Chapter 121 Congratulations, you have seen some beautiful scenery
“...We know that when studying algebraic curves, the selection of ridges and the construction of automorphic forms are the key...the key to its biggest problem The point is that Galois means that it can It can only be valid under a specific p-adic environment. When we establish a p-adic number field..."
Professor Everton's report continued to penetrate into Qiao Yu's ears, but Qiao Yu At this time, Yu's mind was completely filled with all kinds of lines.
Just a little bit, a little bit...
It's not these things...
Because it has been demonstrated in the paper...
The author very carefully used many restrictions to ensure the correctness of the results, and found another way.
Wait...
You should not be bound by existing ideas when making mistakes. As long as it is within the framework established by the other party and does not exceed the framework, he can freely define it...
An extraordinary singular point, but not a common singular structure...
"Yes!" Qiao Yu suddenly shouted excitedly.
The conference room suddenly became quiet, and countless eyes focused on the front row.
The professors in the back row could only see the backs of their heads, but the big guys sitting in the first row and Professor Everton on the stage stared at this sudden shout with confused eyes. An excited young man.
After all, this is really rude, even if Qiao Yu is just a minor.
Especially Pan Jingyuan, who was sitting closest to Qiao Yu, was frightened by the sound just now. It was so inexplicable...
Qiao Yu also reacted quickly: Fuck, you got into trouble!
So the young man jumped up from his chair as if on a conditioned reflex, and immediately apologized: "I'm very sorry, Professor Everton, and all the teachers, what Professor Everton just said was really too much. Wonderful!
It inspired me so much that I suddenly thought of a very special counterexample, which seems to prove that Professor Dennis and Professor Sam have recently A series of papers published on ArXiv contained local-global errors in the proof of the Ambidexterity theorem.
I was too excited about this idea, and I was so absorbed in thinking that I forgot to attend the lecture. Sorry, really. I’m very sorry!”
After saying that, Qiao Yu bowed slightly to Professor Everton on the podium.
After Qiao Yu finished speaking, the conference room became quieter.
There are many relevant professors invited to participate in this series of seminars, but whether it is Yuan Zhengxin or Tian Yanzhen, it is naturally impossible for those who invited these professors to tell the truth because their own students want to prove whether A recent paper published by Dennis and Sam.
After all, that would be too offensive.
I just invited people here in the name of discussing the geometric Langlands conjecture together.
Professors from abroad, domestic, Huaqing, Yanbei and Shuangdan University gathered together to discuss and discuss.
Although everyone knew that after several exchanges, the five papers that had been in the spotlight recently would definitely be involved, but probably no one expected that in the first lecture, the youngest guy in the conference room would jump up and start planning. Smash the place opposite.
Yuan Zhengxin didn't expect it either, so he also stared at Qiao Yu.
It is a good thing to have inspiration, and it is understandable. It's normal to even be excited, but I have doubts about whether the counterexamples in my mind have any value!
Well, Professor Everton on the podium naturally didn't expect it. He subconsciously glanced at Pan Jingyuan next to Qiao Yu.
Professor Dennis once introduced this student to him, so he naturally knew him.
Last night, he invited Pan Jingyuan to discuss some ideas about the certification process between him and his mentor.
He couldn't quite figure out why the young kid next to Pan Jingyuan suddenly stood up and said such words.
Professor Pan's expression was indeed very strange at this time...
But he didn't look at him, but stared blankly at Qiao Yu standing next to him.
Professor Everton’s eyes fell on Qiao Yu. After thinking about it, he said: "I can accept your apology, but you have to convince me with what you just thought of. If you can make me think This is indeed a great idea. Not only am I willing to forgive you, but I would also like to thank you for making this lecture have some different value.”
Qiao Yu subconsciously turned his head and glanced at Grandpa Shi, who was sitting in the first row.
Mr. Yuan first glared at him, and then nodded inconspicuously. Qiao Yu became rude and immediately said: "Okay, Professor Everton, that's what I think. First of all, Let's assume..."
Everton waved at Qiao Yu and said: "My child, it's not polite to stand down and talk about your thoughts. Come on, come on stage and speak. I think your brain must not have prepared the PPT for you, so..."
As he said that, Everton looked back and smiled: "There happens to be more here. Blackboard. "
The boss said so, and Grandpa Shi agreed. Qiao Yu, who has never been timid, immediately left his seat and walked to the podium.
