December 13th.
Xiao Yi sat in his office and turned on the computer.
First of all, I clicked on a piece of information, which was named [Exchange List and Student Information of Recommended Students on December 13].
And below, there are the 14th, 15th, and 16th.
For four whole days, Xiao Yi had to spend his time communicating with these recommended students.
What else could he say to this?
First, I took a look at the people I will be interviewing today.
Hmm...
The first person is from the School of Mathematics, and he is from Beijing University. I don't know what this guy from Beijing University is thinking, but he actually applied for their recommended student USTC.
Although Peking University's graduate school admission rate is quite high, if you can get a graduate school admission place at Peking University Mathematics Department, you must have performed very well during your undergraduate studies.
In this case, why not stay at Peking University or go to another strong mathematics school?
Although USTC is also very strong in mathematics, it is not as good as those at the top.
As for whether it was specifically for him, when the list of recommended students was announced, he had not yet confirmed that he would serve as a graduate tutor.
Xiao Yi thought in his heart, and then looked at the name of the first student, called...
Looking at the name on the information, Xiao Yi was immediately stunned.
"Chen Muhua?"
This kid...
Wasn't he the person who took the mathematics entrance examination with him?
And he often hangs out with that Joint Examination Group, so Xiao Yi is somewhat familiar with this person.
But when I think about it and calculate the time, the group of people they were in are now in their senior year.
The number of places for exemptions has been determined in the first semester of senior year, and now it looks like...
Well, time flies by so fast.
Xiao Yi sighed in his heart.
Look at the time, there are still ten minutes left, you can get ready and enter the online meeting room.
On the other side, in a certain student dormitory of Beijing University School of Mathematical Sciences.
"I'm blanching, brothers, I'm so excited!"
A boy rubbed his hands, looking nervous and excited.
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 would soon enter the online conference room.
Thinking of this, he turned his head and looked at the roommates in the dormitory and said, "Brothers, aren't you excited?"
Everyone else in the dormitory looked at him with envy and jealousy.
Damn it, when Chen Muhua applied for USTC, they thought this kid was crazy. With Chen Muhua's grades, he could definitely go to some well-known foreign universities. But if it really wasn't possible, even if he stayed at Beijing University, there would be no problem at all.
Actually go and sign up for USTC?
This must be crazy.
However, Chen Muhua explained to them at that time that they were betting that they could choose Xiao Yi as their mentor.
Regarding this, several of his roommates were non-committal at the time.
After all, Xiao Yi had not yet served as a graduate tutor at that time, and they could not find relevant information online.
So instead of betting on this, they might as well choose better schools honestly.
For example, Lu Ping, Lu Ping and Chen Muhua are also roommates, and he has now confirmed that he will go to Princeton University to study for graduate school.
But in the end, what they never expected was that Chen Muhua actually won the bet.
Xiao Yi actually plans to accept students.
"Don't mention it, you really deserve to die!"
Hearing that this kid was actually shouting now, several people started to curse.
Chen Muhua shrugged and said, "This is what I deserve. As a warrior, what I got is in line with the bet I made."
"You don't call it a warrior, you call it a dog gambler."
Lu Ping rolled his eyes and said.
Chen Muhua chuckled, "How can a child cry every day, how can a dog lose every day, there is no way, you can't envy this kind of thing."
At this time, he received a message, and after taking a look at it, his eyes lit up.
"Okay, okay, Scholar Xiao has called me into the conference room. You can just watch me and Scholar Xiao chatting and laughing."
After snapping his fingers, he put on his glasses and entered the online conference room.
And Xiao Yi is already inside.
Of course, the camera is also on.
Looking at the face on the screen that was as young as himself, Chen Muhua couldn't help but sigh again in his heart.
Scholar Xiao, still no change.
Probably the only difference is that Xiao Yi's status in the world has become more important.
If we talk about the important theoretical conjectures that Xiao Yi has solved before, he has gained the respect of people around the world.
So the application-related things he has recently developed, such as the epoch-making battery technology of lithium-sulfur solid-state batteries, are what really make him someone that everyone has to pay attention to.
Respect does not necessarily mean attention.
Recalling the first time when Joint Examination Group and Xiao Yi chatted, I now have to work hard to express myself and become the other person's student.
"Your name."
Suddenly, the voice of Xiao Yi came from the headphones.
Chen Muhua was stunned for a moment, then replied, "Wei Yimin?"
Xiao Yi twitched the corner of his mouth, and then pretended to lower his head to score. "Well, 10 points will be deducted for impression."
Chen Muhua's eyes suddenly widened and he quickly said, "Brother Xiao is me, Chen Muhua!"
After hearing this, Xiao Yi clicked his tongue twice. "You are really a kid. You are a student of Beijing University. Why do you want to get a scholarship to USTC?"
"Of course it's because of my admiration for you Scholar Xiao that I couldn't help but choose USTC, Brother Xiao. You are mine..."
"Stop it, stop it." Xiao Yi stretched out his hand to stop this guy from continuing. Then he lowered his head and pretended to be grading, and said, "If you try to gain favor by trying to please the instructor, your impression score will be deducted by another 10 points."
"Hiss~" Chen Muhua took a breath of air, and then calmed down decisively.
"Brother Xiao..."
"Also, during the interview, you should state your job title."
Chen Muhua: "Yes, Professor Xiao."
Xiao Yi smiled. He still had to take this video conference as an interview as seriously as possible.
