The top student must be diligent.

Chapter 210: Job Titles Should Be Addressed During Interviews

12 month 13 day.

Xiao Yi sat in his office and turned on his computer.

First, I clicked on a document named [List of recommended students for exchange and student information on December 12].

And below, there are the 14th, 15th and 16th.

For four whole days, Xiao Yi spent his time communicating with these recommended students.

What else could he say about this?

First, I took a look at the people I was going to interview today.

Ok……

The first person is from the School of Mathematics, and he is from Kyoto University. I don’t know what this Kyoto University guy was thinking, he actually applied to be a recommended student from their University of Science and Technology.

Although the admission rate to graduate school at Peking University is quite high, to be able to get a place in the School of Mathematics at Peking University, one must have performed very well during undergraduate studies.

In this case, why not continue to stay in Kyoto University, or go to other strong mathematics schools?
Although HKUST is very strong in mathematics, it is not as good as the ones ranked above.

As for whether it was specifically for him, when the list of recommended students was announced, it had not yet been confirmed that he would serve as a graduate student supervisor.

Xiao Yi thought about it, and then looked at the name of the first student, which was...

Looking at the name on the information, Xiao Yi was stunned.

"Chen Muhua?"

This kid...

Isn't he the person who took the mathematics joint examination with him?

Moreover, he often hangs out in the joint entrance examination group, so Xiao Yi is somewhat familiar with this person.

But if we think about it again and calculate the time, that batch of people are indeed now in their senior year.

The recommendation quota was confirmed in the first semester of the senior year, and now it seems...

Well, time flies by so fast.

Xiao Yi sighed in his heart.

Look at the time, there are ten minutes left. You can get ready and enter the online meeting room.

……

On the other side, in a student dormitory of the School of Mathematical Sciences at Kyoto University.

"Hey guys, I'm so excited!"

A boy rubbed his hands, his face full of nervousness and excitement.

He is Chen Muhua.

When he learned that he would be the first student to communicate with Xiao Yi, he was already extremely excited, not to mention that he was about to enter the online conference room.

Thinking of this, he turned his head and looked at several roommates in the dormitory and said, "Brothers, aren't you excited?"

Everyone else in the dormitory looked at him with envy and jealousy.

Damn, when Chen Muhua applied to USTC, they thought this guy was crazy. With Chen Muhua's grades, he could definitely go to those famous and strong universities abroad. If not, even staying in Peking University would be no problem.

You actually applied to a university of science and technology?
This must be crazy.

However, Chen Muhua explained to them at that time that it was a gamble that they could choose Xiao Yi as their mentor.

His roommates remained noncommittal about this.

After all, Xiao Yi had not yet become a graduate student supervisor at that time, and they could not find any information about him on the relevant Internet.
So instead of betting on this, they might as well just choose better schools.

For example, Lupin, Lupin and Chen Muhua are also roommates, and he has now confirmed that he will go to Princeton University for graduate studies.

But in the end, what they never expected was that this kid Chen Muhua actually won the bet.

Xiao Yi actually planned to accept students.

"Don't mention it, you deserve to die!"

Hearing that this kid was still shouting, several people started cursing at once.

Chen Muhua shrugged and said, "This is what I deserve. As a warrior, what I get is in line with the bet I made."

"You are not a warrior, you are a gambler."

Lupin said, rolling his eyes.

Chen Muhua laughed, "How can a child cry every day, or a gambler lose every day? There is nothing we can do about it. You can't envy such things."

Just at this moment, he received a message, and after taking a look at it, his eyes lit up.

"Alright, alright, Xiao Shen asked me to come into the meeting room. You guys just stand by and watch me and Xiao Shen chatting and laughing."

He snapped his fingers, then put on his glasses and entered the online conference room.

And Xiao Yi was already inside.

Of course, the camera is also on.

Looking at the face on the screen that was as young as his own, Chen Muhua couldn't help but sigh again.

God Xiao, there is still no change.

Perhaps the only difference is that Xiao Yi's position in the world has become more important.