It happens that things in my mind are a bit messy, so I can use some explanation to clarify my thinking.
"Dear teachers, this is what I think. First, suppose a type of singular point of an algebraic variety. Well, this singular point is similar to the singular structures we know, such as cusps, nodes, and Or the cone-shaped singular point is different, and has a complex ridge-like expansion globally.
The point is that its local geometric structure is related to other points at the far end of the algebraic variety, and even at the same time. There is a conjugate relationship between non-adjacent singular points. So, first we have to define its local representation. Assuming that in A3 or a higher-dimensional geometric space, its characteristic equation should be..."
With that said, Qiao Yu picked up the chalk and wrote a line of equations on the blackboard: "f(x,y,z)=z^2x^3y^2+sin(xyz)".
After finishing writing, Qiao Yu took a step back, calculated silently in his heart for a moment, and then continued: "I believe everyone has seen that the equation is somewhere near the point (0, 0, 0) There is a local ridged limit structure at the location.”
"Well, the conjugation relationship is manifested in the singular points on the algebraic cluster. When P1 and P2 respectively have local ridge singular point structures, their local geometric properties influence each other through a nonlinear homology mapping. < br>
Obviously this means that the local module structure of singular point P1 will Depends on the local properties of the other remote singular point P2. Note that this conjugate relationship cannot be inferred through simple local geometric observations..."
At this point, Qiao Yu's voice suddenly stopped. And stop...
The audience was also silent, but the reactions were different.
Some people have frowned, picked up pen and paper, and started calculating on the manuscript paper they carried with them; some are still listening carefully; and some are still stunned, watching the development of the situation.
However, Everton on the stage stared at the equation written by Qiao Yu with great interest.
As for Pan Jingyuan in the audience, he was definitely the one with the deepest frown. As the person most familiar with that series of papers, he had vaguely guessed the general idea of Qiao Yu, but he had not yet figured it out. What method will Qiao Yu use to break the situation?
But he quickly reacted, glanced at Yuan Zhengxin next to him who was also looking at Qiao Yu seriously, and then took out his mobile phone...
The old man may not necessarily take out the live video. , he might as well record a section himself before talking about it.
……
At this time, Qiao Yu's brain was also thinking rapidly.
Although he found the key points, he still had to design an algebraic variety background based on the framework built in a series of five papers.
The incident happened suddenly. He just had a direction. He had to design this background in a hurry. The test was his ability to perform on the spot. Fortunately, it would probably take some time to calculate the equations he threw in the audience.
Qiao Yu didn't bother to care what others thought of him now. Anyway, no one was urging him now, so he just thought about it silently.
After thinking like this for five minutes, Qiao Yu, who was standing in front of the blackboard, suddenly picked up the chalk again. This time he didn't speak, but started writing directly on the blackboard.
“Consider a high-dimensional algebraic variety X, defined as an algebraic variety of the following form: }."
After finishing writing, Qiao Yu took a step back again and began to calculate quickly and silently in his brain. It took another minute before he spoke: "Based on the explanation just now, you should be able to find that the algebraic variety
More specifically, P1/P2 are two singular points with the same structure. Yes, that’s right! Then we need to consider just now! The ridge structure under the p-adic framework mentioned by Professor Everton
As you can see, there are two local homology algebraic structures near the singular points P1 and P2 of X. The first one is near P1. , the flatness and projectivity of the local p-adic mode M1 extend to the distal P2 through the ridge network, so that the flatness appears near the point P1 The module no longer maintains projectivity.
Secondly, because of the conjugate structure of the two, the singular points P1 and P2 interact with each other through nonlinear homology algebraic relationships, causing the Ext group to behave abnormally near the ridge. . That is, the local module structure near P1 cannot be correctly globalized, which undoubtedly destroys the local-global equivalence.
That's all I can think of for now. Of course, this is the first step, and it will take some time to analyze the local module structure. Then higher-order category theory is introduced to derive the failure of functors.
If you have read the first paper by Professors Dennis and Sam on the proof of the Langlands Conjecture in geometry, you should know that if it can be proved that the derived functor from local to global cannot satisfy the consistency in the homology category, That is: RHomC(M1, M2)LHomC(M1, M2)
Then it is enough to prove that the local to global equivalence in the Ambidexterity theorem fails in this context. The local homology algebraic flatness condition assumed by the theorem is likely to no longer hold in the presence of such structures. "
After saying that, Qiao Yu put down the chalk, clapped his hands, and carefully looked at the two formulas he left on the blackboard, then turned around and faced all the professors in the audience for the first time. , and Professor Everton standing next to him
Then Qiao Yu realized belatedly that everyone at the scene, yes, everyone, one by one, was in an extremely strange state. Status.
