Tian Yanzhen was not wrong about Qiao Yu at all. This guy is a person who is very good at enlightening himself, or in other words, very good at reconciling with himself.

Yes, in his life before he was eleven years old, Qiao Yu's grandfather told Qiao Yu what kind of man he should be through words and deeds.

For example, repay kindness with kindness and repay grievance with directness; for example, think twice before doing something and decide to take immediate action; for example, men should take on men's responsibilities, saving money is something women need to consider, and men should be responsible for making money; for example, responsibility only

For something worthwhile and...

Anyway, quite a lot.

It's all thanks to Qiao Yu's good memory, otherwise he really wouldn't be able to remember so much.

In the next five years of living independently, Qiao Yu learned to be good at reconciling and compromising with his stubborn temperament when appropriate.

Generally speaking, a person who clearly knows his own advantages will be very competitive, while a person who clearly knows his own shortcomings will be terrible. Qiao Yu has both.

Therefore, his competitiveness is really strong, and for his enemies, he is actually quite scary. People with good memory remember kindness and hatred.

After many people come into contact with Qiao Yu, they will think that this child is a person with high emotional intelligence. If he is willing, he can make everyone around him feel like a spring breeze. But in fact, everything is an illusion.

Separating IQ from EQ is actually a very funny thing.

Because people with high IQs can easily be backward compatible. It just depends on whether these people with high IQs are willing to accommodate themselves downwards. Just like when Qiao Yu was in Class 13, he could easily get along with his classmates and also

Can have excellent popularity.

This depends on strong observation and empathy.

Show yourself when you should show off, and hide your clumsiness when you should hide it. When you satisfy the self-esteem of your classmates, you can also gain friendship. For Qiao Yu, all these behaviors are subconscious actions to maximize interests based on logic and rational thinking.

.After all, he has a family to support.

This can be seen when the two eldest brothers in Class 13 argue about who invites Qiao Yu to go online more often.

Some people are like this. They clearly take advantage of the other person and make the other person feel like a spring breeze. I wish this person could make more money. In Qiao Xi's words, Qiao Yu has engraved rational calculation into his bones. What he lacks most is sincerity.

.

It's just that Qiao Yu hid this very cleverly.

He carefully hides his pride and looks harmless in front of everyone. He uses his occasional small pride to hit those close to him to maintain his innocent persona.

This way of dealing with others that maximizes strengths and avoids weaknesses has become almost instinctive for Qiao Yu.

Therefore, although there has been little progress on the two-dimensional generalization of Chevalet's theorem during this period, Qiao Yu is not in a hurry. He will carefully record the results of each failed attempt and then send it to Professor Li via email.

He will also attend the meetings of the research group on time. However, in every meeting, he has a strong idea in mind and will not overwhelm others. After all, it is their project. He will wait until the three professors have finished speaking before he makes a speech.

. He very humbly put forward some of his whimsical opinions and suggestions, kept a very low profile, and was very polite and respectful to the three professors and even the other graduate students attending the meeting.

This also allowed Qiao Yu to quickly win the favor of everyone in the entire research team from top to bottom.

A sixteen-year-old kid has just made an achievement that can be said to be eye-catching in the world of mathematics. He is not proud at all. He respects the professors very much. It is really easy to get a good impression. The other one is good.

The news is that Tian Yanzhen also directly submitted his paper to Invent.Math for him. It has now passed the editing stage and has entered the stage of finding reviewers.

The only difference is that when submitting this time, Tian Yanzhen called Qiao Yu to the office and taught Qiao Yu step by step how to submit a manuscript. Including introducing him to how to use the different submission systems of the four top journals. Same as last time.

The difference is that this time Tian Yanzhen did not put Qiao Yu's paper on the pre-release website.

I gave a special lecture in Huaqing, and there were at least five world-renowned experts in the field in the audience. If this situation can still cause controversy in the academic world, then it will really have to turn the table. As for Yuan Zhengxin, there is another

He praised Qiao Yu fiercely.

There is no doubt that from the perspective of Mr. Yuan, Qiao Yu is not only talented, but also extremely motivated. No matter how impressive his achievements are, he has never slacked off. This attitude towards mathematics is even worse in the eyes of the old man.

Talent is more valuable. Love is doubled.

Qiao Yu may not realize it himself, but at this time he told Mr. Yuan that he wanted the soil on the moon, and Mr. Yuan decided to help him find a way. Anyway, after not making so many demands for himself, Qiao Yu felt

It was actually quite easy.

