Stable local behavior.

This is the best solution to this problem at present, Qiao Yu even thinks there is no such solution.

In fact, Dennis was not the only one. Two professors from Yanbei also looked at the limit structure constructed by Qiao Yu and the new operators introduced, and fell into thinking. After reading the process written by Qiao Yu, Tan Zhiqing subconsciously looked up.

He glanced at Qiao Yu and said, "Filtering?"

Qiao Yu thought for a while, then nodded and said, "Well, it's a bit like it."

Professor Su from the School of Mathematics also spoke up: "It is indeed a good idea, using alternating symbols and hierarchical weighting to gradually filter out the self-noise at each level."

Dennis frowned, stared at the formula, and nodded after a while: "Well, the hierarchical processing method can indeed ensure that noise can be effectively eliminated at different levels of coherence without destroying the autonomy of the overall structure." After speaking,

, Dennis raised his head and asked, "What then?"

Qiao Yu spread his hands helplessly and said: "The next step is to make global consistency corrections. But I haven't figured out how to deal with this yet. Although I have a little idea, it still takes time to perfect. After all, we have to

Let local system characteristics be embedded into the global system smoothly enough.

This even involves the technical analysis of the mapping homomorphic space when the local system is mapped to the global system. So I still need time to think, maybe a day or two, maybe a month or two.

Sigh... Professor Dennis, to tell you the truth, I rely heavily on sudden inspiration for this kind of research, and I may need to read some literature during this period, so I really can't guarantee when I will be able to completely solve this problem.

I made that call to Professor Pan simply because I promised him before that as soon as I think of a solution, I will notify him as soon as possible. Well, I think I have already thought of this solution. Of course, there are still some key points next.

There are many steps, but please believe that I can definitely help you and Professor Pan solve this problem completely."

Dennis could see sincerity on Qiao Yu's face.

Well, there is indeed no way around this. In fact, Qiao Yu's being able to come up with this idea has already helped him a lot, and it has indeed provided an excellent way to solve the problem. But this has made the problem complicated again.

.

Dennis glanced at the two professors at Yanbei, then looked at Qiao Yu and asked: "Qiao Yu, are you willing to join our team and share this idea with us? You should know who is on our team, right?

For example, the main collaborators include Professor Sam, Professor Frank, Professor Pan, and..."

Qiao Yu directly interrupted Dennis and said: "Professor Dennis, of course I know the members of the team. After all, I have read all your papers. And I am also very willing to join your research team, but I hope to be able to participate in this meeting."

We will discuss this issue later.

You know, this is my first time to participate in this kind of world-class mathematician conference. Professor Tian asked me to prepare the content of the report for this conference in advance. After all, this is really important to me. "Qiao

What Yu said was very sincere and very appropriate.

Putting it another way, if he were a student of Dennis who was invited to attend such a meeting at the age of sixteen and could still give a thirty-minute report, he would probably put the conference first.

So Dennis nodded and said, "Of course, you are right. Professor Pan will be here in two days, so we can discuss this matter after your report meeting. What do you think?" "Of course,"

It's a great honor for me to be with you, Professor Dennis."

Qiao Yu answered politely, and then said with concern: "And I don't think it's suitable for you to continue thinking about academic issues now. You should go to rest first to take advantage of the jet lag. To be honest, I don't think you are in a very good condition right now."

"Well, yes, I haven't slept for nearly twenty hours. Damn low-cost airlines. You can't even imagine what kind of guy would be sitting next to you. Not only can he fall asleep sitting down, but he can also sleep after falling asleep.

I can grind my teeth! These eight hours were like a thriller movie!"

Dennis complained.

Obviously, today's trip was not a pleasant one for the Harvard professor. But Qiao Yu couldn't relate to it at all.

After all, he slept through it. It was a bit cold at night, and someone covered him with two blankets.

..

"Then believe me, the most important thing you should do now is to rest, Professor Dennis." Qiao Yu said politely.

After saying goodbye to Professor Dennis who was in poor condition, and briefly chatting with the two professors, Qiao Yu called Tian Yanzhen, and then went to Director Tian's room. It was equivalent to returning to his own room, because

His room is next door to Director Tian's.

Although the plane is in business class, the accommodation is an ordinary single room. But then again, even the price of such an ordinary single room is not cheap. After all, they charge Euros.

