Chapter 105 The young man was proud and scolded Fang Qiu
The first day of lecture is over.
After giving the latest results, Robert Green began to explain the research process of him and his team.
For the professors and doctoral students who came to listen to the lecture, the research process is obviously more important than the conclusion. This is the real stuff. It involves the use of a series of mathematical tools, and these usage methods can often provide ideas for everyone's research.
It is this kind of thinking that is communicated in mathematics.
Mathematical tools themselves are neutral and widely applicable, and different researchers may use these tools in unique ways in their specific fields to create new ideas and methods.
Although no new mathematical tools were born during this process, in fact, those who can do this are already quite good mathematicians.
As for those who constantly create mathematical tools, such as Isaac Newton who came up with calculus, John von Neumann who made game theory, and David who created Hilbert space. Hilbert, as well as Riemann, Gauss...
People such as Edward Witten who are still alive,
the status of these people in the world of mathematics is probably the same as that of the major sects in fantasy novels There is no difference between the ancestors.
The reason why Peter Schulz is praised by Western mathematics tycoons and hailed as the greatest mathematician of the younger generation is precisely because his work has developed a series of new mathematical tools and methods.
That is to say, he is still young now, and in a few decades, there is a high probability that he will also be the grand master of the founding sect in the eyes of future generations.
If he can really solve a series of problems of the Langlands Program in his lifetime, then it may be controversial to say that his status surpasses his predecessors such as Newton, Hilbert, Gauss, and Grothendieck, but There is no doubt that they are comparable.
After listening to the lecture, Qiao Yu didn’t know whether others had gained something, but he had indeed learned something.
The main gain is a deeper understanding of the Chabauty method. Professor Robert developed a local correction technique that promoted the application of Chabauty. Specifically, he used Padé approximation and local height theory to more accurately control the distribution of rational points at different positions on the curve.
The other is to solve the homogeneous indefinite equations in the p-adic range and use the local geometric information in the p-adic analysis to limit the possible rational points. Especially suitable for curves with a slightly lower genus but still with complex geometric structures.
Similar techniques were used by Qiao Yu when he wrote his paper. But it is obviously not as smooth as the method developed by this professor and his team.
In short, after listening to the lecture, he was quite grateful to the journal that included his paper.
Sure enough, compared with others, the methods he used were quite low.
The only bright spot is probably that he made some small improvements to the classic elliptic curve descent method when solving.
Of course, he didn't know about this highlight originally, but Xue Song told him.
Today’s lecture does not have a question and answer session. It is said that the more specific communication and question session will be placed on the third day of the lecture.
However, after the lecture, Professor Robert on the stage was still surrounded by several professors in the front row. Obviously, everyone was not satisfied with the exchange on the last day. Qiao Yu originally wanted to join in the fun and become familiar with everyone, especially since he could get close to Dao Tian, but Xue Song stopped him: "Let's go. We are still busy."
"Huh? What are you busy with?" Qiao Yu was a little confused, and then looked at Director Tian not far away, but Director Tian didn't look at him.
"Are you going to the impromptu seminar held in the afternoon with this manuscript? At noon, I will re-edit your manuscript, enter it into the computer, and then print out at least ten copies. Do you still feel very free? No lunch?
Besides, you also need to think about how to explain your ideas to the professors participating in the discussion. The afternoon discussion is forty-five minutes, so you should talk for at least half an hour. Now that we have finished chatting, what should we do in the afternoon? " Even if a tutor wants to praise his students so much, he most likely doesn't have the courage. Even if he has the courage, he doesn't have the resources.
A forty-five-minute seminar can't be held without asking. First of all. We have to give everyone the face to participate
For example, it was him who convened this seminar. I just told a senior professor that the content of this seminar is to discuss some mathematical ideas of my fifteen-year-old student. Although what he proposed has not been proven, it is not possible. It's quite immature, but I think it's interesting.
If they didn't just kick him out, they would probably invite him out politely, and then directly put him on the blacklist, and we would never have contact with him again.
But Lao Tian is different. Even if he slanders in his heart, he will most likely agree with a smile.