I was too lazy to stay in his hut every day. I studied the class schedules of various departments of Yanbei University every night. When I saw classes that interested me, I went to listen to them during the day.

It is not limited to pure science and engineering courses such as mathematics, physics, and chemistry. He will also listen to the content of literature, philosophy, sociology, communication and law. But when it comes to the humanities field, Qiao Yu will look at the students'

Evaluated.

Specially select the kind of boss-level professors whose lectures are very interesting according to students' evaluations and do not follow the textbooks.

For this reason, Qiao Yu even bought two pieces of veteran cadre clothing online, just to look more mature. After all, he just wanted to hide in the corner and listen to the class quietly, and had no other purpose.

And his young and handsome face always brings him some trouble - such as being teased by Yanbei's seniors. Really, boys must learn to protect themselves when they go out. This has never been so obvious.

Qiao Yu also thought that after all, he was now a celebrity in the field of mathematics, so many people should know him.

After all, the photos of him and two math giants are widely circulated on the Internet.

But it is a pity that on the Yanbei University campus, apart from being recognized when attending classes in the two colleges of Mathematics and Physics, few people in other departments have recognized him.

This also made Qiao Yu realize that many times the omnipotent Internet seems to give people an illusion... They always feel that they are already a big shot, but in fact they may not be as famous as they think. Everyone

The influence of mathematics is probably limited, especially in mathematics, where it seems quite difficult to break through.

Of course, it may also be that his appearance is not very recognizable, he is just ordinary handsome and ordinary confident. At the end of April, the visa for France was also issued.

Speaking of visas, there is a small episode.

On the day of the appointment for the interview, Professor Zhou, who had obtained Qiao Xi's power of attorney, accompanied Qiao Yu.

When talking face to face with the visa officer, it was obvious that the other person had some doubts about Qiao Yu's age and asked a few questions in this regard. "Hello, what kind of visa are you applying for?"

Professor Zhou stood by and helped Qiao Yu answer: "My student was invited to Paris to attend the World Conference on Algebraic Geometry next month. He is one of the speakers invited by the conference."

The visa officer looked at Qiao Yu and asked, "Oh, you are invited at such a young age? Qiao Yu, can you briefly tell me the purpose of attending this meeting and the content of your report?"

Qiao Yu patiently replied: "Do you know about the geometric Langlands conjecture? Recently, a mathematician claimed to have proved this problem, but I found a small mistake. Then they invited me to explain the mistake."

The visa officer nodded and continued to ask: "In other words, the importance of your participation in this meeting is to correct a mistake. Do you think such a report is worth bearing all the travel expenses? In addition, have you considered staying in China? Continue studying mathematics in France?"

Qiao Yu became a little impatient and said directly to the visa officer: "That's alright, what kind of questions are you asking? Didn't you study mathematics when you were in college? Do you know if you proved a certain widely accepted theorem? is wrong, how many mathematics papers will be removed from the shelves?

Also, have you stayed in this house every day since you came to Beijing and never gone out? If your country hadn't produced mathematicians like Poincarais, Hilbert, and Gauss, this algebraic geometry conference would be just the right time. Over there, how much do you think I want to go to your place?

You can’t have some idea of ​​what Paris is like now? The Seine River is like that. I don’t even dare to drink your tap water when I go there. Are you still afraid that I won’t come back if I stay there? Isn’t this confidence a bit inexplicable? I Now I am a student at Yanbei University. My teacher is a Chinese academician. Why should I stay with you to study?

Look at the invitation letter clearly. I decided to go after being invited by the organizing committee! I won’t go unless I sign. Do you think it’s my loss? That’s a loss to the world of mathematics!” Really, after hearing Qiao Yu suddenly said such words. Professor Zhou Liang, who was accompanying him at the time, was so frightened that he broke into a cold sweat and for a moment he forgot to explain.

Fortunately, the visa officer on the opposite side was just stunned, hesitated for a moment, then lowered his head expressionlessly and began to check the documents silently. After a while, he said directly: "Okay, your information looks very complete, and the visa will usually be issued within a week. As a result, you will be notified when the time comes."

Qiao Yu immediately stood up, turned around and left.

Professor Zhou stayed behind and added: "Mr. visa officer, the geometric Langlands conjecture is an important issue in cutting-edge research in the field of mathematics. Qiao Yu's speech this time can be said to be of great significance to the field of mathematics. I suggest you You can contact the organizing committee of this meeting before making a decision.

