The first phase of IMO training was over. Although Qiao Yu planned to take a rest, he still honestly wrote a paper about his experience in reading the paper and sent it to Director Tian and Mr. Yuan from Huaqing. This time it was really not to let the two mentors know.
No matter how hard you work, you have a purpose.
Because he has been studying the geometric Langlands conjecture paper during the entire training period.
Director Tian didn't know if he would find someone to check his experience, but Qiao Yu believed that Mr. Yuan would casually forward it to Professor Pan. In this way, if he had any problems with his understanding, Professor Pan could point it out to him.
.
The main reason why he didn't send it directly to Professor Pan himself was because Qiao Yu felt embarrassed. Don't do to others what you don't want others to do to you.
If someone thinks of a question every day, just send it to him directly... And he can summarize several questions every day, and this continues for nearly half a month. Qiao Yu feels that he has blocked this person directly.
Although Professor Pan did not block him, he had clearly felt that Professor Huaqing's messages were getting slower and slower.
Anyway, in the first two days when I joined him, he was the quickest in replying to messages. Almost every time I had a question, I would reply immediately. After that, the reply to messages became slower and slower. During the training period, there were even questions he sent the day before. After a full time
It took Professor Pan a day and a half to reply.
Qiao Yu didn't consider whether the questions he asked were getting more and more tricky, and Professor Pan needed to discuss it with someone before he dared to reply. Moreover, Professor Pan didn't tell him that he was not in Huaqing at all, but was going abroad for a meeting.
Went.
Qiao Yu just sensitively felt that Professor Pan had probably changed and was beginning to annoy him. It was difficult to ask this question directly, so he had to make a roundabout way. There was nothing to say in the next week, so he continued to read books and papers.
read.
It was just that Qiao Yu was supposed to read the paper on prime numbers before, but instead read the more than 800-page paper on the geometric Langlands conjecture. Reading and learning at the same time would undoubtedly slow down the speed of reading the paper.
In the eyes of normal professors, the books I read this week are beginning to look unsystematic. But this one is what Qiao Yu is best at, finding books to read as needed.
There are quite a lot of books to read about the Langlands Program of Geometry. Qiao Yu felt tired before because he had no direction, but now that he has a goal to strive for, this kind of task does not feel so tiring anymore.
Moreover, the training time schedule is not too tight. The collective life also ensures that Qiao Yu can go to bed on time at 11 o'clock every day and get up on time at 6:30 in the morning. The sleep he lost some time ago was fully made up during the training camp.
By the way, there is one more thing worth mentioning.
Yu Yongjun also brought Gong Jiatao into his friend group.
There is no way, the two of them have been getting along best these days. However, as the group leader, when Qiao Yu saw these two people in the same group, he decided to talk less in the group in the future. After all, it is easy to hide from the obvious.
, it’s hard to guard against darkness.
Yu Yongjun is a standard bright and coquettish character, with extremely strong brain jumping ability, but he only talks but does not do all kinds of shameless coquettish operations.
Gong Jiatao is naturally a secret coward. He looks like a dog to ordinary people, but he is very liberal in playing various tricks. We will wait for him to do it first. As for Yu Wei...
Originally, Qiao Yu thought that he was the only kind and good person in the group, but he was a bit withdrawn. But now it seems that this guy can lie without blushing and his heart does not beat, and he looks very sinister.
At this time, Qiao Yu suspected that the reason why these people wanted to participate in the competition instead of taking the college entrance examination normally was probably because if they took the college entrance examination, everyone would find out that based on their ideological and political level, they should be arrested and shot immediately.
Of course, the feeling is mutual.
What Qiao Yu didn't know was that when Yu Yongjun and Gong Jiatao often chatted in private, they actually had similar views... For example, non-human beings like Qiao Yu should not participate in math competitions with them, and their destination should be sent to a certain place. A high-end biological laboratory conducts direct biopsy research.
