Chapter 146: Dual Mentors Deligne and Witten

Hearing this, Professor Deligne was slightly stunned, and then asked in surprise: "Do you want to major in both?"

Xu Chuan nodded and said: "When I was studying in China, I studied mathematics and physics, and obtained a dual degree certificate from Nanjing University. I am also very interested in physics, and I hope to be exposed to this knowledge during my studies in Princeton."

Professor Deligne thought for a while and then said: "Princeton does not support dual degrees. Here, you can only choose one subject as your major."

"If you are also interested in physics, then I suggest you take the path of mathematical physics."

"In this regard, , Professor Edward Witten is a good fit for you. ”

“He specializes in quantum field theory, string theory and related topology and geometry, proof of the positive energy theorem of general relativity, supersymmetry and Morse theory, topological quantum field theory, superstring compactification, mirror symmetry, supersymmetric gauge field theory, and conjectures on the existence of M theory. These are his contributions to physics. ”

“Although he is a physicist majoring in physics, his mastery of mathematics is unmatched by few mathematicians. His research in pure mathematics has far-reaching influence and he has won the Fields Medal. ”

Although he was a little surprised by Xu Chuan’s choice, Deligne still recommended a candidate to Xu Chuan.

It’s just that he was a little regretful, after all, he originally planned to personally accept Xu Chuan as a student.

In his opinion, the talent of this young man in mathematics is unprecedented and rare, and it is even difficult to find another mathematical star who can be compared with him in the world.

Even Peter Schultz, who was previously recognized as the most outstanding mathematician of the younger generation, is slightly inferior to him.

After all, compared to the time when he made great contributions, his age is too young.

At the age of 18, he was able to solve a world-class mathematical conjecture.

Although it is uncertain what peak he will reach in the academic world in the future, as of now, there are only a few people who can be compared with him throughout history.

Professor Deligne naturally hopes to recruit such a genius. He studied under Grothendieck, the Pope of mathematics, and is eager to carry forward the ideas and works left by his teacher.

He originally saw this hope in Xu Chuan, but now it seems a pity that this young man is not interested in the field of pure mathematics.

After hearing Professor Deligne's introduction, Xu Chuan shook his head and said, "I am very interested in mathematics and physics, but I want more."

"If Princeton does not support double majors, then at least I hope I can take the same courses with other physics students and choose the same physics tutor."

"I can pay the tuition for both mathematics and physics, even if I can only get a degree certificate from the Department of Mathematics in the end."

"I just want to learn both mathematics and physics at the same time. If I choose only one, I feel that I may regret it in the future."

Hearing this, Professor Deligne raised his eyebrows, thought for a while and said, "If this is the case, maybe it can be done."

"Although Princeton pays great attention to rules, for a genius like you, some rules can be broken."

"So, can you tell me about your tutor choice now?"

One student with two tutors may be a little rare in China, and some are in line with the default academic rules, but abroad, especially in Princeton, this is nothing.

It's just that one student with two tutors will definitely be more tired.

Especially at the graduate and doctoral stage, tutors will also have their own scientific research experiments and tasks, and need the help of students.

But Xu Chuan didn't care about this. Academics are still worried about being tired, so don't take this path. Just become a civil servant.

"In terms of mathematics, I'm very interested in number theory and differential equations recently, and I plan to study these two areas in depth."

After a pause, Xu Chuan looked at Professor Deligne in front of him, and then said: "In these two areas, you are undoubtedly a top mathematician, so I hope to apply for your doctoral degree. I wonder if you welcome it, professor."

Before coming to Princeton, he had already considered his choice.

If he majored in mathematics in this life and couldn't double major in Princeton, then he could only take the path of mathematical physics.

However, he still fought for himself and barely won the qualification to study mathematical physics at the same time.

As for the tutor, the old man in front of him is a very good choice.

Professor Deligne is a student of Pope Grothendieck and a leader of the Grothendieck School. He has made great contributions in mathematical fields such as number theory, algebraic geometry, and differential equations.

He won the three top mathematics awards, the Fields Medal, the Wolf Prize, and the Crafford Prize. He is one of the only two people in the world who have won two mathematics grand slams.

In addition to his great achievements in number theory and algebraic geometry under his teacher, Professor Deligne also collaborated with others to construct representations of algebraic groups using flat cohomology, established the theory of mixed Hodge structures, unified Hodge theory and L-advanced Galois representations, developed Shimura cluster theory, and collaborated with Mostov to study the monogenetic group theory of differential equations.

In the fields of group construction and differential equations, it can be said that he perfectly meets his goals. With the knowledge of this old professor, he will definitely learn a lot.