In addition, all the expenses for Qiao Yu’s participation in the conference were fully borne by the Yanbei International Mathematics Center. The materials we submitted included relevant financial certification information.”

The visa officer raised his head and glanced at Professor Zhou, and replied with an expressionless face: "Please believe in my professionalism. Personal emotions will not affect whether the visa is approved, sir."

After walking out of the visa center, Professor Zhou couldn't help but start scolding Qiao Yu: "No, Qiao Yu, your temper came suddenly, didn't it? What did I tell you before I came here? Just tell the truth when the visa officer asks you.

Just answer it."

Qiao Yu immediately lost his rebellious look, raised his head, with a sunny boy's smile on his face, and responded: "Professor Zhou, you are right. But respect is mutual. That guy just now was too annoying.

I was angry. Even though it was written in the information that I was from Yanbei University, he actually asked me if I wanted to stay in France to study mathematics?

Think about it, doesn’t this look down on our Yanbei University? That’s why I’m so angry. How is our School of Mathematics at Yanbei University worse than those universities in Paris? Who gave him the face? Really, it doesn’t matter if he looks down on me.

But I can’t bear to look down on my future alma mater, Director Tian, ​​Mr. Yuan and you.

Whether you can attend the meeting or not is not a big deal, the face of your alma mater and tutors is the big deal!" Professor Zhou opened his mouth, but suddenly he didn't know what to say.

Forget it, he didn't bother to say anything anymore, it was really no big deal.

If your visa is really rejected, you can contact the organizing committee of the conference to explain the situation and think of a solution. If it doesn't work, France is one of the Schengen countries, so you will have to change planes... Anyway, Qiao Yu's mentor has great powers.

The most important thing is that after listening to Qiao Yu's explanation, Professor Zhou also felt that the question was a bit too much. And it probably offended the two bosses, Tian Yanzhen and Yuan Zhengxin. Anyway, he reported the situation truthfully, and the two bosses

Even if I don't say it, I'm probably satisfied in my heart.

On the way back, Professor Zhou's biggest emotion was that young people today are so amazing.

Just as Lao Zhou imagined, he reported this matter to Tian Yanzhen on the phone. Tian Yanzhen just said lightly on the phone: "Haha, this kid has a pretty bad temper. It's okay. I should be able to get the visa."

Yes, I really can’t get through it, so I’ll ask again.” Then nothing more happened.

But on the third day, Professor Zhou received a call informing him that Qiao Yu's visa had been approved.

I went there again and got Qiao Yu's passport. When I saw the label on Qiao Yu's passport indicating the validity period and the number of entries, Professor Zhou was filled with emotion. I always felt that he applied for a visa when he was studying abroad.

Sometimes, my attitude towards the visa officer was a bit too reserved, and I was really not relaxed at all.

Of course, he didn't have such a powerful teacher at that time who could tell everything.

But then again, Qiao Yu didn't ask Academician Tian to help, so that was too much.

It seems that what this kid said is right, respect should always be mutual.

There is really no need to be too polite when you can't gain respect.

When Qiao Yu learned that the visa had been approved, he was listening to a class in the philosophy department of Yanbei University. After checking WeChat, he obediently put his phone back in his pocket and continued to listen to the class seriously.

This is a big class, an introduction to Chinese and Western philosophy, but there don't seem to be many students studying philosophy, so it can definitely be seen on the stage if you are not paying attention to the class. And to be honest, the visa has just been approved, so Qiao Yu doesn't feel too excited.

Having had the experience of standing on a podium to give a report, Qiao Yu knew very well that the instructor was standing on top and could see all the little movements of all the students below at a glance. It was clear at a glance whether they were listening to the lecture or in a daze.

"..What is truth? Aristotle once said: Truth is to say what is that it's, and what is not that it's not. My understanding is that truth is a state that is consistent with things.

For example, when we say that snow is white, its truth depends on the fact that our common snow is indeed white. But are there any places where the snow is other colors, or even black? Of course it is! For example, after a volcanic eruption, the ash

Falling at the same time as snow will cause the snow to appear black or dark gray, especially in high mountain areas.

So the question arises, is truth subjective or objective? In different cultures, different understandings of morality and ethics will lead to different understandings of truth? This is the relativity of truth.