The friendship formed during the competition is so pure and beautiful. Of course, this does not mean that the two sides will really be on the same page.
In fact, everyone has been learning from each other. It's like Qiao Yu thinks that he should learn from Yu Yongjun and Gong Jiatao's shamelessness, and Gong Jiatao and Yu Yongjun have agreed that after returning to school this time, they must find some classmates and play with them. A game where you can solve problems while playing.
They even tried it secretly in private and found that if they replaced the Olympiad questions with ordinary high school practice questions, they could still handle it. Of course, the rules of the competition would have to be slightly modified, and they would not be able to play against those who were very good at playing games.
But these don't seem to be problems. For ordinary students in the high school they live in, just being able to keep up with most of their classmates requires them to do their best, and there isn't much left to devote to games.
After all, those who are really qualified to waste some time on games during their studies these days have to be primary school students...
But their reasons are also very good. Only by regaining the self-esteem that has been stepped on by others can they regain their confidence and achieve good results in international competitions. From this point of view, among the four friends, they can write in one stroke Yu Wei is probably the only one who can be said to be kind.
But Qiao Yu didn't care.
The only thing that made him feel sad was that recently, even Director Tian and Grandpa Shi across from him were getting slower and slower in replying to his messages.
Well, at the beginning of the semester, the bosses are all very busy, Qiao Yu comforted himself like this.
But there are still gains. For example, Professor Pan, who was getting slower and slower in replying to messages, suddenly one day sent an address directly to Qiao Yu and gave him an account password. After logging in, Qiao Yu discovered the latest few messages in it. These videos are all videos of various recent seminars on the geometric Langlands conjecture.
Although the lectures were still given by the two main leaders, Dennis and Sam, they also included everyone from the entire team, including Professor Pan, and the focus of the demonstrations in the several lectures was also different.
Qiao Yu also noticed keenly that the man appeared in the third most scenes...
There is no doubt that for Qiao Yu, the discussions in these seminars were very useful and indeed answered many of his questions.
For example, if you have a high-level understanding of the overall proof idea of ​​the paper, then when you read through the details of the paper, you will be able to solve many problems that you did not understand before.
Most importantly, it made him more certain that his intuition might be right.
When extending consistent equivalence results to general situations, it is necessary to frequently use local-global phenomena in algebraic geometry or category theory to locate and interact with the global. Then if there are some minor errors in local calls, it will inevitably
Will cause a global error.
This may even lead to the key theorem proved by the authors - that the applicability of Ambidexterity may be limited in certain situations.
You must know that the last paper uses this conclusion to extend the conjecture to general situations. If the applicability of the most critical Ambidexterity theorem is limited in the situation discussed in the paper, then this time the proof of the geometric Langlands conjecture is only
Can declare failure.
But Qiao Yu wants to prove this is still not an easy thing.
Because the paper itself relies on specific axioms and assumptions, the results in higher-order category theory are correct in a specific context, but if the axioms or category structure change, the applicability of the theorems may also be affected.
Even in the geometric Langlands program, some complex homological algebraic problems treated by this theorem have been successfully solved.
In words that ordinary people can understand, this paper is the result of an environment constructed by mathematicians themselves, relying on specific theoretical background and assumptions. To prove that there is a problem, Qiao Yu may need to find a way to prove the construction.
The entire framework presented has logical holes.
We must know that in modern mathematics, the autonomy of axiomatic systems and category theory frameworks is inherently rigorous. Any work that questions or attempts to find logical loopholes must be based on more rigorous reasoning and innovative perspectives, which makes questioning this structure
The task is extremely difficult.
But when you want to prove an error in mathematics, there is a trickiest way, which is to construct a counterexample.
Counterexamples are a very powerful tool in mathematics, which can directly show that a certain theorem or inference is not valid under certain conditions. In theory, as long as he can carefully design an algebraic geometry situation within the logical framework established by the other party, and let
This goal can be achieved if local objects cannot globally satisfy the requirements of the Ambidexterity theorem.
