think about it too, if this problem can be solved so easily, is it worthy of being a problem?

By the time the two big brothers finished chatting, the sky had already completely dimmed. Professor Bourgain stood up and bid farewell to Professor Witten. Wang Yun stood behind Professor Witten and did not speak for a while.After Professor Witten sent Professor Bourgain away, he returned to the office, looked at Wang Yun and asked, "Wang, aren't you going to eat?"

"Professor." Wang Yun thought for a while, "I want to tell you something."

"Oh?" Professor Witten looked at Wang Yun curiously, and joked, "Could it be that you can't figure it out and want to come back and study Hilbert's conjecture with me?"

"It's really about Hilbert's conjecture." Wang Yun said in a deep voice, "It's a friend of mine who is a sophomore in the Department of Mathematics at Princeton. He's actually quite smart, but he has no goal. I am very interested in Albert Space, and there must be quite a few people who have participated in the subject taught by you, right?"

Professor Witten looked at Wang Yun and said seriously, "Wang, do you think he is really qualified for the job of assistant?" The assistant Professor Witten mentioned was not his assistant, but the assistant of doctoral students and graduate students under him.

As a top professor in the world, Professor Witten cannot have Wang Yun as a doctoral student, nor can he have no other students.Wang Yun is his most promising student, not his only student.His subject is extremely grand, although Professor Witten can solve it directly for him.However, in order to test his student, Professor Witten has actually disassembled this subject and handed it over to his doctoral students. If the undergraduate Wang Yun mentioned is really interested in Hilbert, it’s okay to try it.

It wasn't his assistant originally, Professor Witten's own assistants were Robert and Wang Yun.Especially Wang Yun, although this guy is very interested in the NS equation.But Professor Witten knows that solving the NS equation is not something that can be done overnight.

During this period, he also had many opportunities to teach Wang Yun about quantum physics.He could see that although Wang Yun was obsessed with the NS equation, he was not resistant to other knowledge.

Just like today, Professor Witten actually checked whether Wang Yun resisted knowledge in other fields.However, I am very happy, Wang Yun has a happy mood for the knowledge he can receive.It's like—he seems to be curious about everything.

"If he can persevere, then he can go to the Institute of Physics in Princeton to find Bill and the others tomorrow." Professor Witten said calmly, "Wang, you have to prepare. I will take you to the Institute for Advanced Study in Princeton tomorrow." .Where you will receive the influence of many theories, which I believe will be very helpful to you."

"Thank you, Professor, for your generosity." Wang Yun laughed, and Professor Witten shook his head, "Wang, as I said, you are the most outstanding student I have ever seen, and you are not one of them. Alright, You go back and make good preparations. Maybe tomorrow you will meet someone at the Institute for Advanced Study in Princeton, who will be a 'big shot' who has won an international award."

Professor Witten tried to speak about this matter in a relaxed tone, and Wang Yun kept Professor Witten's words in his heart.When Wang Yun turned around, Professor Witten suddenly remembered something and said, "Oh, yes, Wang."

"Professor, do you have any instructions?" Wang Yun turned around and looked at Professor Witten with a trace of confusion in his eyes.

"That's right." Professor Witten laughed, "I have received an invitation from the International Union of Mathematicians. At the end of November, there will probably be a meeting held in the capital of China. I don't know, have you Interested in participating?"

"The summoning meeting of the International Union of Mathematicians? And it's still in the capital of China?" Wang Yun was stunned for a moment, "Can I also participate?"

"Of course." Professor Witten nodded slightly, "Your name is on the invitation letter. I think there will probably be some kind of reward awarded to you."

Wang Yun shook his head and said, "Probably not possible."

"Wang, you have to have some confidence in yourself. Unraveling the Kakutani conjecture is already a very proud academic capital." Professor Witten said with a smile, "Of course, it seems that it is still not enough in Princeton."

"Thank you, Professor, for your reminder." Wang Yun is not really looking forward to the meeting held by the International Union of Mathematicians, but he is more looking forward to what will happen when he goes to the Princeton Institute for Advanced Study tomorrow.