Obviously the ancient Greek philosophers did not think so. For example, in Plato's theory of ideas, he believed that truth is an eternal and unchanging idea that transcends changes in the material world. Note, students, here Plato emphasizes the persistence of truth.

Nature and immutability are not even affected by changes in the physical world.

It is an absolute, eternal existence, so if we have the opportunity to talk to Plato about truth, we will be discussing a universal principle or law that transcends specific things and instantaneous changes. In order to help everyone understand this concept better, I

Let me tell you a story..."

A class lasted about one hundred minutes, and Qiao Yu listened with great interest.

The first half is an introduction to mainstream international viewpoints, which are mostly content in textbooks, but the second half is where the professor gives free rein.

In addition to well-known celebrities such as Kant and Nietzsche, William James, Ludwig Wittgenstein, Michel Foucault... A bunch of Western thinkers have quoted various arguments and various examples at their fingertips.

What about relativism and absolutism, pragmatism, Tractatus Logico-Philosophicus, power and truth, paradigmatic truths of scientific theories...and even truths based on gender and identity...

Really, there is no need for PPT. He controlled Qiao Yu for more than an hour. The most amazing thing is that after talking so much, the professor did not give a final concept of truth until the end of get out of class. Instead, he put this question It was treated as an after-school homework and assigned.

The topic was very simple, asking the students to understand what the truth is and write an article and submit it. Listening to the uproar from the brothers and sisters sitting in front, Qiao Yu was quite satisfied.

This is the benefit of taking classes.

Not only can you hear a lot of interesting knowledge and enrich your knowledge base, but you don't have to be responsible for the homework assigned by the instructor. Just listen...

Writing homework is impossible.

In addition, the professor of the philosophy department seems to be quite easy to be a professor. The word "truth" is extended to more than a hundred minutes of content, and in the end, no conclusion is given. If the mathematics department behaved like this, the students would probably go crazy. After the class , just in time for dinner.

The Department of Philosophy is very close to the Nanyuan Canteen.

Qiao Yu usually doesn't attend classes in the morning, so after finishing classes at whichever college he goes to, it's almost time to eat, so he eats in a nearby cafeteria. During this time, he ate all the cafeterias on Yanbei campus. .

I also have a mental recipe for each family’s special dishes.

While I was enjoying my meal, I received another call from Senior Brother Chen. "I...Qiao Yu...you, you, you..."

"What's wrong with you, Senior Brother Chen?"

"You, you were invited to attend the World Congress on Algebraic Geometry, and you have to give a thirty-minute report at the conference?" After a while, Chen Zhuoyang on the other end of the phone finally managed to make this sentence fluent.

"Ah? Isn't it? Senior Brother Chen, this matter has been settled a long time ago. You are Bai Xiaosheng from our Numerical Research Center. How did you know?" After a long while, the other person held back a sentence: "No one told me, You didn’t say anything, how could I know?”

Qiao Yu replied: "Well...I am not thinking that Senior Brother Chen will leave school next month, so I don't want to cause trouble for you. No, who is so talkative..." "Professor Zhou just handed over your passport When I was sent to Director Tian, ​​I happened to bump into him, and Professor Zhou casually mentioned this matter."

Qiao Yu feels that Senior Brother Chen knows how to flatter people without leaving any trace. For example, through the way he was so excited that he was incoherent just now, and the tone that seems a little aggrieved now, he can gain a lot of emotional satisfaction.

So Qiao Yu followed what Senior Brother Chen said: "That's it, Senior Brother, it's just an algebraic geometry conference, not the World Congress of Mathematicians, so you don't have to be too excited. If I can be invited to do it at the World Congress of Mathematicians next time Report in sixty minutes, it’s not too late for you to be happy for me.”

Saying this is really not to show off, but to let senior brother know that he has understood these subtle flatteries. "Oh, where are you now?"

"Nanyuan Canteen."

"Why do you have to travel so far just to have a meal?"

"I just went to the philosophy department and took a class. The professor talked about the truth. The professor's lecture was very exciting, but I didn't seem to listen. Hey... maybe I'm not a budding student of philosophy?"

"Why do you go to the philosophy department to listen? What can they teach that is useful? The truth, the definition of philosophy is very erratic, and the argumentation process can be directly idealistic. Let me tell you, mathematics is the truth. What is right is right. It’s wrong! It’s very clear.”

"Hey, senior brother, you don't know, my brain has been swollen from the recent projects. Listening to these contents is very interesting and can relax my brain."