If he can go one step further and use this counterexample to discuss the reasons for the axiom mismatch, for example, through the technical assumptions in the backtracking proof, to deduce the loopholes in this paper, and give a preliminary solution, then he can probably become a
A star in mathematics...
Of course, this is still not a simple matter.
In fact, it is much more difficult than any problem Qiao Yu has encountered so far.
Anyway, the week after the training camp passed so uneventfully. He thought about it while reading books and papers, and even thought about it while taking a shower and sleeping, but he still couldn't construct a suitable counterexample.
However, while sitting on the high-speed train from the capital back to Star City, Qiao Yu still shared his work experience this week with Director Tian and Grandpa Shi across from him as usual.
"Dear Master Tian/Grandpa Shi: My main job this week is still to read in depth about the proof of the geometric Langlands conjecture. The main gain this week is that I have some thoughts on one of the key conclusions, namely the Ambidexterity theorem. Special report to you.
The Ambidexterity Theorem plays a very important role in this series of papers, especially in generalizing the conjecture from specific situations to a more general algebraic geometry background.
But as I further looked at the structure of the theorem and its application in the proof of the geometric Langlands conjecture, I began to have some doubts about its applicability, especially when dealing with situations involving singular points or complex geometry.
According to my superficial understanding, this theorem relies on a certain equivalence of local and global objects, especially in the framework of homologous algebra and category theory, which requires locally defined geometric objects to be globally consistent.
This kind of local-global equivalence seems reasonable in the context of smooth geometry. The paper also discusses some special cases, but when I am thinking about some more complex cases, such as the case where an algebraic variety contains extraordinary singular points ,Are there possible limitations?
Specifically, I suspect that local structure near some specific singular points may cause certain properties in homology algebra, such as local flatness or projectiveness, to not globalize correctly.
That is, if the Ambidexterity theorem must rely on this good behavior of local geometric structures, is there a limit to the applicability of the theorem to algebraic varieties where such specific singular points exist?
I haven't found a specific counterexample yet, but in next week's training event I plan to think deeply from the following two aspects: 1. Whether there are extraordinary singular points that will affect the properties of local homology algebra and trigger local problems of the theorem. —Global equivalence is broken.
2. The proof of the Ambidexterity theorem involves certain axiomatic structures in higher-order category theory. I would like to further explore the performance of these category theory axioms in singular geometric situations, and whether there are some implicit assumptions that cannot be used in more complex situations. Established in geometric background?
Although my ideas may certainly seem naive to you, I think they have some exploratory value. The proof of the geometric Langlands conjecture is very complicated, and the Ambidexterity theorem is a key conclusion in it, and any potential applicability issues may Have an impact on the validity of the proof.
So I hope to start with the local geometric structure at the singular point to further verify the limitations and potential problems of the theorem. If you have a better idea, please tell me quickly, your dearest student/grandson, this week For the first time, I felt the pain of losing hair."
This experience was sent by Qiao Yu to his mentor and grandpa Shi while he was sitting on the high-speed train. The person sitting next to him was Professor Zhou Liang, the leader of this IMO team.
But in fact, he had already edited this content last night and saved it on his phone. What he just did was copy, paste and add the names of the people, then slightly change the self-identification at the end, and then click the send button.
The main reason for doing this is to avoid being asked by the tutor or the master to give him a lecture again, saying that he does not know how high the sky is. It has only been a few days since I read the paper, and I want to find loopholes in others - this is very possible.
The old man is more accepting of the fact that he found loopholes in the process of learning, and his thinking was obviously based on the idea of ​​​​causing faults in other people's papers.
But there is no way. An honest and step-by-step report cannot reflect the seriousness of this problem. He is in great need of help from the two big guys now. It is best to mobilize many brains to start from this direction and give him some construction. Inspired by sexual thoughts.
Naturally, he must tell his thoughts truthfully.