Some people may even feel it is an honor to receive an invitation.
Hey...
It can only be said that people’s decisions will be completely different if their status and realm are different. There is no pattern or pattern, it’s just that the more resources you have, the less you need to care about other people’s opinions, especially when doing things that do not violate any principles.
This is true between people, and it is the same between countries.
For example, if China suddenly showed up with more than 20 aircraft carrier battle groups, thousands of fifth-generation fighters and bombers, and then told the world that everyone must watch the gala together during the Spring Festival this year, especially the wealthy people who live in the west end of the village Friends, hurry up and buy the broadcast rights.
I guarantee that even if the show is a mess, the ratings will soar in a flash. It is truly unprecedented and unprecedented.
……
Qiao Yu didn't think so much, but felt that what Lao Xue said made sense.
So I didn’t want to join in the fun anymore. I followed Lao Xue back to his room and turned on the computer to get busy.
"What do you want to eat for lunch? I'll bring you some food." Xue Song asked when he saw Qiao Yu starting to work.
I feel more and more like a nanny, but fortunately, the doctoral student he brings will come to school in two days.
"Well, just grab a box lunch. I'm not picky about food. By the way, there's more meat." Qiao Yu said.
"Then I'll add two chicken drumsticks for you?"
"Okay!"
Xue Song curled his lips and left. After a while, there was a knock on the door of the room, and Qiao Yu nodded. He said without raising his head: "Please come in." . "
The door was pushed open and Tian Yanzhen walked in. Qiao Yu turned his head and looked around, and quickly called: "Director Tian."
"Yes, I'm doing it. Are you ready?”
"Yes!"
"Let me take a look."
"Sit down."
"Change it here. When you have not completed the proof, the wording should be More rigorously, based on geometric intuition, it can be inferred that there is a constant C that depends on the geometric and arithmetic properties of the curve X, such that the number of rational points on the curve N(X)≤C ”
“. Oh.”
"And here, your description is that the homology category QH(Cp) is an enhanced homology category... This does not emphasize its difference from the general homology category. I have thought about your idea carefully.
If you want better To analyze the local homogeneous behavior of curves in p-adic complete space, you can introduce a quantized homology category. If you introduce quantized features at the homology level, you may be able to capture subtle local changes in the geometric structure."
“ Huh? Quantization? But this has nothing to do with quantum physics?"
"I mean quantization in mathematics, which refers to discretization or upgrading of classical structures. The process of more complex structures, this process Cheng is usually non-commutative."
Seeing that Qiao Yu didn't quite understand, Tian Yanzhen picked up the paper and pen on the table and said, "I don't have much time. Let me explain it to you using geometric quantization as an example.
First we need to select a polarization in the phase space. You can understand it as determining a direction or coordinate in the classical phase space to simplify the complexity of the problem. Selective polarization can be seen as choosing a decomposition so that a part of the coordinates are used to describe quantum states, and the momentum becomes a differential operator acting on these quantum states.
Then, a Hilbert space is constructed through polarization conditions, which can be regarded as a certain function space of the classical phase space. This function space contains all possible quantum states, that is, wave functions, and its structure depends on the symplectic structure of the classical phase space and the result of polarization selection. "
As Tian Yanzhen spoke, he had already begun to write down a specific example.
"Look, if the phase space of a single resonant oscillator consists of position q and momentum p , forming a plane (q, p). The symplectic form can be written as ω=dq∧dp. We now need to quantize this plane into a Hilbert space, first choose the polarization as /p=0..."
Qiao Yu listened quietly to the instructor's explanation, and asked questions when he didn't understand anything. , just ten minutes later, he suddenly became enlightened again
"Oh, I understand, my Q can represent quantized invariants, etc., let me think about it, I need a quantized homology category to decompose the homology group of the curve, so that I can explain the curve on the curve through quantization processing The behavior of rational points in local quantum structures, right? Director Tian?"
"Well..."
"Yes, yes, that's it. Let me use the pen. Well, in a quantized homology category..." Qiao Yu said and took the hand from Director Tian. He took out the pen and quickly filled in the first formula he had pondered last night on the manuscript paper.