If the important theoretical conjectures that Xiao Yi had come up with before had earned him the respect of people all over the world.

His recent application-oriented things, such as the epoch-making battery technology of lithium-sulfur solid-state battery, have truly made him a person that everyone has to pay attention to.

Respect does not necessarily mean attention.

Recalling the first time I chatted with Xiao Yi in the joint entrance examination group, I now have to work hard to show myself and become his student.

"your name."

Suddenly, Xiao Yi's voice came from the headphones.

Chen Muhua was stunned for a moment, then replied: "Wei Yimin?"

Xiao Yi pulled the corner of his mouth, and then pretended to bow his head to give a score: "Well, deduct 10 points for impression."

Chen Muhua's eyes suddenly widened, and he quickly said, "Brother Xiao, it's me, Chen Muhua!"

After hearing this, Xiao Yi clicked his tongue twice: "It's really you, kid. How come you, a student from Peking University, want to be admitted to USTC as a postgraduate student?"

"Of course it's because of my admiration for you, Mr. Xiao, that I couldn't help but choose HKUST. Brother Xiao, you are mine..."

"Stop, stop." Xiao Yi reached out to stop the guy from continuing, then lowered his head and pretended to give points, saying: "Trying to gain favor by currying favor with the instructor, I'll deduct another 10 points from your impression score."

"Hiss~" Chen Muhua took a breath of cold air, and then decisively calmed down.

"Brother Xiao..."

"Also, during the interview, you have to refer to your position." Chen Muhua: "Yes, Professor Xiao."

Xiao Yi smiled. He still had to take this video conference which was considered as an interview as seriously as possible.

After confirming that the guy in front of him was Chen Muhua, he also opened the guy's information again.

"Okay, since this is an exchange meeting arranged by the school, it can also be considered an interview for you, so we won't waste so much time talking and will directly start the formal part. Please introduce yourself first."

"Okay." Chen Muhua nodded, and then became serious.

Don't be fooled by the fact that he was laughing just now, as if he wanted to play the relationship card with Xiao Yi, but in fact he never had such intention.

He believed that he was definitely one of the best students among all those who wanted to choose Xiao Yi as their mentor.

And since we have this strength, why do we need to resort to unconventional methods?
"Hello, Professor Xiao. My name is Chen Muhua. I am a student at the School of Mathematical Sciences of Shangjing University. My average GPA for three years is 3.88. If you take into account various bonus points, my total GPA is 4.27."

"In addition, I have independently completed three papers in the past three years, and all of them have been published, including two Chinese core papers and one international zone II SCI."

"At the same time, I participated in two Qiu Chengtong College Mathematics Competitions and won two individual first prizes. In addition, I participated in the China Mathematical Society and was invited to give a lecture once..."

When introducing yourself, it is natural to introduce the various achievements you have made in the past.

Hearing about the many achievements made by Chen Muhua, Xiao Yi also raised his eyebrows slightly.

It can be seen that Chen Muhua did not waste his talents and time during his three years as an undergraduate.

Obviously, everyone is working hard in their own world.

As he finished his introduction, Xiao Yi nodded.

"Very good, I can see you really work hard."

He looked at the titles of the three papers in the information and said, "Hmm... the research directions of your three papers are all algebraic geometry. It seems that you are very interested in algebraic geometry."

"Yes." Chen Muhua nodded. "Algebraic geometry is one of the most important directions in modern mathematics. At the same time, I am very interested in the Langlands Program, so I also want to develop my research in number theory."

“The Langlands Program.”

Xiao Yi nodded slightly, and after thinking for a moment, he asked: "So what do you know about number theory now?"

Chen Muhua: "At present, I have studied books on analytic number theory and algebraic number theory. Well... I have basically understood the basic concepts of algebraic number fields and algebraic integers. I have studied some basic properties of unit groups and class numbers, and read several papers. a"

Xiao Yi nodded slightly.

He thought for a moment and then said, "Then I'll give you a question. Try to solve it."