To put it bluntly, I want to make full use of the resources around me, but I don’t want to bear the responsibilities caused by it. After all, I was led astray by two guys, Yu Yongjun and Gong Jiatao.
..
At Yanbei University, Tian Yan really didn't expect that Qiao Yu would suddenly send such a report today.
Because he had to participate in the training camp, Tian Yanzhen had actually agreed that Qiao Yu could take a break this week. Who would have thought that not only did Qiao Yu not take a break, but he also showed him how scary it is to be serious!
In fact, the proof of the geometric Langlands conjecture has not triggered much discussion outside the mathematical community.
Because the Langlands Program is too far away for ordinary people, it is not even as friendly as the Riemann Hypothesis, N-S equations and other things.
This is not to say that the Langlands Program is necessarily more difficult than solving these world-class conjectures. The main thing is that the threshold for anything involving the unity of basic theory is extremely high.
For example, the main problem that needs to be solved in the Langlands Program is to establish a bridge between Galois representations and automorphic forms on algebraic number fields. You can know this thing just by looking at the definition without spending several years on algebraic geometry, number theory, and representation theory. I can't even understand the question at all.
Really, if you don’t believe it, you can go to various major mathematics colleges for interviews. Just a self-contained form can make countless college students and graduate students overwhelmed by their studies, and they still only half understand it, and some even know nothing about it.
If it is the automorphic representation involved in the Langlands program... it would be even more embarrassing. After all, automorphic forms are just abstractions, while automorphic representations are higher-level abstractions. How does the algebraic group described act in On a specific Hilbert space or Banach space, the elements in these spaces may be analytic functions or some special structures.
The geometric Langlands program studies the correspondence between local systems on algebraic curves and the geometrization of automorphic forms. It simply replaces the number theoretical objects involved in the classic Langlands program with algebraic geometry objects.
The main research is to geometricize abstract number theory problems so that they can be processed in the algebraic geometry framework. This can be said to not solve specific problems, but to provide valuable tools for mathematicians to solve more specific problems. It has such a wide range of application potential.
This field also mainly attracts mathematicians who wish to open new paths in number theory and algebraic geometry.
The geometric Langlands Program can even be understood as an important mathematical tool like calculus. Like the Langlands Program, the birth of calculus was not to directly solve a specific problem, but to build a system to deal with continuous changes and limits. Problem Tools.
Therefore, the Geometry Langlands Program may completely change the way future mathematicians deal with certain problems, just as calculus changed the way mathematicians of this era deal with changes. It is natural that those who are interested in this area are also mathematicians. them.
Because once someone succeeds, it means that when we study number theory problems in the future, we will have a new framework that can be used directly. We will deal with classic number theory problems through a new dimension.
One day in the future, it will become a compulsory course in college mathematics just like calculus.
In fact, Tian Yanzhen has always been concerned about the development of the proof of the geometric Langlands conjecture. He is also very optimistic about the results obtained by this research team. But who would have thought that Qiao Yu suddenly gave him a big one.
My own students suspect that the results they finally released after more than fifteen years of research have loopholes?! How can I say that...
If there is really a loophole in this, it would be easy to say, but if it is just a conjecture, it would really offend people.
Of course, considering that Qiao Yu is only sixteen years old, probably no one will really care about him. But it is also considering that Qiao Yu is only fifteen years old. Seeing this weekly report posted by Qiao Yu makes Tian Yan really worried. Some started playing the drums.
Still a bit too much.
I’ve only read the paper for a few days, but I can already have so many ideas?!
Regardless of whether the idea is right or wrong, it at least shows that when Qiao Yu read the paper, he was really deconstructing the most basic things in the paper. In the field of mathematics, this is really strong.
In other words, being able to quickly grasp the core of a paper and deconstruct its basic content is definitely an ability that many mathematicians seek.
Deep understanding, quick learning ability, and strong mathematical intuition are all indispensable.
If you add that this kid is really bold, Tian Yanzhen only feels like him even more.
Really, he felt that with such a lantern, there wouldn't be another one in a short time unless the world went crazy...