Tian Yanzhen looked at the series of formulas written by Qiao Yu and said without changing his expression: "Where is the proof process?"
"First of all, Q has been determined to act on the curvilinear homology group. The quantum operator, then the first step is to construct a quantum homology category. First, decompose H to construct a new quantum state, and then use the quantum state dimension to describe the curve homology.
The second step is to find the relationship between the quantized homology group and the rational points. It is obvious here that the dimension of the homology group is directly related to the genus g of the curve. The larger the genus is, the higher the geometric complexity of the curve is and the number of rational points is relatively small.
By adding Q at this time, we can get dimQH1(Cp)=f(g, Q). This is to make the changes in the local geometric structure more sensitive and further limit the number of rational points.
Then use Jacobian to limit the rational points. This is the method used by Professor Robert in today's lecture. We can change it and put it into the complete space. According to previous research, the higher the order of the Jacobian, it means that the number of rational points that can be assigned on the curve may be smaller.
Finally, just build this function. The first half of the right side of the function is the quantized homology group dimension, which depends on the genus g of the curve and the quantum operator Q. The second half reflects the geometric structure of the curve and the limitations of rational points.
You are so awesome, Director Tian. With just a few words of advice, I took a big step towards proving the existence of this constant C! ”
Qiao Yu thanked him sincerely.
Tian Yanzhen was silent as he watched the proof process that Qiao Yu quickly wrote on the manuscript paper.
He could feel his heartbeat speeding up.
"Bang bang bang..." It's like a war drum being beaten.
What is the speed of comprehension? He originally thought that it would take at least half an hour to simply explain quantization to Qiao Yu, because it involved many complex mathematical concepts, many of which he was not sure whether Qiao Yu had ever been exposed to.
After all, Qiao Yu had not received any systematic mathematics education, but as he talked, this guy suddenly made a superficial idea from yesterday clear to this point? And looking at the process, it seems that there is nothing wrong and it is quite rigorous.
It’s not a problem, but for a fifteen-year-old child, he really can’t ask for more!
"Have you come into contact with Xin Jiujie before?" Tian Yanzhen suppressed the excitement in his heart and asked in as stable a tone as possible.
"No." Qiao Yu shook his head.
“Have you ever studied quantum physics?” Tian Yanzhen asked again.
"No, I just know a little bit about the wave function and the fact that there is no certainty in the microscopic world, only probabilities. I haven't studied it specifically. I just read some popular science and understand the wave-particle duality." Qiao Yu shook his head again. Shake his head.
“Then you understand?”
“I understand. The principle is to make the curve contain quantum variables or quantum structures for micro-manipulation and expand its operability. You all It’s explained so clearly. If you still don’t understand, isn’t that stupid? ”
After saying that, Qiao Yu suddenly felt something was wrong. He reacted and asked cautiously: "Ah...could it be that my pushing process was wrong?"
Tian Yanzhen took a deep breath, shook his head, and suddenly felt Some of his students who seemed quite smart before now seem to be a bit stupid indeed.
Then he slowly answered: "The mathematics test is divided into right and wrong, but there is nothing right or wrong in cutting-edge mathematics research. Judging whether the derivation process is correct only depends on whether you can justify yourself within the given theoretical framework and not be singled out. Logical loopholes.
I haven’t seen any logical loopholes in your derivation process yet, but I can’t speak for Peter Shu. Ertz’s research is limited to understanding, including the homology theory of P-adic geometry, and he is not proficient in it. You can record all of this into the manuscript of the afternoon seminar and analyze it with everyone.”
Qiao. Yu nodded quickly and said, "I understand, Director Tian."
While the two were talking, the door was suddenly pushed open, and Professor Xue appeared at the door carrying two boxes of lunch.
"Qiao...uh, Mr. Tian, are you here too?"
"Well, at noon, I asked some school leaders to accompany Professor Robert to dinner. I was thinking about Qiao Yu's first seminar and explaining something to him."
"Oh, you also You haven’t eaten yet? Why don’t you eat first?”