They also include his senior teacher, Mr. Yuan, and Professor Everton on the stage.
It can’t be said to be dumbfounded. Anyway, everyone’s expressions are different, but they all seem to be frozen.
This reminded him of a very ancient Japanese TV show. The protagonist on the TV had the ability to stop time, and then only he could move...
Of course Joe What Yu thought of was "Dinosaur Express", but he couldn't Let’s just say that people who think crookedly have unhealthy thoughts. After all, there are too many movies like this...
In short, everyone’s reaction made Qiao Yu a little uneasy, and then he couldn’t help but coughed twice: "Ahem , that...Professor Everton, shall I go down first?”
"Oh... um... okay... you can go down first, kid. By the way, if I guess correctly, you are Professor Yuan's grandson. Your name is Qiao Yu, right?" She came back to her senses. Professor Everton asked.
"Yes, Professor Everton." Qiao Yu, who had just stepped off the podium, turned around and answered.
"Sixteen years old?" Everton asked again.
Qiao Yu nodded.
Professor Everton pursed his lips, glanced in the direction of Yuan Zhengxin, then gave a thumbs up and said: "You are great!"
Then watching Qiao Yu sit back in his seat, he glanced at his PPT and continued: "Then let's continue... Forget it, let's do some rough calculations that Professor Yuan's grandson Qiao Yu just gave us The counterexamples cited..."
As he spoke, Everton simply turned around, picked up the chalk, and began to perform some simple deductions on the blackboard.
After a moment, Everton suddenly turned around and asked: "Qiao Yu, this is a type of singularity you defined for the first time. Maybe you should give it a name, otherwise I don't know how to do it. Express it."
"Uh..." It was obvious that Qiao Yu had not thought about this problem at all and was stunned.
"Well, it seems you haven't thought about it yet, so let's call him JOE." Everton shrugged, then turned his head and continued to deduce on the blackboard.
Qiao Yu took a deep breath and didn't watch the old professor's deduction process. He had already calculated it in his mind and it should be fine. So I just secretly glanced sideways at Professor Pan Jingyuan beside me.
Speaking of which, the person he felt most sorry for for doing this was Professor Pan.
He had patiently guided him for so long, and he was somewhat embarrassed to turn around and prove that the paper he had been involved in researching for many years was flawed.
Who knew that while he was secretly looking at others, Professor Pan turned to look at him openly, their eyes met, and Qiao Yu felt even more embarrassed.
He smiled coquettishly and said in a low voice: "Well, Professor Pan, please don't be depressed first. What I'm thinking may not be right."
"Hmm..." Pan Jingyuan responded, the pronunciation was soft. Qiao Yu couldn't figure it out and didn't know what it meant, but his sitting posture and expression were in sync with each other, and there was no hint of any embarrassment.
The same thing is said, no matter how much armor the mentor and grandpa Shi add to him, the increased armor will be magic defense, but they cannot prevent physical attacks. Brother Pan is right next to him, so he must be more honest in this situation.
It is a well-known fact that it is terrible for an honest person to get angry.
......
Professor Everton stood on the podium silently and calculated that the time had exceeded the originally set time. Gradually, some people in the audience might have thought of something and directly He stood up and walked to the podium to discuss with Professor Everton, so there were more things written in different handwriting on the blackboard.
With the first, there will be the second...
Soon, the podium was surrounded. In the process, even Pan Jingyuan next to him stepped onto the podium.
Qiao Yu was stunned...
What are you doing? Is this lecture finished? Can he leave?
So Qiao Yu looked at Mr. Yuan on the other side.
The old man was smiling and watching the discussion on the stage. Then he seemed to realize something and turned to look at Qiao Yu, who was fidgeting. Probably guessing what Qiao Yu was thinking, he waved slightly to Qiao Yu.
Whether Qiao Yu's sudden idea is right or not is not important anymore.
It already explains a lot if the big guys in these research-related fields can pay attention to it and start discussing it.
Especially that JOE point.
When Professor Everton asked that question in public, Qiao Yu had achieved great success today.