Or maybe a new era of technological explosion is about to begin, just like after quantum physics was proposed, a bunch of talented people successively paved a broad road based on this foundation, explaining how electrons cross the pn junction through quantum mechanics, and how Controlling current in field-effect transistors has laid a theoretical foundation for the development of the semiconductor industry.
This paved the way for human society to officially enter a new era of electronic information. Children in the new era have begun to be unable to understand things like telegraphs that have been buried in the dust of history. In fact, it is only a few short years since telegraph technology was officially eliminated. ten years.
Typewriters, fax machines, and even early dial-up Internet access are gradually being forgotten. In a few years, these products that once represented advanced productivity will become memories in history books.
Once this idea came to mind, Tian Yanzhen suddenly felt excited. What a coincidence...
Qiao Yu turned out to be his student, it was like a dream.
After thinking for a long time, Tian Yanzhen took out his mobile phone. There was a phone number in the address book. Although he had spoken to the owner of this number once before, Tian Yanzhen always felt that there was a high probability that he would not actively call this number.
.
But at this moment, the emotions I once had faded away, really faded away.
With such a student, Tian Yan really felt that he could face everything in the past calmly.
No matter what, when Qiao Yu is introduced in the history of mathematics in the future, there will definitely be a sentence saying "studied from the famous Chinese mathematician Tian Yanzhen". This is actually enough. When a person reaches his age, it is almost impossible to achieve any more achievements in mathematics.
It's possible.
But his students have unlimited possibilities, so why bother with so much? Men, be more open-minded, it's really okay.
Sometimes people are like this, one thought makes the world wide open.
So when he pressed the dial button, Tian Yan was really calm and calm.
The phone rang for more than ten seconds before being answered, which probably meant that the old man opposite had gone through some mental processes, but it didn't matter. "Hello, Mr. Yuan, hello."
"I don't want to take it, I don't want to take it. What advice does Professor Tian have?" Alas, the old man is still a little narrow-minded.
Tian Yanzhen said gently: "Mr. Yuan, there is no need to be aggressive. You should also think that I am making this call because of that child Qiao Yu. I think he also sent you a copy of his study summary report this week, right?"
The person on the other side became quiet, and after a long while he responded: "Yes, I received it, I forwarded a copy to Professor Pan.
Tian Yanzhen said the purpose of the call: "That's what I thought. We also have scholars at the Mathematics Research Center who focus on research in this field, such as Professor Tan Zhiqing, who has been doing research on P into the Langlands Program for these years.
Topic.
In particular, there have been many breakthroughs in the direction of local analytic representation and L-invariant theory. Why don't we wait until Qiao Yu comes back from Star City and we can jointly hold a series of exchange meetings on the geometric Langlands program? What do you think?"
The person opposite meditated for a moment and then asked: "Where will it be held?" By asking this, the old man opposite was obviously interested.
Tian Yanzhen said grandly: "Why don't we do it in Huaqing? It's so close anyway, and we've done so much for him, so it's appropriate to let that kid take a few more steps." "Then the time will be after the Qingming Festival.
, Professor Pan from the research group will not be able to come back until then.”
Tian Yanzhen asked: "No problem. You can arrange the specific time. Let me clear the air first and see which other professors can be invited to participate. By the way, Professor Pan, can you invite Professor Dennis?"
"It's probably difficult. Dennis and Sam probably won't have any good impressions of Qiao Yu's idea. But you can ask Professor Everton at Princeton if he has time. He has experience in both geometric representation theory and p-adic Hodge theory.
He has extremely profound attainments, and having him help make judgments should be of great help to Qiao Yu."
"Then I invite you in your name?"
"Professor Everton, let me invite you. By the way, you and Professor Felice are the judges of the same Abel Prize, so you should be familiar with him. He has been working on the verification of the geometric Langlands conjecture. If you can invite him
If you come, it should help even more."