Tian Yanzhen hesitated for a moment, then nodded and said, "Okay, then I'll eat here. Don't stop running back and forth. I'll send a message to Xiao Li and ask him to bring you a portion. Come back.”
Originally, he didn’t plan to eat here.
But there is no way, teaching students like Qiao Yu is really addictive, because it is especially easy to gain a sense of accomplishment.
In particular, this child's basic knowledge of mathematics is like a mixed abstract painting, but he can find his own context in this abstraction. This talent is probably no worse than that of Peter Schulz.
Tian Yan really believes that no matter who has such a student, he probably wouldn’t mind communicating with them for a while.
"No need to go to such trouble, I happened to ride a bike to the cafeteria to eat and then come back."
"That's okay, you come back as soon as you finish eating and help Qiao Yu put his things away Sort it out and record it into the computer. I'll tell Qiao Yu something in advance." Tian Yanzhen nodded and said.
Xue Song nodded with a complicated mood and replied: "Okay. I'll do it as soon as possible." After saying that, he immediately turned and left. Tian Yanzhen opened the lunch box and said: "Hurry up and finish the meal. You still have Let me briefly explain a few propositions to you.”
"Okay, Director Tian."
Many times, when you really like someone from the bottom of your heart, your behavior is similar.
……
“…if ”
“But have you ever thought about it, there will be one more exponent that needs to be related to the properties of the homology group of the modular form, which greatly increases the complexity of the result. ”
"Director Tian, how do you think this should be handled?"
"I think it would be better to directly introduce Schultz's p-adic Hodge theory and analyze the behavior of the curve in the p-adic number field Qp , get further geometric constraints. ”
“You mean to globalize local properties? But local information is usually associated with a specific prime number p, and different prime numbers may lead to different local behaviors. Is this more difficult? ”
"But this is what you proposed, so you need to think about it. But as far as I know, in p-adic geometry, etale homology groups can be used to describe the local properties of algebraic curves. And as you just said , the completeness condition has ensured that we can deduce the global result from the local geometric structure, so this path is definitely feasible."
"Oh, I have to think about this again...but still. Do you want to introduce a constant? ”
"You really have to think hard and carefully. Qiao Yu, you have to remember that when mathematics proves any mathematical conjecture, the biggest gain for a mathematician's academic level is the proof method, not the simple result..."
< br>Xue Song, who had a quick meal, took over from Qiao Yu and began to do the input work. The discussions and instructions between the master and the apprentice continued to penetrate into his ears.
The mood became more complicated again.
I envy Qiao Yu for being given such careful guidance by a big-shot academician. This is the kind of treatment a true direct disciple would receive, and he is the kind of person who is particularly pampered.
Not to mention academician tutors, even ordinary tutors are unlikely to be so attentive and devoted when instructing students.
Anyone who has worked as a graduate student for big bosses with specific administrative positions knows that big bosses basically don’t PUA students, but they also basically don’t care about your thesis, your studies, and whether you can graduate. Even when you graduate, they will I don’t necessarily remember that there is a student like you...
Usually there is only one junior director who is responsible for leading people. Of course, the degree of responsibility of the junior director varies from person to person, so the master’s level led by the big boss also has Extremely variable.
And Qiao Yu is enjoying the special treatment of being an academician tutor who takes time to tutor even if he only has a box lunch for lunch.
Of course, Xue Song also understood that this was thanks to Qiao Yu being able to accept this special treatment.
Discuss, discuss, there must be back and forth before we can discuss.
The academician tutor gave a few words of advice, but the student ended up acting like a fool, looking confused and not knowing how to answer the question. Then there would be no next time.
Obviously, Qiao Yu accepted this treatment, and then he really became a handyman.
Well, at least I’m still the director!
......
Tian Yanzhen left at 1:30 in the afternoon. In fact, he still had some basic theories and mathematical principles that he wanted to tell Qiao Yu, but he had no choice and no time to talk more. Yes, he still has things to do.
The afternoon was the first seminar for his students, and he was still a little worried about leaving the organization work to others.