The old man was very happy at this time, even happier than he had made the results.
Qiao Yu also quickly came over.
“Did you just suddenly think of it?” the old man asked.
Qiao Yu nodded repeatedly, with an innocent expression like a child's.
"Really! Grandpa Shi, it just suddenly occurred to me."
Mr. Yuan smiled and said: "Okay, you go back and think about the complete proof process first. It's best to sort it out as soon as possible. Don't let the inspiration go to waste. We will choose a day for you to give the lecture, and we will set up a stage for you. You go up and speak boldly, don’t be afraid.”
Qiao Yu nodded immediately.
He had nothing to fear in the first place, but now that Mr. Yuan has said this, he is even more open-minded.
"Also, regardless of whether your idea is right or wrong, set a time to invite Professor Pan to have a meal. I will make the appointment for you. Thank you Professor Pan."
"No problem "Master, I'll go back first." Qiao Yu nodded repeatedly, then stood up and sneaked away.
The old gentleman is right, the next proof will have to be done by him himself.
Now that the professors were calling him up, Qiao Yu had nothing more to say. As he just explained, now he has only constructed a counterexample. He still has to think carefully about the specific argumentation process. Again, mathematical proofs must not have logical loopholes.
......
Qiao Yu left, and the discussion and even debate on the podium continued. There were no professors in the audience who had not come to the podium to participate in the discussion. They watched Qiao Yu sneak up to Mr. Yuan. After the two chatted for a few words in a low voice, the child crouched and sneaked away, probably feeling envious in his heart.
Other professors were using their mobile phones to use various chat tools to discuss the counterexample Qiao Yu had just designed in another way.
In short, the conference room at this time was full of chaos.
Especially on the podium, the sound is getting louder and louder.
In addition to the two equations left by Qiao Yu on the blackboard, the derivation process next to it has been erased and written, written and erased, and has been changed several times.
In the audience, Mr. Yuan just smiled and watched quietly, not knowing what he was thinking, as if he was remembering the good times.
Pan Jingyuan also stood on the podium, watching silently. He came on stage because too many people covered the blackboard. Occasionally, someone would whisper to him, but he just shook his head slightly and didn't say anything.
Actually speaking, he was probably the one who could best follow Qiao Yu's thoughts at the scene. After all, Qiao Yu had been discussing a series of issues with him, but he really didn't want to talk at this time.
Not only did a sixteen-year-old boy find a loophole after six years of hard work, so it felt bitter. The key is that this boy only took about a month to do it!
This made him suddenly feel that all the work he had done before had no sense of accomplishment.
Hey, I feel tired!
...
Qiao Yu walked out of the conference room without thinking about the mood of the professors who were still present. His mind was not idle. On the one hand, he had to think about how to provide a complete proof. On the other hand, he also had to think about any methods to solve the problems he raised.
As long as one counterexample is found for this kind of problem, Qiao Yu feels that he can find many counterexamples to invalidate the theorem. For example, after opening up the idea, the structure of the local coordinate ring of a similar singular point can produce infinite levels of high-order perturbations in conventional decomposition.
Then the p-adic module or ridge structure exhibits fractal characteristics at these singular points, and its complexity cannot be described by finitely generated local modules. Therefore, derived culprits cannot satisfy the consistency in the homology category anyway.
If they are not equivalent, the theorem cannot be established.
Of course, you can also continue to restrict conditions and throw out such counterexamples. But once this is done, the influence of the so-called proof of the geometric Langlands conjecture will be greatly reduced. After all, none of the theorems can be completely established in a smooth geometric background, and the application is naturally greatly restricted.
How to fix this vulnerability is much more difficult than finding it.
This is actually the same as in reality, destruction is always easier than construction.
Qiao Yu doesn’t know what to do for the time being, but he can sort out some ideas.
If we can find a way, we can send it out at the right time.
In short, asking yourself questions and then giving answers is a way of learning.
Of course, Qiao Yu was still very excited at this time.
He has already won half the game in this peak duel game. Next, the question is thrown to the opponent's geometric Langlands conjecture proof team. After he announces the complete proof process, it will be seen whether the opponent can defeat them. This issue is expected to be resolved within the expected time limit.
It's a pity that in reality this kind of game can only be turn-based, and it is not as exciting as games such as FPS or MOBA.
But it doesn’t really matter.
Returning to his room excitedly, Qiao Yu stretched and was about to turn on the computer when there was a knock on the door.