"Okay, I'll send him an email right away. If he doesn't have anything special to do in the near future, he should be able to come. But you have to confirm the time first." "Wait... Well, April 5th to April 8th
No. I just need two days on the weekend.
"Okay. I have received the message and will contact you at any time. "Okay."
"Mr. Yuan, I'll hang up first.
"Dududu..."
Tian Yanzhen smiled mockingly to himself. The old man still had a vigorous and resolute temper. It didn't matter that he just hung up the phone. At least now everyone has the same goal.
After hanging up the phone, Tian Yanzhen opened WeChat. He originally planned to send a message to Qiao Yu, but after thinking about it, he might as well forget it. Wait until this series of meetings are prepared.
Moreover, there is Qiao Yu's senior master opposite... They have already decided to do it in Huaqing. Let's just let the opposite party sell it. There is no need to fight for this kind of thing. With Qiao Yu's cleverness, in his heart
Of course there is a scale.
..
Classmate Qiao Yu, who was worried, finally returned home after riding the high-speed train for six hours.
He only reported for training on the second day, and Qiao Yu came with the team leader just to go home a day earlier.
Zhou Liang naturally couldn't disagree with such a small request. For safety reasons, he even arranged for someone to take Qiao Yu to the gate of the community before leaving. Although this seemed to Qiao Yu to be completely unnecessary.
Star City is his territory. He has been touring the entire Star City with his grandfather since he was a child. He is definitely more familiar with it than Professor Zhou, a foreigner, and even the dirty taxis can't rip off his money.
"Open the door quickly, the community is here to send you warmth!" Standing at the door, Qiao Yu knocked on the door and shouted in a low voice.
Soon the sound of footsteps was heard, but before the door was opened, a woman's voice was heard inside: "You're back when you're back, what kind of community can you give me warmth? Why are you still so childish after you've gone to college? You haven't grown up at all.
Look."
After the words fell, the door was fully opened. When their eyes met, Qiao Yu felt full of frustration and asked unhappily: "No, how did you know that I was back?"
"Hehe...Teacher Lan, you called me early in the morning and said you would be back today. The newly appointed Principal He just called me again to ask if you had arrived. How could I not know you were back?
?」
Okay, the case is solved.
However, the coordination between the two parties was so good. He just set off from the capital in the morning, and his high school alma mater received the news. Was he afraid that he would get away on the high-speed train? He originally wanted to give Qiao Xi a surprise, but in the morning
Just know it.
"Wait...how did you become Principal He? Where did Lao Zhang go?"
"What are you talking about, old Zhang and Xiao Zhang? Principal Zhang has been transferred to the district education bureau chief. Are you hungry? Do you want me to give you a bowl of noodles? But I suggest you stay away for now. Principal He just said that tonight Director Zhang wants to come and invite us to have a meal together, and I can't refuse.
Well, being unable to refuse means that Qiao Xi has already declined in every possible way, but she is no match for Principal He's cleverness.
Qiao Yu nodded. He hadn't seen him for only two or three months. Principal Zhang had been promoted. This was something he didn't expect. Moreover, it was indeed necessary to eat this meal. It was not to congratulate Principal Zhang on his promotion. Mainly because he was still thinking about Qiao Xi borrowing the school laboratory
If you choose physics and chemistry, the college entrance examination will require biology, chemistry and physics experiments.
Not only because these three courses cover the most majors, but also because Qiao Yu knows Qiao Xi’s strengths. Social candidates have to rely on two more difficult courses, physics and chemistry, to improve their scores. The choice of pure science subjects is more competitive. force.
But the college entrance examination also requires an experimental test, and it must be included in the total score.
"Just eat, but mom, I really miss you when I go to Yanbei this time. You have to work hard and get admitted to a university in the capital." Qiao Yu said seriously, then took a step forward and gently said Hug Qiao Xi.
"Is there a possibility that you think I'm just sixteen years old? If you wait until you are twenty, I'm afraid you will be far away from me." Qiao Xi said it habitually, but she still raised her eyebrows He started to rub Qiao Yu's head with his hand.