After Tian Yanzhen left, Qiao Yu obediently took over Xue Song's work, mainly because after the discussion just now, he felt that some things needed to be modified, and there was still time anyway.
"I think you need a printer here, preferably a laser. Remember to mention it to Mr. Tian later." Xue Song said suddenly.
"Ah? Is it necessary?" Qiao Yu was stunned.
"It doesn't seem necessary now, but it will be needed often in the future." Xue Song said with certainty.
"Hey, by the way, I forgot to tell Director Tian about the first phase of IMO special training." Qiao Yu suddenly said in annoyance. "What happened to the special training?"
"It's held at our Yanbei University, so I don't have to waste time running around."
"Huh... you Hurry up, the seminar is about to start in eighty minutes, and we need to finish it at least half an hour in advance."
Xue Song didn't bother to comment on this, because he felt that this reason might be really convincing. Tian Yan really wants to say something about this matter.
Admired, even though this situation can be said to be dominated by him.
......
On the other side, after Tian Yanzhen walked out of Qiao Yu's room, he took out his mobile phone and made a call.
After the phone rang a few times, it was connected.
"Mr. Zhang, I heard you returned to China a few days ago?"
"Yeah, come back to do some errands." He said in a calm tone.
"Are you in Huaqing now?"
"What's the matter? Professor Tian." The other person did not answer directly.
"That's right, I have accepted a student, he should be a closed disciple."
"Congratulations."
"He has a habit, much like you."
"Oh?"
"Come up your own questions and solve them yourself."
"Well, this is a good one I have always emphasized that students should have this ability."
"By the way, he is also similar to you. He mainly relied on self-study before. So far, he has not studied systematically in the undergraduate program. Mathematics Tutorials for Stages ”
"Your student has not received systematic undergraduate education?"
"Yes, but he can independently understand Peter Schulz's thesis. And he has unrestrained plans to use Peter Schulz to build a complete Space system to solve the upper bound of rational number points on curves The problem of accurate prediction. I exchanged ideas with him and thought it was very feasible. "
The other person was silent for a long time before he said, "Professor Tian, you. Are you calling me specifically to tell a story? ?”
“At three o’clock in the afternoon, there will be a seminar on these ideas in the P2 conference room of Building 1 of the Research Center. Professor Robert from New York University will also participate. Can I tell you a story? Got it. By the way, he was born in 2009. He is fifteen years old and is from Star City, China."
After waiting for a few seconds and receiving no reply, Tian Yanzhen said calmly: "That's it for now. I personally hope you can come in person. See if I’m lying, bye.”
Then hung up the phone directly.
In the world of mathematics, there is a very interesting ranking method.
Fields Medal mathematicians, one-hour lectures on mathematicians, 45-minute lectures on mathematicians, 30-minute lectures on mathematicians and others...
Both of them belong to the one-hour class Most of the more powerful ones have won the Fields Medal. So in fact, everyone with similar status is the legendary touchstone for the Fields Medal, so there is no need to be too polite.
As long as the notice arrives, Tian Yan really feels that if the other party doesn't come, it will be the other party's loss, not his.
...
Across from Yanbei, in a certain office at Huaqing University.
"Tian Yanzhen's phone number?"
"Yes."
"What does he want from you?"
"He accepted a student who was fifteen years old and had never studied undergraduate mathematics courses systematically. Not only could he independently understand Peter Schulz's paper, but he also independently proposed a solution to the number of rational points on an algebraic curve based on Schulz's theoretical framework. "
After he finished speaking, the old man on the other side was stunned and said in surprise: "Fifteen years old?"
Zhang Shuwen nodded.
"Do you believe it?"
Zhang Shuwen shook his head, and then said: "But he said that if you don't believe it, you can go and see it with your own eyes. At three o'clock in the afternoon, that child will host a seminar on this issue."
Silent...
"Go and have a look. If it's fake, expose him directly without saving any face."
Zhang Shuwen: "..."
… …
At 2:30 in the afternoon, Xue Song had already brought Qiao Yu to the P2 conference room in Building 1.