"Don't listen to those messy words. If you really want to talk about the collision of ideas, mathematical descriptions are the most beautiful. My boss once said something in a lecture when he was talking about symmetry: look for invariance in change, and seek simplicity in complexity.

.Isn’t this kind of mathematical thinking more interesting than the mysterious and mysterious things in philosophy? You must not be misled by those mysterious theories.”

Chen Zhuoyang's words penetrated into Qiao Yu's ears, as if activating a switch, causing Qiao Yu to subconsciously ask: "Wait, senior brother, what did you just say that Director Tian said? Change that..." "Yeah

?Looking for the constant in the change, what’s wrong?”

"Oh, it's nothing. I just didn't hear it clearly. I'll go back after dinner. I'll hang up now."

"Hey, there's no rush. I just called you to ask about the situation...Hey...um, hang up?" Qiao Yu hung up the phone directly. He didn't hear what Chen Zhuoyang said next.

Seek consistency amidst change, seek simplicity amidst complexity.

Qiao Yu thought that Professor Zhang seemed to have had a similar conversation with him before, but of course the words were different.

However, combined with the issues he had been pondering recently, he seemed to feel like a ray of light had entered his brain.

The core of the exchange heap is a set of exchangeable elements. In a exchange heap, the arrangement of different elements does not affect the properties of the whole, which itself constitutes a symmetry. Then the question arises, some global functions in the exchange heap

Will it also exhibit similar invariance?

One of the biggest difficulties in Professor Li's current project is that the calculation of global functions usually involves multiple variables and complex combinations. All his previous attempts have faced high computational costs and then reached a dead end. If

Being able to effectively use symmetry to extract invariant features may turn cumbersome calculations into more intuitive analysis.

Especially if the global function can be regarded as an invariant form under the action of a certain transformation group, can the relationship between the global function and the Whitaker layer be revealed through this perspective?

If successful, then it is obvious that analyzing global functions from the perspective of invariance will make complex problems clear. This transformation, if feasible, will not only be a theoretical breakthrough, but also provide a concrete calculation method. Thoughts

After hearing this, the thoughts in Qiao Yu's brain immediately began to diverge.

The first step is naturally to construct an appropriate transformation group to analyze the performance of the global function under the action of this group.

The brain quickly constructs various possible transformation methods, how to map the global function to a new space through transformation group action, and use the space to simplify calculation and analysis.

"Hey, Xiaoyue, do you think that guy keeps staring at you? Xiaoyue."

Zhao Xiaoyue followed the gaze of her best friend next to her and said angrily: "Don't make trouble, she is obviously in a daze." "Yes, I was shocked by your beauty, so I was in a daze. Haha..."

Zhao Xiaoyue glared at the indifferent woman beside her angrily...

Although she is confident about her appearance, she has had many suitors since junior high school. In high school, some classmates even found a way to unlock the camera of the tablet used in class, secretly took a video of her during class, and sent it to On a certain small video software.

Not only did the video become a hit, with more than 300,000 likes, it also received a bunch of comments such as "It's over, I suddenly want to fall in love" and "It completely matches all my fantasies about my first love." But Zhao Xiaoyue still I really don't think she is so beautiful that any boy in the cafeteria can look at her in a daze.

Of course, the appreciation of beauty is a very subjective thing. But Zhao Xiaoyue knew that the boy was simply in a daze.

Because when she and Tang Jing sat down just now, she happened to glance at Qiao Yu. At that time, Qiao Yu was eating normally, and it was obvious that he became like this after answering a phone call. Especially at this time, Qiao Yu had a hand on his hands. Holding the mobile phone, frowning slightly, his eyes were obviously blank and unfocused.

It didn't look like he was staring at someone, but Zhao Xiaoyue found it quite interesting to see Qiao Yu able to maintain such a posture. Isn't his hand numb and his neck sore?

wrong..

"Wait a minute, Tang Jing, don't you think he looks familiar?"

"Isn't it? Xiaoyue, is it true that the real man is interested in having a concubine? But he looks very small, smaller than us. So you like this type? But speaking of it, he looks good, but his clothes are poor. It’s a bit too old, and it’s dressed in an old-fashioned way.” “Are you still making trouble? To be honest with you? Take a closer look!” Zhao Xiaoyue frowned and said.

"Huh? If you say so, it does look familiar." "Change into that gray casual sportswear..."

"Oh.........that one from the Mathematics Academy, that one, Qiao, Qiao, Qiao Yu?"