Of course, Qiao Yu didn't pay much attention to the accommodation environment. In fact, Qiao Yu felt that the small single room in the Mathematics Research Center, which Mr. Yuan had picked out a lot of problems with, was quite comfortable.

"Sent Professor Dennis away?"

When he came to get the room card, Qiao Yu was teased by Tian Yanzhen.

Qiao Yu nodded honestly and replied: "Well, I told him my general idea, but the professor seemed to be in a bad state, so I advised him to go to bed first. By the way, he invited me to join the project. group, but I think this matter should wait until after my report meeting.

After all, you also said that there will be reporters from China attending this meeting, and my report may even make the news. So I don’t have time to discuss this now."

Tian Yanzhen looked at Qiao Yu and said, "You only talked about a general idea? The timing is very coincidental. If you can have a complete idea, you can contact the organizing committee. The thirty-minute report meeting may become four Fifteen minutes. Of course, maybe you need to get a heavyweight mathematician to approve your idea. Dennis is indeed not suitable.

Qiao Yu blinked, and immediately put on a childish smile on his face: "Hey, Director Tian, ​​you have seen through it again. I feel quite embarrassed to join Dennis' team at this time. Didn't you say that Professor Schultz would be there tomorrow?" Are you coming? I plan to discuss my thoughts with Professor Schultz first.

If he also suggested that I announce this idea directly at the report meeting, he would naturally help me contact the organizing committee by then, right?

Tian Yanzhen stared at Qiao Yu and asked, "Do you really have a complete idea?"

Qiao Yu stopped smiling, nodded, and said seriously: "It's true, and I think it's definitely no problem. It's quite offending. As you know, the loopholes I found before mainly came from Professor Sam and Professor Frank. Proof process.

They completed the local-to-global mapping by proving that each feature layer can be related to white noise in some way. And completed the proof of the geometric Langlands conjecture. The conjugate ridge singularity I found , leading to potential local-global mismatch.

My current solution directly bypasses their method. Through a new paradigm, the local-global interaction is reconstructed. So I dare not tell the truth to Professor Dennis."

Qiao Yu said honestly.

Tian Yan was really startled, and then he realized that this was indeed a very offensive thing, and he could even offend people to the point of death...

But the next moment he smiled.

"You're right. You should be careful. Especially when your results have not been announced to the public. But you don't have to take it too seriously. Anyway, you have nothing to do with those two professors. Do whatever you want. That’s it.

Although I don’t know much about the geometric Langlands conjecture, there is still no problem in protecting your results. In this way, I will say hello to the organizing committee tomorrow and you will explain your proof process later. Send it to me by email. I will find someone to check it for you first. Well, by the way, just follow your usual habit and send a copy to Mr. Yuan.

After finishing speaking, Tian Yanzhen paused, and then said domineeringly: "As for offending people, that is inevitable. There are too many academic projects that collide with each other. Whoever solves the problem first will have the results of the published paper. It cannot be avoided. If they said they did the research first, then the results must be theirs. Everyone depends on their ability. Your results are there, and with me and your senior master here, you can rest assured that no one can take away your results."

Qiao Yu nodded repeatedly and said, "That's okay, but can I post it later? For example, wait until the afternoon? You know, I just told Professor Dennis that I haven't figured out the complete proof process yet. Suddenly I posted the complete proof process again. I felt quite embarrassed when I took it out."

"What's so embarrassing about this? Why can you just say that he knows what he knows... Hey, forget it. Let's just have this afternoon..." In the end, Tian Yanzhen followed Qiao Yu's wishes.

They don't care what Sam and Frank think, but Pan Jingyuan has provided a lot of help to Qiao Yu on this issue, and Dennis is Pan Jingyuan's mentor. This should really be paid attention to. It's just that the way Tian Yanzhen looks at Qiao Yu is different. .

At only sixteen years old, he takes care of all aspects, which is quite thoughtful.

"Well, then in the afternoon I also sent an email to Professor Pan and Dennis, saying that I had been inspired to figure out the complete process. Then I said that I didn't sleep after getting off the plane and kept thinking about math problems. I went to bed when I was too tired.

Professor Pan was still in China, and Professor Dennis must not have gotten up at that time. By the time they saw the email, I was also asleep. We can just wait until Professor Schultz comes tomorrow to discuss it together. What do you think? There’s not much going on today anyway, and you don’t let me go out for a walk by myself.”

Qiao Yu completed the whole process with great interest.