Qiao Yu stood up again and opened the door. Senior Brother Chen was standing outside.
That's all, Qiao Yu could see that the senior brother looked at him very strangely, and he didn't say anything, so he just looked at him blankly, which was even more strange.
Qiao Yu subconsciously touched his face. It was smooth and tender. Although he did use facial cleanser today, he shouldn't be so handsome that even his senior brothers would be surprised, right?
"Well, Senior Brother Chen, is there nothing on my face?" Qiao Yu asked.
Chen Zhuoyang shook his head and said: "No, little junior brother, you are in the limelight again today!"
That tone was filled with admiration that could not be concealed at all.
Qiao Yu immediately retorted: "No, senior brother. Although we have a good relationship, if you slander me, I will still sue you for defamation. How can I, an honest person like me, be in the limelight? You go to the IMO training camp Ask the team, who doesn’t know that I, Qiao Yu, is the most low-key?”
Chen Zhuoyang looked at Qiao Yu and said in amusement, “Stop pretending, I was just discussing the graduation defense with my boss. Professor Tan from the Research Center directly sent a video of you explaining it to a room of professors on stage.
The boss watched it with great interest, and after watching it, he looked at me differently. The thing that makes me most uncomfortable is that the boss also sent me the video of you showing off! Let me see how you do it! By the way, junior brother, this isn’t your report meeting today, is it?”
< br>
A statement full of resentment.
As expected, people are still most afraid of comparison.
Qiao Yu could imagine the scene. The student and the teacher treated each other as guests, discussing face to face about their upcoming graduation.
You must know that for students of big bosses like Tian Yanzhen, this kind of opportunity is too rare.
Maybe Chen Zhuoyang got the opportunity because he had been staying in the research center to deal with some trivial matters, and Qiao Yu also spoke for him.
If it were the boss and other students with average talents, this kind of thing would probably be settled in a few words on WeChat.
It was supposed to be a beautiful memory in life, but it was rewritten by a video. It is indeed a very depressing thing.
But Qiao Yu felt that this had nothing to do with him. Senior Brother Chen should blame Professor Tan who sent the video to his tutor...
But seeing Chen Zhuoyang's disappointed look, Qiao Yu also said There's no such thing as shirking responsibility After thinking about it, he encouraged him simply: "Brother, don't you think that compared to me, you are just a little less confident?"
Chen Zhuoyang said in a low voice: "It's just a little less confident Feel more confident? ”
Qiao Yu said categorically: "It's inevitable! You didn't go to today's lecture. In fact, if you did, you would have ideas. If you have ideas, you should speak out. So what you lack is really confidence. I don't Nothing else but confidence.
Anyway, I don’t know whether those thoughts are right or wrong, but if the professor asked me, I dare to say that in fact, everyone is an ordinary person, but the more ordinary you are, the more confident you are! It’s a fool!”
Chen Zhuoyang shook his head. He shook his head and smiled: "Okay, junior brother. Don't call yourself an ordinary person. In fact, it's not that I'm not confident. I've just been here for a long time and I really can't be confident.
But there are already My senior brother said that my situation will be solved after I graduate. Just go to work. As long as you stay away from non-human beings like you and get along with other colleagues, you will find that you can still do it, and your confidence will gradually return."
Qiao Yu nodded suddenly. I found that my senior brother might be more comforting than him.
But seeing that Senior Brother Chen was in a normal mood, Qiao Yu was too lazy to talk nonsense to him, so he said, "Senior Brother, do you want to come in and sit down?"
Chen Zhuoyang shook his head and said, "Oh , No. The instructor asked me to come over. He said that when he saw you came back, he asked you to go to his office. He was waiting for you in the office today. I was still thinking about you. I will definitely have to finish my meal in Huaqing before coming back. I didn’t expect you to come back early, so I’ll chat with you a little more.” Can you just tell me if you have something to do? Then I’ll go to Director Tian’s place first! Let’s talk later!”
After that, Qiao Yu closed the door and rushed towards Director Tian’s office.
When a mentor is called, one must be active.
...
Five minutes later, Qiao Yu arrived at the door of Director Tian’s office. As usual, he opened the door and went directly. Then he asked generously: "Director Tian, just now Senior Brother Chen said you were looking for Me?"