Hearing Xu Chuan's choice, Professor Deligne nodded and said, "Of course you are welcome. I have some understanding of number theory and differential equations, and I should be able to answer some of your questions."

After a pause, Professor Deligne then asked: "It's just that these two fields are relatively broad, and there is quite a lot of content that can be studied and researched. Do you have specific learning and research goals?"

"If you have no research goals for the time being, you can also choose to join my research group. I am currently studying the 'standard conjecture' left by my mentor Grothendieck, if you are willing."

Xu Chuan pondered for a moment and said: "The standard conjecture is a bit too difficult for me. I prefer my own goal."

"Before coming to Princeton, I talked with Professor Artur Avila about some of the methods used for the Weyl-Berry conjecture I proved last time, such as the domain and domain expansion of the Dirichlet function and how to transform the function Chengziqun seems to be worthy of further in-depth research.”

"As for the research direction, based on the automorphic forms and automorphic L functions in the Langlands program, we may be able to try to make some breakthroughs in this area."

Professor Deligne had no dissatisfaction or displeasure at being rejected by Xu Chuan. On the contrary, he admired Xu Chuan's ability to stick to his own ideas and the owner's independent research goals.

For someone like him who has reached the pinnacle of the mathematical world, he hopes that the mathematical world can develop prosperously.

After pondering for a moment, Professor Deligne said: "The Langlands Program is a huge proposition. Automorphic forms and automorphic L functions have greatly promoted the development of analytic function theory. I don't have much research in this area, but I have some basic ideas. When you get used to life here, maybe you can come and share them with me.”

Xu Chuan: "The next few years will be up to you."

Deligne smiled and said: "You're welcome. Now that the mathematics aspect has been determined, what about the physics aspect? Do you have a favorite candidate? I can be your lobbyist."

Xu Chuan: "Excuse me, sir. As for physics, I would like to study under Professor Edward Witten. He is very suitable for me."

As a tutor in physics, it was no surprise that he would choose Professor Edward Witten, his tutor in his previous life.

Professor Witten's knowledge is too extensive. Even if he studied there in his previous life, he has not exhausted Professor Witten. There is still a lot to learn in this life.

Moreover, Professor Witten is the top boss of the European Atomic Energy Laboratory. With him, he can stay there and obtain first-hand collision data. When applying for a collision experiment, he can also obtain greater benefits. Opportunity.

Hearing Xu Chuan's choice, Professor Deligne frowned and said, "If it were someone else, or if you chose to study mathematical physics, I think Professor Witten would accept you as a student without hesitation."

"But I'm afraid it's a bit difficult now. Professor Witten is more stubborn than me. I'm not sure enough to convince him."

"Although there are dual tutors at Princeton, they are usually in the same subject, such as dual mathematics tutors in the mathematics department."

"Dual tutors like you, who are divided into two completely different subjects, have never appeared before."

Xu Chuan smiled and said, "I know this very well, so I made some preparations before coming."

As he spoke, he took out a stack of manuscript papers from the backpack behind him and handed it over.

"These are some of my ideas and calculation manuscripts in physics. Although they are not as outstanding as my achievements in mathematics, they may be able to impress Professor Witten."

Hearing this, Deligne raised his eyebrows and curiously took the manuscript information from Xu Chuan's hand.

"The Mystery of the Proton Radius, a mathematical method to accurately calculate the proton radius." 》

"A method to calculate the functional relationship between the typical distance l between particles in the Bose-Einstein condensation phenomenon and the particle number density n. 》

Professor Deligne turned over the manuscript paper in his hand, and the title he read surprised him.

At first, he thought it was Xu Chuan's achievements in astronomy and physics, that is, the application of Xu-Weyl_Berry's theorem. He was about to say that those things were of little use to Professor Witten.

Unexpectedly, it turned out to be information manuscripts from other fields.

After flipping through the information manuscripts in his hand and looking at the calculation formulas and data on these manuscripts, Professor Deligne began to read through them carefully.

Although he does not understand physics, there is no big problem in understanding the mathematical formulas and data calculations in these manuscripts.

In this way, after remaining standing for more than ten minutes, Professor Deligne finally came back to his senses.

He breathed a sigh of relief and said: "It's a pretty good calculation, but unfortunately I don't understand physics very well and can't be sure whether these things are correct."

"Let's go. Professor Witten happens to be at the institute today. I'll take you there. Maybe these materials can impress him."

"It's usually difficult to see him. Although he is a professor at the Institute for Advanced Study in Princeton, he is usually based at the LHC."