Tian Yanzhen shook his head and said, "Actually, you don't need to be so careful."

Qiao Yu denied: "I'm not being cautious. In fact, I just want Professor Dennis and Professor Pan to stay in a happy mood. After all, they are very nice people. This is a good thing. Their paper only needs fine-tuning. It can be published together with my paper.

But it would be bad if good things were overshadowed by other people's reasons. After all, Professor Sam and Professor Frank must be very unhappy, and they have been cooperating with Professor Dennis for so long. This way of handling it can make those two The two collaborators cannot blame Professor Dennis and Professor Pan.

As for me, it doesn't matter. Anyway, I am young, and you and Grandpa Shi are protecting me. I have nothing to do with the two professors. Anyway, I am not afraid of offending anyone at all. At most, wherever they appear in the future, it will be over if I don't go. !

Well, good boy, you are really comprehensive and have thought of everything. The key is that you are still so responsible and take the initiative to help Professor Pan, who has helped him, to share the pressure of favors...

"Okay, you can do whatever you want with your results. Just put all your thoughts into...forget it, go back to your room and pack your things first." Tian Yanzhen waved his hand and said. Originally, I subconsciously wanted to ask Qiao Yu to focus on mathematics, but after thinking about it carefully, there was actually no need to say this.

After all, given the current situation, no matter how strict the instructor is, they cannot deny Qiao Yu's achievements in mathematics. This kid is about to usher in a harvest period.

After this report is completed, if it can be approved, it means that Qiao Yu will already have three first-author papers in hand.

At the age of sixteen, he has three first-class papers in mathematics. If the results of Huaqing's project come out, there will be at least one four-year first-class paper. This makes Tian Yan really unable to bear any harsh criticism. Looking at mathematics In world history, probably only mathematical wizards like Gauss and Ramanujan can compete.

Geniuses really have many things in common. For example, these people all relied on self-study to achieve these achievements. The same is true for Qiao Yu. So far, his mentor has almost done nothing except assigning him a bunch of required readings.

Qiao Yu seems to be very adaptable to this self-study model. Alas...it can only be said that his talent is enviable.

Really, now Tian Yanzhen has no interest in accepting any more students.

Seeing Qiao Yu dragging his suitcase with a sneer on his face, turning around and about to leave, Tian Yanzhen suddenly thought that this kid was going to attend IMO in July.

.

After this report meeting, he was probably qualified to sit on the IMO judges' bench and chatted and laughed with the judges. However, his age supported him to participate in this kind of competition that only high school students can participate in. Just think about Tian Yanzhen They all thought this was outrageous.

On the other side, Qiao Yu put away his luggage. He originally planned to call Qiao Xi to talk about his plans, but gave up. He still planned to wait until he finished the matter before telling Qiao Xi in person.

After all, there isn't much material to tell right now.

After the report meeting, the respected Professor Frank will probably hear about it regardless of whether he came to attend the meeting or not. At that time, no matter what considerations, Dennis or Professor Pan will definitely want to obtain the information from Professor Frank. contact.

Then he could inquire about Professor Frank's reaction through Professor Pan.

Of course, it would be best for Professor Frank to attend the meeting in person, so that he could see the big boss's reaction with his own eyes, and then go back and describe the scene to Qiao Xi.

Just as Tian Yanzhen thought about it, Qiao Yu is still only a sixteen-year-old child anyway. He really has no bad intentions. He just wants to show off his abilities in front of his mother and tell Qiao Xi that he has grown up. Not only is he capable of protecting his mother, but he can even help her vent her anger.

Men, when they grow up, there will be this stage. They can’t wait to prove that they are no longer a kid who doesn’t understand anything. It’s just that very few succeed, and some even do some very stupid things in this process. Things that happened so much that when I think about it in the future, I feel like I can’t hold my head up.

But Qiao Yu is obviously not among them.

After all, he took every step steadily and won the support of everyone around him. The only accidental injury among them was probably Professor Sam.

But having said that, being able to work with a self-interested and hypocritical guy like Frank for so long is probably not a good person. Moreover, this professor is not young anymore, and he has no career in mathematics anyway... In short, Qiao Yu's mentality is very calm.

Especially after he confessed to his tutor, he felt even more relaxed. After packing his luggage, he took out a book and started reading happily. When he went out for a meeting, he did not forget to read and study. The tutor and his master would definitely praise him severely.
To be continued...