"It's not the School of Mathematics. It's jointly trained by Yanbei University and Huaqing Mathematics Research Center."

"Wow, this is a real master! Do you think if we could make friends with a master, would we be able to pass subjects such as advanced mathematics, linear algebra, and probability and statistics easily?" Zhao Xiaoyue and Tang Jing are both economics students at Yanbei University. student in the economics department of the college.

In fact, it is not just the School of Economics. For most students who are not in the School of Mathematics and Physics, as long as their major requires courses related to mathematics and big physics, it is the most troublesome. Even if it is just a B in advanced mathematics and a B in big physics.

Of course, even high-level mathematics C and general physics courses can give many students majoring in liberal arts a headache. After all, many students choose liberal arts because they are really afraid of mathematics and physics.

Otherwise, the Internet would not put high-level numbers and big things together to make fun of them.

"Just pass it by casually? You think so. But if you can increase the WeChat account of the master, there will be someone to ask for advice on advanced mathematics problems in the future." Zhao Xiaoyue glanced at Tang Jing and said.

In fact, Qiao Yu is not needed.

The content of High Mathematics B can probably be easily handled by any student from the School of Mathematics at Yanbei University.

The only problem is probably that everyone has their own social circle. Students in the School of Mathematics will not carry the word mathematics on their heads. But Qiao Yu is different. He is more or less a celebrity and can still be recognized.

The most important thing is the strong-willed mentality, which everyone has.

How about we sit over and have a chat with him?" Tang Jing came up with an idea.

"Forget it, it's better not to go through. It's not good to disturb others." Zhao Xiaoyue hesitated and shook his head. Tang Jing rolled her eyes and said, "Then I'll go alone."

After saying that, he stood up directly holding the dinner plate.

"Ah? Are you really going? I think he might be thinking about something, so I'd better not bother him."

"What are you afraid of! I have no intentions towards him, can't we just make friends? Besides, I can wait for him to come to his senses." After saying that, Tang Jingzhen walked towards Qiao Yu's seat with the dinner plate in hand.

Zhao Xiaoyue was a little confused, but after thinking about it, she still didn't go crazy like her best friend... It would be bad if it disturbed the master's thinking.

Qiao Yu, who knew nothing about the outside world, had just completed the deduction in his mind that related the global function and the Whittaker layer. Just when he was feeling excited, he suddenly discovered that there was a senior student on the opposite side.

But Qiao Yu didn't take it to heart. He encountered this situation often. After all, the canteen is public.

Putting down his cell phone, Qiao Yu planned to finish his meal quickly and then go back to record the reasoning process in a mathematical way. To his surprise, his senior sister recognized him.

"Hello, are you Qiao Yu from the Mathematics Research Center?"

"Hello, yes. Who are you?" Qiao Yu nodded and responded cheerfully.

Look, he is indeed a celebrity, and he can be recognized even if he eats in the cafeteria. After all, this is not the territory of the mathematics department.

"I am studying economics at the School of Economics. My name is Tang Jing, great master. We are sisters in the same dormitory. Well, the one sitting over there is called Zhao Xiaoyue. She is your fan and has followed your Weibo. She is embarrassed. I came to say hello to you, so can you add her WeChat so that I can push your WeChat to her?"

Qiao Yu blinked, turned his head and looked past Tang Jing, and glanced at the senior sister opposite who was eating elegantly. Hey, she is really beautiful, she seems to be on par with Xia Keke.

Then Qiao Yu withdrew his gaze and said seriously: "Sister Tang Jing, the question I was thinking about just now is about the two-dimensional generalization of Chevallet's theorem. An extremely important technology is used here, which is Langlands duality. To put it simply, It is said that through this tool, a direct connection can be established between algebraic geometry and representation theory. To be honest, this is a very difficult task. "

"Um...Master, what do you mean?" Tang Jing asked.

Qiao Yu replied seriously: "It means that the communication between people is different from mathematics. If you need to establish a connection, it can be less complicated. For example, your sister can come directly to ask for my WeChat. If there is an extra person in the middle steps, many complex variables will appear.

For example, maybe your sister is your shield, or maybe you are playing truth or dare and making fun of me, so senior Tang Jing, ask your sister to ask for it next time, or admit that you are my fan. ..Well, in short, I will definitely do it next time!”

After saying that, Qiao Yu quickly took a few mouthfuls of rice, then stood up and ran away under the dazed gaze of the senior opposite him. Of course, it was not because he was afraid of the senior opposite, but simply because he had to go back and clear out the things in his mind. Record it.