【Let Q be the field of rational numbers, L be a finite extension field, and Gal(L/Q) be its Galois group. Let π be an automorphic representation on GL2(Q), and ρπ be the associated representation of Gal(-Q/Q). Prove that if π is an automorphic representation corresponding to a modular form, then ρπ is continuous, and its trace function tr(ρπ(Frob_p)) satisfies a_p=tr(ρπ(Frob_p)) with the p-coefficient a_p of the modular form, where Frob_p is the Frobenius element of prime p. 】

After writing down the question, Xiao Yi continued, "This question is deeply related to the Langlands Program. Since you want to study the Langlands Program, this question may give you some understanding."

"By the way, to solve this problem, you first have to pay attention to the relationship between modular forms and automorphic representations, such as the relationship between the Hecke eigenvalues ​​on GL2 and the representation of Frobenius elements."

"Then there is the Langlands correspondence, and the two concepts of Frobenius elements and trace functions are used emphatically, and we should think carefully about their roles."

"Okay, let's get started."

Listening to Xiao Yi's words, Chen Muhua was already a little dazed.

How could Xiao Shen...come up with such a complicated question so easily?

But considering that this is a question about the Langlands Program, the complexity is indeed normal.

It involves algebraic geometry, number theory, and representation theory, the three major components of the Langlands program.

He looked at it with a slight headache and tried to solve the problem.

And Xiao Yi also began to wait.

Time passed slowly.

10 minutes later.

Chen Muhua still gave up.

He shook his head and said, "I'm sorry, Professor Xiao, I can only explain this much now. I still don't know enough about representation theory."

Xiao Yi smiled. He was not surprised by this.

"It's okay. Strictly speaking, the difficulty of this question is at the doctoral level. It doesn't matter if you can't solve it, but your first few steps were correct."

"First, let f be a modular form with weight k, and its Fourier expansion is f(z)=∑(∞,n=1)ane^(2πinz). The key point of this step is the relationship between modular forms and automorphic representations. It is good enough to think of this."

"The following is the correspondence between automorphic representations and Galois representations. This is the key point in representation theory. It requires a lot of knowledge. It's normal that you don't understand it."

"We use the Langlands correspondence, where each modular form f corresponds to a two-dimensional Galois representation ρπ."

[ρπ:Gal(-Q/Q)→GL2(Ql), where l is a prime number. This Galois representation is continuous and closely related to the modular form f. ]

"After that……"

Xiao Yi slowly explained to Chen Muhua the process of solving this problem.

Although some of it was still not clear, Chen Muhua roughly understood the method of proof.

"…Finally, let me summarize the whole process. The key points are the three tips I just gave, and the breadth of knowledge."

“For example, we need to use the Hecke eigenvalues ​​of modular forms, the Langlands functor property, and finally the work of Deligne.”

"Deligne has previously shown a relationship between the p-coefficients of modular forms and the trace of Galois representations. Specifically, for a new form f with weight k and its corresponding Galois representation ρπ, we have: ap = tr(ρπ(Frobp))."

"So, if you want to study the Langlands Program, knowledge is very important. If you can master so much knowledge and use it without any hindrance, then you can become a true Langlands Program mathematician."

Listening to Xiao Yi's words, Chen Muhua couldn't help but feel excited.

Become a real mathematician?
For those who study mathematics, becoming a mathematician is what they most desire.

"Yes! I understand!"

He said.

"Well, I'll continue to expand my knowledge, especially in number theory and representation theory."

Xiao Yi said, "This is the starting stage in mathematics, and it is also the most boring stage. Just stick with it."

Chen Muhua nodded heavily.

But then, he couldn't help but ask, "But, Brother Xiao... Professor, how did you accumulate your knowledge? I always feel that you have more knowledge than those big guys in their sixties and seventies."

"I?"

Xiao Yi smiled and shrugged, "Of course I read books, but my reading speed is... well, a little faster than yours."

a little?
Chen Muhua curled the corners of his mouth.

Are you sure it's not 100 million points?

……

My elderly family member was hospitalized due to cerebral infarction. I went home to visit him today, so the update is late.

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(End of this chapter)