Hearing this, Professor Deligne was stunned for a moment, and then asked with some surprise: "Do you want to practice dual cultivation?"
Xu Chuan nodded and said: "When I was studying in China, I studied mathematics and physics, and got a double degree certificate from NTU. I am also very interested in physics, and I hope to be exposed to this aspect while studying at Princeton.
knowledge."
Professor Deligne thought for a while and then continued: "Princeton does not support double majors. Here, you can only choose one subject as your major path."
"If you are also interested in physics, then I suggest you take the path of mathematical physics."
"In this regard, Professor Edward Witten is very suitable 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 the conjecture on the existence of m-theory are all his contributions to physics."
"Although he is a physicist majoring in physics, his mastery of mathematics can be matched 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 feels a little regretful, after all, he originally planned to personally accept Xu Chuan as his student.
In his opinion, this young man's talent in mathematics was unprecedentedly rare, and it was even difficult to find another rising star in mathematics who could compare with him.
Even Peter Schulz, who was previously recognized as the most outstanding mathematician of the young generation, was slightly inferior to him.
After all, compared to the time when he made huge contributions, his age is too young.
At the age of eighteen, he can solve a world-class mathematical conjecture.
Although it is impossible to determine what peak he will reach in the academic world in the future, looking at it now, there are only a few people throughout history who can be compared to him.
Professor Deligne naturally hoped to take such a genius under his tutelage. He studied under the Pope of Mathematics, Grothendieck, and eagerly hoped to carry forward the ideas and works left behind by his teacher.
Originally he saw this hope in Xu Chuan, but now it seems that it is a pity that this young man does not aspire to the field of pure mathematics.
...
After hearing Professor Deligne's introduction, Xu Chuan shook his head and said: "I am very interested in mathematical physics, but I want more."
"If Princeton doesn't support double majors, then at least I hope I can take the same classes as other physics students and choose the same physics instructor."
"I can pay the tuition for the dual subjects of mathematics and physics, even if I can only get a degree certificate in the mathematics department, it doesn't matter."
"I just want to study mathematics and physics at the same time. If I choose only one subject, I feel that I may regret it in the future."
Hearing this, Professor Deligne raised his eyebrows, thought for a moment and then said: "If that's 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 your choice of mentor now?"
One student and two mentors may be a bit rare in China, and it also conforms to the default academic rules, but abroad, especially at Princeton, this is nothing.
It's just that if there are two tutors for one student, the student will definitely be tired.
Especially at the graduate and doctoral level, tutors will also have their own scientific research experiments and tasks and need help from students.
But Xu Chuan didn't care about this. Those who are engaged in academics are still worried and tired, so don't take this path and just become a civil servant.
"As for mathematics, I have recently become very interested in number theory and differential equations, and I plan to study these two aspects in depth."
After a pause, Xu Chuan looked at Professor Deligne in front of him and continued: "In these two aspects, you are undoubtedly a top mathematician, so I hope to apply for your doctorate. I wonder if you would welcome it, professor?"
."
He had already considered his options before coming to Princeton.
He majored in mathematics in his life, and if he couldn't double major at Princeton, he would have no choice but to take the path of mathematics and physics.
However, he still fought for himself and barely obtained the qualification to study mathematics and physics at the same time.
As for the mentor, the old man in front of me is a pretty good choice.
Professor Deligne is a student of Pope Grothendieck and a leader of the Grothendieck school. He has made huge contributions in the fields of number theory, algebraic geometry, differential equations and other mathematics.
He has won the three top mathematics awards, the Fields Medal, the Wolf Medal, and the Crafford Medal, and is the only person in the world to have won two mathematics grand slams.
In addition to his great achievements in number theory and algebraic geometry under his tutelage, Professor Deligne also collaborated with others to construct representations of algebraic groups using flattened cohomology, established the theory of mixed Hodge structures, unified Hodge theory and l-advance
Galois said that he developed the theory of Shimura clusters and collaborated with Mostov to study the single performance group theory of differential equations.
In the fields of group structure and differential equations, it can be said that they perfectly meet his goals. With the knowledge of this old professor, he will definitely learn a lot.
Upon 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."
This chapter is not over, please click on the next page to continue reading! "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 Di
It seems that further in-depth research can be done on the domain and domain expansion of the Ricray function and how to convert the function into a subgroup."
"As for the research direction, based on the automorphic forms and automorphic l-functions in the Langlands program, we may be able 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 while, 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 haven't done much research in this area, but
I have some more basic ideas. When you get used to life here, maybe you can come and share them with me."
Xu Chuan: "Then I'll leave it to you for the next few years."
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 so extensive that 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 get 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 also 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 no 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 long sigh of relief and said: "It's a pretty good calculation, but unfortunately I don't understand physics very well, so I 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."