..

Tang Jing sat there stunned for a long time, then picked up the dinner plate and returned to her sisters.

Zhao Xiaoyue held back her smile and asked, "Tell me, how did you scare the great god away?"

Tang Jing said dullly: "It's true that Shuyuan is the first of the four major lunatic asylums. I told that Qiao Yu that you were his fan and wanted his WeChat. As a result, he made a lot of mess. What is Chevalet's two-dimensional generalization, what is Langlands duality...*

"Wait, what did you tell him?" Zhao Xiaoyue stopped smiling and stared at Tang Jing in shame.

"You are his fan. Didn't you apply for a Weibo account to follow him that day?" Tang Jing said confidently.

"How many times have I explained that it's because I found it interesting to watch the Great Reconciliation of the Mathematics Century in the group chat, so I follow his Weibo. If there are any latest developments, I can know about them as soon as possible. What kind of fan is this?" Zhao Xiaoyue He said helplessly.

"But don't you think this is fate? This is not the place at the Math Center. We suddenly wanted to come here to have a meal and bumped into each other? Well... Xiaoyue, could it be because I said you wanted to join? He texted me on WeChat, but he turned around and ran away, so are you angry?" Tang Jing blinked and asked thoughtfully.

"I didn't!" Zhao Xiaoyue replied decisively.

Tang Jing nodded and said: "As expected, it's okay. The master also said just now that if you ask for WeChat by yourself, he will definitely give it to you." "Heh."

"Suppose the global function is f:C→C, where C is the swap heap."

"The transformation group G, which acts on the global function, is defined as: g·f(x)=f(g^—1·x), for all g∈G, x∈C."

"Define the Whitaker layer W so that it is invariant under the action of the algebraic group, that is: W(x)=iaioi(x), where φi is the characteristic layer under the action of the algebraic group." Through the properties of the characteristic layer, you can Introduce the following mapping: middle:C→W, making: (=gEG2gf."

Using the principle of categorization shrinkage, it can be proved that: vg∈G, g in (f = in (f. Therefore, ( is an invariant function and can be regarded as an automorphism of the Whitaker layer. "By It can be seen that: f can be described by the automorphism of Whitaker layer."

..

When Qiao Yu returned to his cabin, he quickly opened LaTeX, wrote the above content, saved it directly and sent it to Professor Li from Huaqing opposite. It was a very short proof process, but that's how mathematics is sometimes.

It was so difficult when I didn't expect it, but as soon as inspiration came, the problem was solved naturally.

Probably because he has been thinking about this issue recently, Senior Brother Chen's phone call just now, when he relayed Director Tian's description of symmetry, suddenly made him think of a geometrically intuitive idea: treat the global function as an invariant form under certain transformations.

.

After hanging up the phone with Senior Brother Chen, he completely planned in his mind how to combine the feature layer theory and the principle of categorization shrinkage, understand the properties of the global function by constructing a transformation group, and consider the Whittman function under this transformation.

Changes in layers, thereby revealing the relationship between them.

After sending the email, I checked my proof process again, then picked up the phone and dialed Professor Li directly across the street. Although what he wrote was very brief, Professor Li, who had been studying this issue for a long time, was sure

Can understand his thinking.

The call was answered soon.

Why don't you take a look at what I think now?" "Have you fully proved it?"

"Well, it's just written a bit briefly."

"Wait a minute, don't hang up yet. I'm right next to the computer. Let me take a look first."

There was a noise of dragging keyboards and mice on the phone. Qiao Yu simply turned on the speakerphone and put the phone on the table. There was no response from the other party for a while, and Qiao Yu's thoughts began to wander.

Well, a senior asked him for WeChat just now. This seems to be the first time this kind of thing happened to him at Yanbei University... No, he shouldn't have run away just now, he looked very lackluster...

Does the senior think she was scared away?

Speaking of which, that fan girl seems pretty pretty, but I don’t know if she’s smart or not.

No, mathematics is the most beautiful. Qiao Xi is second, and Ke Ke is third... "This... proof, this proof. How did you come up with it?"

The voice that came from the phone again finally brought Qiao Yu's divergent thoughts back together.

"This is a long story. It starts with the fact that I attended a philosophy class on truth this morning. Well, Professor Li, are you sure you want to listen now?" "Forget it! I want to verify it first.
Chapter completed!