Although generally speaking, the keynote speaker should arrive last. But Xue Song felt that Qiao Yu was already too arrogant. If he was too indulgent, he would be too eccentric to recognize himself.
Especially considering that Qiao Yu is only fifteen years old, he should be allowed to develop a good habit of humility.
The two of them stayed in the conference room for less than five minutes before Chen Zhuoyang walked in.
"Senior Brother Chen." Qiao Yu took the initiative to say hello this time.
Anyway, there was no one in the small conference room. Unlike in the morning, when he arrived, the conference room was already full of unfamiliar people. Qiao Yu was embarrassed, but now the situation could still support his performance. Show your courtesy.
Chen Zhuoyang curled his lips. He didn't really want to deal with Qiao Yu.
Especially when I learned that the protagonist of today’s discussion was this junior fellow student, I was a little confused.
He doesn’t even get this treatment.
The most annoying thing is that this little talkative kid holds a seminar and he has to be busy.
Chen Zhuoyang asked: "Well, will you use PPT later?"
"Thank you, Senior Brother Chen, for your concern, but no, I don't have time to do it, and I don't know how to do it. I will just write on the blackboard later. Huh? There is no blackboard. Senior Brother Chen, how about you get me a blackboard?" Just put it there..."
Qiao Yu pointed to the open space in front enthusiastically.
Chen Zhuoyang rolled his eyes, he might as well make a PPT.
"Okay, I know where to put it. I'll ask the staff to move one over later. Is the 90X120 one okay?"
"Okay, please trouble Brother Chen, oh, yes Don’t forget to ask for a pen.”
Chen Zhuoyang curled his lips and turned away.
"Hey, Senior Brother Chen is good at everything else, but he is too serious. I can't see him smiling all day long." Qiao Yu commented.
Xue Song stood silently beside him. He could understand Chen Zhuoyang.
If he were Qiao Yu's senior brother, he would probably be very annoyed to have such a junior brother.
Soon, several more professors walked into the conference room. Chen Zhuoyang had also returned to the conference room, and assumed the responsibility of a senior brother and began to take the initiative to introduce Qiao Yu: "Qiao Yu, this is Professor Zhou Yang of the research center mainly studies low-dimensional topology and geometric group theory..."
"Hello, Professor Zhou."
"You are Qiao Yu. Mr. Tian values you very much. Keep working hard."
"Thank you, Professor Zhou, for your encouragement."
"This The position is Professor Cai Wenyuan, who mainly studies algebraic geometry and Lie groups..."
"Hello, Professor Cai..."
"Professor Chu Weihua, a very high achievement in the field of algebraic topology..."
With Chen Zhuoyang's introduction, the atmosphere in the conference room gradually became familiar. To be honest, the professors were quite unfamiliar with this child, Qiao Yu. Everyone came to this seminar just for Tian Yanzhen's sake.
As for Qiao Yu's idea, it is simpler. It doesn't matter if he is unfamiliar. Everyone will understand him later.
And with Senior Brother Chen as a tool beside him, Qiao Yu soon got to know all the professors who came to participate in the seminar.
The mobile blackboard was also pushed into the conference room by the staff while everyone was chatting.
Soon, only three minutes before the seminar started, Tian Yanzhen, Robert, and another person Qiao Yu had never met walked into the conference room.
Qiao Yu, who had sat back in his seat, clearly felt that the atmosphere in the conference room was suddenly a little stagnant...
It wasn't that Qiao Yu was being sensitive, it was mainly because everyone was so obvious.
We were still discussing quietly just now, but when the three people walked in, everyone suddenly stopped talking.
We won’t suddenly become so disciplined just because foreign friends are here, right?
Qiao Yu turned around and was about to express his thoughts to Xue Song, when he suddenly found that old Xue was staring at the three people who had just come in with a strange expression.
So he asked in a low voice: "Teacher Xue, what's wrong with you?"
Xue Song turned around and said softly with an expressionless face: "You will talk carefully later, don't waste it, Director Tian." A stage for you!"
Qiao Yu understood the implication of this sentence and immediately looked at the person he didn't know yet.