"Hmm . Several professors from the research center just sent me messages, reporting on your great achievements today. How does it feel to make a scene at the Huaqing Conference?" Tian Yanzhen looked up at Qiao Yu, joked, and then put it down. picked up the mobile phone in his hand.
Seeing this action, Qiao Yu was very suspicious that before he came, the instructor was still chatting with the professors who stayed in the Huaqing conference room.
Qiao Yu said with embarrassment: "Director Tian, please don't be ugly to me... you know me. At that time, I really suddenly thought of a very clever way, but I really It’s not intentional!”
Tian Yanzhen suppressed his smile, looked serious, and asked again: "No, Qiao Yu, I'm asking you very seriously, how does it feel to make a big fuss at the Huaqing Conference Hall?"
"Uh... " Qiao Yu looked at Director Tian's serious look, thought for a moment, then nodded and said, "That... actually feels pretty good, especially the conference room. There were so many professors below, but I actually felt quite happy when no one raised any questions.
Oh, by the way, there was also the Everton professor who asked me what the point I constructed should be. How to name it? I didn’t say anything, so I just named it JOE. When I did it, it felt very different. It felt like You're secretly proud of it."
Listening to Qiao Yu's serious and slightly proud tone, showing off his mentality at that time, Tian Yanzhen smiled again and said warmly: "Well, I hope you can always remember this. It is best to become addicted to this feeling. The process of mathematical research is often very boring, and more fun actually comes from the end. The results.
Especially when you will be exposed to more difficult problems in the future, you may be stuck in a place without answers for a long time. You have not experienced the pain yet, but everyone will. Those who are truly determined to make achievements in mathematics may encounter it in the future, and it may even be the norm in life
Otherwise, there have been so many amazing mathematicians in history with amazing achievements. Why did they leave behind not only theorems, but also conjectures that have troubled mathematicians for decades or even centuries?
You are lucky to experience the joy of mathematical results at such a young age. Remember this feeling. If you really encounter a bottleneck in the future and feel that you can't hold on anymore, just think about how you feel today!
And your age is the time to show off! Don't care what others say. Young people don’t want to steal the limelight, so why should a bunch of old men take the limelight? As long as you have the ability, just perform, the teacher will guide you! ”
Qiao Yu nodded in a learned manner, and then became even more arrogant.
Well, he was indeed very happy today, but it was obviously not just because of his appearance in public at the venue. The reason for the slight limelight. But hearing his mentor say this made Qiao Yu feel even more proud.
Director Tian has said this, and he will have something to say if any senior brother or brother tries to eat it again in the future.
After all, he is also in a difficult situation. He is just pretending to be cool. If you have any opinions, please go to Director Tian. It is none of my business...
"By the way, Professor Ding just said I'm still saying that the professors at the meeting are already arguing. Some people think your idea is right, while others think your idea is whimsical.
Professor Tan is very supportive of your idea. , he said that you should be right. Try to write out the detailed proof process in the next two days.
But don't feel pressured even if it turns out to be wrong. It doesn’t matter, you must know that the people participating in this meeting are top experts in the relevant fields. Your ideas can arouse their debate, which is a success.”
Qiao Yu curled his lips and said: "Director Tian, although I agree with most of what you said, there is part of your last sentence that I cannot agree with!"
After being criticized, Tian Yan Zhen was not annoyed and asked with a smile: "Oh? Which part do you disagree with?"
Qiao Yuyan said firmly: "You said that the people attending this meeting are all top experts in the relevant fields. Let's put it this way, I explained the problem to them so clearly, but they still thought I was fanciful. This is enough to show that they are half-empty. , Definitely not a top expert!”
One sentence immediately silenced Tian Yanzhen.
He suddenly felt that calling this guy here specifically was a waste of time.
This mentality is God knows how many times better than when he was young.
Good guy, the complete proof process has not been given, and people have questioned it with half a glass of water. This confidence is definitely more than 99% of my peers. At least in terms of not being superstitious about authority, this kid has already stood at the top of the world pyramid.
But then again, Tian Yan really likes Qiao Yu's strong temperament. And this kind of character is really suitable for carrying the banner of Yanbei School in the future.
The only problem is probably that when this kid grows up and retires, if there is any disagreement in the future, he probably won't be able to influence this kid's decision-making. But it doesn’t matter.
As long as Qiao Yu can win the Fields Medal before the age of thirty, this kid will probably be the one to carry the banner of the Chinese mathematics community in the future. He will take a look at it then. I hope that Qiao Yu can give him a surprise by then, so that the Chinese mathematics community will have a higher voice in the world of mathematics.