"Of course it's not possible. We have agreed to depend on each other for the rest of our lives. Let me tell you, going to the capital this time is very interesting. I will tell you in detail what happened between me, my mentor, Lao Xue, and Grandpa Shi.
"Well, then I won't write papers today. Thank you for giving me half a day off!"
"You don't have to be so polite. As long as you agree to wait until you finish the college entrance examination, I will go to whichever school you go to and be your teacher. How about that?" Qiao Yu, are you trying to get Yanbei University to recruit me in some other way? ah?"
"Haha, you also admit that I am a treasure. Yanbei University will definitely be reluctant to let me go, right? I have told you a long time ago that I am just a piece of gold, and you were still praising me at that time!"
"hehe."
In the living room, Qiao Yu chatted with Qiao Xi about what he had learned during his trip to the capital, such as how he got in touch with Mr. Yuan Zhengxin, and how much the old man cared about him. Any student card for entering and exiting Huaqing would be worth it. It allowed him to live a prosperous life for four years in college, but it almost made him lose the motivation to make money.
Of course, he also vividly described to Qiao Xi how beautiful the scenery of Yanbei University and Huaqing University was, and how loving the classmates were. He also proudly told Qiao Xi that he had even been able to help his senior brother solve a huge problem.
In fact, they talked a lot, mainly focusing on two things, introducing how comfortable and beautiful college life is, and how much attention he is now. As for the man, neither of them mentioned it.
Just as Qiao Xi said, no matter what his goal is at this time, there is no need to mention that man to spoil the fun and change the flavor of this warm moment. It is enough for mother and son to be happy when they reunite after a long separation.
But most of the time, Qiao Yu talked incessantly, while Qiao Xi listened quietly.
After all, her life at home was very simple. There was really nothing to say. She just answered questions every day and watched TV when she was tired. Even after Qiao Yu left, she didn't even bother to cook. She just ordered takeout when she was hungry. , or a bowl of instant noodles.
Life was simple.
Just when Qiao Yu felt that he had said everything he needed to say and couldn't think of anything else to say, Director Zhang, Principal He and Lan Jie came to the door together. When there was a knock on the door, Qiao Yu Subconsciously, I glanced at the time displayed on the old wall clock on the wall. It was half past five, which was almost time for dinner.
...
After a few words of greeting, it was time to eat. When going to the restaurant, Lan Jie walked beside Qiao Yu and asked about the recent situation. Qiao Yu also answered every question he had about Teacher Lan, who had put him on the right path.
Then we had a meal together.
While Zhang Tiejun was having dinner, he specifically mentioned to Principal He the contracts he had signed with Qiao Yu before. Naturally, Principal He repeatedly promised that they would fulfill them. Qiao Yu also casually mentioned the matter of Qiao Xi borrowing the school laboratory.
Principal He naturally patted his chest and agreed.
There was even an invitation to go to class with the freshman in high school, but Qiao Xi naturally declined politely.
It's quite interesting to go to college, but to be honest, even Qiao Yu thinks it's too cruel for an adult to attend classes with high school students. After a meal, both host and guest enjoyed themselves. By the way, Qiao Yu was confirmed to come to Xingtie The time to give a speech in No. 1 Middle School was set on the afternoon of the last exam.
The main reason is that after the training camp, Qiao Yu will return to the capital with Team Leader Zhou the next day, and he cannot stay in Star City for a long time. He might as well take half a day off during the training camp. Anyway, this matter has been agreed with Professor Zhou a long time ago.
Although the things that should be discussed were all discussed at the dinner, Zhang Tiejun still pulled Qiao Yu to talk for a while after the meal before letting Qiao Yu go home. Regardless, returning to Star City still made Qiao Yu feel the enthusiasm of his alma mater for him. ,fine.
Moreover, Qiao Yu also heard a lot of good news about Xingtie No. 1 Middle School from Zhang Tiejun.