Simple reasoning for him.
Director Tian had already made it clear that he would invite Professor Robert to participate in this seminar, so this was expected. Lao Xue once again emphasized not to waste Director Tian's opportunity. It could only be that this stranger had a great background.
But he just looks like a thin and serious old man. Apart from a certain aura, there seems to be nothing special about him...
Fortunately, there is no time for Qiao Yu to think about it. His mentor once again Take on the role of host.
“Thank you very much for attending today’s seminar, especially Professor Robert and Professor Zhang Shuwen for taking the time out of their busy schedules to come and personally guide my student Qiao Yu on some of his wonderful ideas in mathematics. Think about it.
The main issue discussed in today’s seminar is about using tools such as complete space, modular form theory and P-adic geometry to study the upper bound of the number of rational points on the algebraic curve X. Okay. , Qiao Yu, you can start speaking.”
After saying that, Director Tian returned to his seat, and Qiao Yu stood up immediately without any stage fright.
“Thank you all teachers for coming to this seminar. Some of my immature ideas have been printed out, which is the pile of manuscript paper placed on everyone’s desk.
< br>By the way, I would also like to express my special thanks to Professor Robert for inspiring me with today’s lecture, and to my supervisor, Professor Tian Yanzhen, for his guidance just now. As the director said, after reading the papers of Professor Schultz and Professor Robert recently, I suddenly had such a bold idea."
As soon as Qiao Yu finished speaking, almost everyone took it. I picked up the report on the table. It was too crude. Everyone had just arrived at the conference room a few minutes early and was busy chatting. No one really picked it up and took a serious look at it.
On the other hand, Zhang Shuwen and Professor Robert, who were sitting next to Tian Yanzhen, had already picked up the simple book and started to look through it.
After Qiao Yu finished his opening remarks, he got to the point.
“My idea is to use the complete space theory built by Professor Peter Schulz, and use modular form theory, progressive geometry and quantized homology categories to derive the upper bound expression of rational points on the algebraic curve .
To do this, First, we need to consider the geometric background of the curve The number of rational points is limited
But this is not enough, because we all want to get a specific upper bound. According to geometric analysis, the higher the genus is, the complexity of the algebraic curve increases, which means that the number of rational points is relatively reduced. So my preliminary. The conjecture is: N(X)≤C(g)
Then I will demonstrate this result from several assumptions. Although I think this result is correct, I cannot prove the specific formula of constant C yet, but I have thought of several interesting methods. to derive the result of constant C.
It's just that these methods haven't been proven yet, so I hope teachers can give me some inspiration. First, we introduce the modulus space, assuming that
Because the modular form is closely related to the modulus space, I understand it as certain functions defined on the modulus space, which provide geometric constraints on the complexity of the curve. In this way, assuming the level of the modular form is k, we then assume that there is a constant A1, such that: N(X)≤C1(g,k)=A1gk^α..."
Everyone in the conference room The professors have put away their previous relaxed
The only ones whose expressions have not changed are probably Tian Yanzhen and Xue Song.
They are sitting at the back. Chen Zhuoyang can testify
He was not interested in what Qiao Yu said, so he paid more attention to the expressions of the instructor and the two great men across from him.
Obviously, Director Tian was in a very relaxed state of mind. He just watched Qiao Yu quietly writing on the blackboard. One of the two bosses beside him had his eyebrows furrowed into the Chinese character "Sichuan" and the other had already picked up his pen. I started writing and drawing next to the manuscript...
Chen Zhuoyang felt a little depressed...
Isn't it, everyone is serious? So it’s not that Director Tian wants to forcefully recommend the younger brother. Can everyone recognize this kind of thing that has not been proven yet?
Yes, when Chen Zhuoyang learned about the seminar this afternoon, he really felt that Director Tian just wanted his junior brother to become familiar with everyone. After all, Director Tian also said that these are just ideas from Qiao Yu...
How can anyone play with ideas like this? Chen Zhuoyang even felt that Director Tian was too anxious. After all, this junior brother was only fifteen years old! Although he was able to participate in CMO and get first place, which proves that he must be proficient in high school knowledge, but he doesn’t even know if he has been exposed to university knowledge. He knows nothing about scientific research!