If Qiao Yu could do this and help him vent his anger, all the bullshit in the country wouldn't really matter.
"Okay, okay, okay, that's very well said. There are still two days left in this seminar. If it doesn't work, you can extend it by one day. The last day is left to you, and you can arrange the time yourself. I just hoped, but Now it’s a request. In short, you have to come up with something complete before the seminar, so that the professors who oppose you have nothing to say.”
Tian Yanzhen made the request. .
This kid is not too polite to himself, and there is no need for him to be too polite.
Qiao Yu patted her chest and said, "Don't worry, Director Tian. I already have an idea. Looking back, I just need to give an accurate definition of this local deformation module structure and then prove it."
You should also know that the Everton professor directly defined the special singular point I conceived as Joe point. Now, isn’t it just a matter of completing the conjugation proof process of Qiao’s points? This is simple and can be done tomorrow night at most. "
Tian Yanzhen glanced at Qiao Yu and said, "Okay, as long as you think there will be no accidents in the proof process, of course I will believe you. After the proof process is completed, please contact me at any time. Send it to me first for a look. "
"No problem, Director Tian! Then I'll go first. In order to let you see my proof process as early as possible, I will race against every second. "
"Okay, go ahead. By the way, Professor Tan's lecture is tomorrow morning, so you don't have to go there. If necessary, I will let him give you a lecture alone. You still have to go to Professor Phyllis's lecture in the afternoon. It's a rare opportunity. "
" Got it, Director Tian. ”
...
Back in the room, Qiao Yu sat in front of the computer and opened LaTeX directly.
The next step is to prove it.
The most important part of the paper is the establishment of the nonlinear conjugate ridge structure, which is a complete proof of the two remote singular points P1 and P2 on the algebraic variety. They have local ridge singularities respectively. and influence each other through nonlinear homology mapping.
On the way back, Qiao Yu had already thought about how to prove it.
The first step is naturally the local structure analysis, which is nothing more than describing the geometric structure of the singular point by defining local equations, then checking the properties of the singular point by calculating the Jacobian matrix, and studying its ridge network using blowing and analytical decomposition. structure.
These are all ready-made methods, and Qiao Yu doesn’t need to think about them.
The key point is the construction of nonlinear homology mapping.
What Qiao Yu really needs to think about is which tool to choose to calculate the local homology of P1 and P2. This is probably the only difficulty. Different homology theory tools will directly affect the solvability when dealing with this part of the content.
After careful consideration, Qiao Yu decided to use layer homology plus Grothendieck local homology to deal with this problem.
Sheet homology can more conveniently capture the local geometric and topological information of algebraic varieties. Grothendieck local homology provides a deeper tool for processing local rings and algebraic structures, which can further analyze the properties of local algebraic rings at singular points and reveal algebraic varieties at singular points. subtle algebraic structure.
This should be the simplest method to relate the local homology dimension of singular points and the properties of local rings through homology mapping.
What Qiao Yu pursues is to use a simple and direct way to shut up the so-called senior professors who think his reasoning is problematic.
In fact, you can also use layer homology plus DeRham homology. Qiao Yu feels that the same conclusion can be reached. However, when dealing with analytic singular points or analytic forms on algebraic varieties, DeRham homology provides a differential geometry perspective, which makes the problem more complex to solve.
There is no need to use analytic geometry to show off your skills here. Moreover, Qiao Yu feels that his analytic geometry is not very strong. If there is any loophole in the DeRham homology proof process, both Director Tian and Grandpa Shi will feel disgraced...
After all, the mentor and Grandpa Shi are both big-shot figures in the field of analytic geometry.
In short, after solving this problem, the entire proof process is mostly completed. What follows is nothing more than step-by-step content. As long as such a point exists, the functor derived through higher-order category theory must fail.
The derivation of functors is not equivalent, and all conclusions are naturally self-defeating.
The real difficulty lies in how to reconstruct the Ambidexterity theorem so that this key theorem can be valid again in the proof of the geometric Langlands conjecture.
At this stage, Qiao Yu plans to solve this problem by himself, but will not tell the other party...
Thanks to book friend 20230114003824260, book friend 20240919204135030, book friend 20241011205517969, and night notes for the rewards and encouragement!
Completed the 36th day of 10,000-word punch-in!
(End of this chapter)