For example, Lao Zhang is trying to find ways to promote the construction of the city's first-class key high school in Xingtie No. 1 Middle School. In vernacular, if successful, Star City will no longer have four large and five small schools in the future, but will be changed to four large and six small schools.
And this idea has received a lot of support. After all, the district where Xingtie No. 1 Middle School is located is recognized as an educationally weak district. From junior high school to high school, there is nothing that is particularly good. Especially high school.
Let's put it this way, Changsha now has six districts. Except for the district that has been divided into county districts in the past two years, only Rongcheng District, where Tieyi Middle School is located, does not have a key high school. Yes, all of the legendary four major and five primary schools Not in Rongcheng District.
It is directly ridiculed by people as an educational resource depression.
Zhang Tiejun's rise to power this time actually has something to do with this. City leaders still hope that Zhang Tiejun can build a key middle school in Rongcheng District, and Tieyi Middle School just caught up with this opportunity.
If done properly and with some policy support, it is really possible to get to the top.
Of course, Qiao Yu just listened. At least for now, he can't make much contribution to his alma mater. However, Zhang Tiejun said something very pertinent before leaving. As long as Qiao Yu continues to work hard and study hard, the higher he will go in the future, Tie Yi Naturally, it will get better and better.
Many times in history, a school's status in the local area was changed because of a famous person. Qiao Yu naturally agreed to this.
Don’t worry if you have a lot of debt.
He has promised Qiao Xi that he will be a man standing on the top of the mountain in the future. Work hard to learn this kind of thing. Even if Lao Zhang doesn't say it, he will do it. He doesn't need to do anything extra to let those who have helped him do the same. If you get what you want, no one will refuse.
That night, Meimei slept in her room, and chatted with Qiao Xi again the next morning until ten o'clock in the morning. Qiao Yu took a taxi and went to the headquarters of the High School Affiliated to Normal University, which hosted the second training camp this year.
There's actually nothing much to say about the second training camp. Qiao Yu's feeling is actually similar to the first time, except that there are fewer people studying together and there are more questions that need to be practiced. But for him, the questions are just for occasional breaks. While thinking about it, he was still thinking hard about the paper on the geometric Langlands conjecture.
Director Tian and his grandmaster didn't even pay attention to him...
Tian Yanzhen probably didn't expect that he thought Yuan Zhengxin would definitely send a message to Qiao Yu, but Yuan Zhengxin thought so too. After all, Tian Yanzhen agreed to hold this meeting in Huaqing, which was considered a concession.
Qiao Yu felt a little sad. Neither his mentor nor his grandpa cared about his hair.
But having said that, he actually didn't lose any hair...it was just an exaggeration to attract the attention of his mentor and grandpa Shi.
But it's a pity...
As for the exam, there is nothing to say.
During weekday self-study, he still had to face complicated papers on the Langlands Conjecture in geometry, but as long as he took the exam and solved those simple questions, he could free up his brain and rest.
Really, ever since he started to come into contact with abstract mathematical knowledge and mastered it, when he looked at these so-called Olympiad questions, he suddenly felt that they were very simple. Basically, he could solve them without much thinking.
He didn't even know how to explain this situation. After all, according to the understanding of many mathematics professors, there is a big difference between doing mathematical research and doing high school mathematics problems. So the only attraction of this training camp for Qiao Yu was probably that it ended Formula.
Because he can directly determine who can become his teammate this year and compete in the 66th IMO together.
But to be honest, there was no big surprise, because the four friends were all there. The most amazing thing was probably the fat guy Yu Yongjun, who always stumbled...but always managed to overcome dangers.
The other two are from Xiaozhou and Jiangcheng, the capital of Xingbei Province next to Xingnan. This makes the six IMO members this year evenly distributed, with six people from Jingcheng, Linhai, Shuangqing, Xingcheng, Jiangcheng, and Xiaozhou. , six cities.
Chapter completed!