He even thought that Qiao Yu was talking in his sleep if he could understand Peter Fields's paper. But now just looking at the expressions of the professors, this is not the case at all, because it can be seen that everyone is really starting to think...
What the hell, is this junior brother really going to go against the grain?
What made him even more desperate was that Qiao Yu on the stage not only didn’t have any stage fright, but also became more and more excited as he spoke, because many professors had begun to read his writing on the blackboard seriously. Wait, Professor Robert even took out He used his cell phone to take a picture of what he wrote on the blackboard...< br>
“…At this point we can introduce the -adic number field and Professor Schultz’s homology theory. We know that for each prime number P, the properties of the etale homology group can constrain the local distribution of rational points on the curve.
Then according to Schultz's -advanced Hodge theory, the following inequality can be derived: N(X)≤C2(g,p)=A2g2log(p). There is an important point here. One of the core characteristics of Schultz's -Hodge theory is its completeness.
So if the inequality we derived holds, we can start from the properties of the curve in the local domain and deduce the global geometric constraints. So we need to prove whether this inequality holds. For this purpose, I followed the guidance of Tian Dao Next, I thought of a way, which is to introduce a quantum homology category..."
In the past half hour, Chen Zhuo Yang just felt like he was sitting on pins and needles
Because there were only two students, Director Tian, in the entire conference room. One was talking in front, and the other couldn't understand what the junior brother was talking about...
However, the conference room was still eerily quiet, there was not even any discussion, everyone was staring at Qiao Yu's writing on the blackboard
Including those three math giants that most professors in the conference room can only look up to.
Finally, Qiao Yu finished speaking...
“The above is my complete idea. The problem is that I am still unable to process the constants in the settings and complete the logic of the specific tools. proof, but I think it should be a A new research direction, because once we derive the result of constant C, it represents the upper bound of the number of rational points that can directly predict the correlation curve."
When Qiao Yu's voice finally dissipated in the air, Chen Zhuoyang said. I finally breathed a sigh of relief and felt better.
But the quiet conference room made him nervous again.
No, professors, aren't you going to say something?
Everyone is an adult, so don’t look at the little junior brother with that incredible expression, okay? He is only fifteen years old, he should receive education about setbacks now! Everyone should severely criticize his ideas at this time!
Chen Zhuoyang thought fiercely in his heart, but when he saw Director Tian opposite him raising his hand first and starting to applaud, he could only immediately raise his hand and applaud in cooperation...
"Pa bang bang..."
The scattered applause seemed to make the professors react, and the conference room was immediately filled with applause.
Fortunately, there were not many people, and within a few dozen seconds, the applause stopped, and then Chen Zhuoyang finally heard the heavenly sound.
"I have a question, Qiao Yu, why don't you just use the Riemann-Roch theorem in the third part?" Chen Zhuoyang glanced at Zhang Shuwen, who was facing him with a serious face. Sure enough, the great professor is so powerful!
"Ah? What is the Riemann-Roch theorem?" Qiao Yu asked with curiosity.
Everyone has different reactions.
For example, Qiao Yu stood there as if nothing had happened, but his nominal tutor, Professor Xue, felt very social and his face suddenly turned red.
As for the other professors, including Robert Green, they were all at a loss. They probably couldn't understand that the little guy who had just talked about algebraic curves for half an hour did not know this important theorem in algebraic geometry and complex geometry.
Tian Yanzhen remained calm and explained in a gentle tone: "Professor Zhang, as I said before, Qiao Yu is only fifteen years old. He is a seedling I discovered in CMO. He has not yet He received a complete undergraduate education, so his knowledge of mathematics is relatively scattered. You can give him some guidance on the spot.”
I would like to recommend this book to everyone, just click on the link below, it is a masterpiece that tells the story of cause and effect!
PS: The 20th day of the 10,000-word update has been completed!
Thanks to book friend 20240903120210936 for the reward and encouragement!
(End of this chapter)