After confirming that the guy in front of him was the 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 regarded as an interview for you, so let's not waste so much words and start the formal part directly. Please introduce yourself first."
"Okay." Chen Muhua nodded, and then became serious.
Although he was joking just now, he seemed to be playing the relationship card with Xiao Yi, but in fact he never had such an intention.
He believes that he must be one of the best among all the students who want to choose Xiao Yi as their tutor.
And since you have this strength, why do you need to engage in heresy?
"Hello, Professor Xiao, my name is Chen Muhua. I am a student of Shangjing University School of Mathematical Sciences. My three-year average grade point is 3.88. Counting various extra points, the total grade point 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 second-district SCI."
"At the same time, I participated in two Shing-Tung Yau college students' Math Olympiad, and won two individual first prizes. In addition, I participated in the Chinese Mathematical Association and was invited to report once..."
Self-introduction is naturally the time to introduce various achievements made in the past.
Listening to Chen Muhua's many achievements, 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 his introduction was completed, Xiao Yi nodded.
"Very good, I can see you are really working hard."
He looked at the titles of the three papers on the information and said, "Well... the research directions of these three papers of yours are all Algebraic Geometry. You seem to be 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 Langlands Program, so I also want to further develop research on number theory."
"Langlands Program."
Xiao Yi nodded slightly, and after thinking for a moment, he asked, "Then what do you know about number theory now?"
Chen Muhua: "So far 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 I have also read several papers. a"
Xiao Yi nodded slightly.
He thought for a moment and then said, "Then I will give you a question. You can try to solve it."
[Suppose Q is the field of rational numbers, L is a finite expansion field, and Gal(L/Q) is its Galois group. Let π be an automorphic representation on GL2(Q), and ρπ be the representation of Gal(-Q/Q) associated with it. Prove that if π is an automorphic representation corresponding to a certain modular form, then ρπ is continuous, and its trace function tr(ρπ(Frob_p)) and the p-coefficient a_p of the modular form satisfy a_p=tr(ρπ(Frob_p)), where Frob_p is the Frobenius element of the prime number p.]
After writing out the question, Xiao Yi continued, "This question has a deep relationship with Langlands Program. Since you want to study Langlands Program, this question may give you a certain understanding."
"By the way, let me give you a hint. If you want to solve this problem, you must first pay attention to the relationship between the modular form and the automorphic representation, such as the relationship between the Hecke feature value on GL2 and the representation of the Frobenius element."
"Secondly, there is Langlands correspondence, and we focus on using the two concepts of Frobenius element and trace function. Think carefully about their functions."
"Okay, let's get started."
Listening to Xiao Yi's words, Chen Muhua was already in a daze at this time.
Scholar Xiao How... can you come up with such a complicated question so casually?
But considering that this is a question about Langlands Program, it is quite normal to be complicated.
It involves the three major components of Langlands Program: Algebraic Geometry, number theory, and Representation Theory.
He looked at it with a slight headache and tried to solve the problem.
And Xiao Yi also started to wait.
Time passed slowly.
10 minutes later.
Chen Muhua still gave up.
He shook his head and said, "Sorry, Professor Xiao, I can only understand it so far. I still don't know enough about Representation Theory."
Xiao Yi smiled, but he was not surprised by this.
"It doesn't matter. The difficulty of this question is strictly at the doctorate level. It doesn't matter if you can't do it, but you are very correct in the first few steps."
"First of all, the first step is to assume that f is a modular form with a weight of k, and its Fourier expansion is f(z)=∑(∞, n=1)ane^(2πinz). The focus of this step is the relationship between the modular form and the automorphic representation. It is already good to think of this."
"The following is the correspondence between automorphic expression and Galois representation. Here is the key content of Representation Theory. It requires the accumulation of knowledge. It is normal if you don't understand it."
"We use Langlands correspondence, and 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.]
"Then..."
Xiao Yi slowly explained the problem-solving process to Chen Muhua.
Although some of them are still unclear, Chen Muhua also generally understands the method of proof.
"... Finally, let me summarize the entire process. The key points are the three tips I just gave, and then the breadth of knowledge."
"For example, we need to use the modular form of the Hecke feature value, the Langlands functor property, and finally the work of Deligne."
"Deligne has proven in the past the relationship between the p-coefficient of the modular form and the trace of Galois representation. Specifically, for a new form f with weight k and its corresponding Galois representation ρπ, there is: ap=tr(ρπ(Frobp))."
"So, if you want to study Langlands Program, the amount of knowledge is very important. If you can master so much knowledge and use it without any hindrance, then you can become a real Langlands Program mathematician."
Listening to Xiao Yi's words, Chen Muhua couldn't help but feel a sense of excitement in his heart.
Become a real mathematician?
For those of them who study mathematics, becoming a mathematician is also what they yearn for most.
"Yes! I know!"
he said.
"Well, let's continue to expand our knowledge, especially in number theory and Representation Theory."
Xiao Yi said, "This is the initial stage in mathematics, and it is also the most boring stage. Keep at it."
Chen Muhua nodded heavily.
But then, he couldn't help but ask, "But, Brother Xiao... Professor, how did you accumulate knowledge? I always feel that you have more knowledge than those big guys in their 60s and 70s."
"Me?"
Xiao Yi smiled and shrugged, "Of course I came from reading, but my reading speed... well, a little faster than all of you."
A little?
Chen Muhua twitched the corner of his mouth.
Are you sure it's not 100 million points?
An old man at home has a cerebral infarction and is hospitalized. He went home for a visit today. The update is late.