On the plane, when the flight aunt asked to turn off the phone, Qiao Yu took out the silent phone, ignored the missed call and hung up the phone.

Yes, in fact, after the May Day trip, Qiao Yu returned to school and took out the memories that he had carefully hidden before to think about it. Then he found that it was very effective. In the next period of time, he mainly relied on this technology to organize the entire memory. The white noise system is removed.

Especially when he discovered that this idea was feasible, all his energy was spent on it during this period. It did involve some very interesting tools.

That is to say, both Tian Yanzhen and Mr. Yuan's trust in him has reached its peak, otherwise he would not be able to hide it from the two of them. But now as long as he achieves results, it seems that there is no need to hide it.

..

Tian Yanzhen silently watched Qiao Yu sitting in his seat, kept looking out through the upper window of the cabin, and asked: "First time flying on a plane?" Qiao Yu looked back at Tian Yanzhen and nodded. Said: "Yes, Director Tian."

Tian Yanzhen smiled and said, "Then you really made a profit. The first time you took a plane was in business class on an international flight."

Yes, in order for Qiao Yu to be refreshed during this trip, Tian Yanzhen booked a ticket for the second-floor business class of a wide-body aircraft like A380. So he chose to travel today and wanted to take Qiao Yu to Paris as early as possible. , choosing an airplane is also one aspect.

It would be really painful to take a narrow-body passenger plane for a long-distance trip of more than ten hours.

Although it was early in the morning, the plane had just started gliding, and the cabin was still a little noisy, so it was a good time to chat. "Who did you call when you were depositing your luggage?"

"Professor Pan from Huaqing."

"Oh." Tian Yanzhen nodded, without going into details, but instead asked: "How did you come up with the idea of ​​inviting Mr. Yuan to attend Chen Zhuoyang's graduation defense?"

Qiao Yu blinked and replied: "Director Tian, ​​it was Senior Brother Chen who forced me to invite... It's really hard to explain this matter. I just invited him casually, but who knew that Senior Master would really agree." ...

Well, Qiao Yu swore that he really didn't care about his senior's salary and bonus that year. He just wanted to know how much an ordinary professor at a double first-class university could earn in a year. This damn thirst for knowledge! But how? Say...

Anyway, on the day of the defense, Senior Brother Chen was obviously much older, but he smiled like a child. Grandpa Senior was not impatient and was always cheerful. Director Tian was also high-spirited that day, and the other invited professors were in different moods. good.

If only one person is happy about something and no one is unhappy, it is 100% a good thing.

If only a few people are unhappy about something he leads and the vast majority of people are happy, it is enough to show that it is a good thing. In short, Qiao Yu feels that he has been busy doing all kinds of good things during this time. Never stopped.

"Don't make random requests to Mr. Yuan from now on. Mr. Yuan is already very old and can't stand your troubles!" Tian Yanzhen said with a straight face, but after saying that, he couldn't stand it anymore. Mr. Yuan is now Maybe you're afraid that Qiao Yu won't make the request? Oh...that's unreasonable.

"Don't worry, Director Tian, ​​I know what's going on. It's not our sect's business, and I will definitely not trouble Grandpa Shi." Qiao Yu said decisively. Well, the sect comes first... There's really no way to criticize this.

Tian Yanzhen could only nod his head. Fortunately, the plane also started to take off. In the middle of the night, after the plane stabilized, the cabin became quiet. "Let's get some sleep. We'll be almost there when we get there."

"Okay, good Director Tian."

Young people sleep soundly wherever they go. Anyway, Qiao Yu slept well. Fortunately, not only was the plane not delayed, but it also landed at Charles de Gaulle Airport half an hour early. The local time was 7:30 in the morning. We got off.

Qiao Yu took a photo of the plane landing and sent it to Qiao Xi: "Mom, it landed smoothly, I'm in Paris."

Of course, Tian Yanzhen is still very popular in Paris. Before Qiao Yu came, he prepared a phone card for him that can roam around the world. Excellent tutors are like this, they can always help students think of everything.

Soon, Qiao Xi replied: "Listen to the teacher and pay attention to safety."

"Don't worry, Director Tian will be by my side." After a brief chat, we started to go through the customs procedures again.

Fortunately, after knowing that the team was here to participate in an international mathematics conference, the group was quickly released, and then took a taxi directly to the hotel designated by the organizing committee of the conference - the Royal Monet Hotel in Paris. It is a short distance from the French Institute of Advanced Sciences.

It's not far, only 3 to 4 kilometers, and it only takes half an hour to walk.

However, even if they are special guests, because they arrive a little early, they can only book a hotel for two nights by themselves, and then the conference organizing committee will make unified arrangements.

In addition to the invitees, there will also be some mathematicians and mathematics students who choose to attend this kind of world-class mathematician conference at their own expense. Therefore, nearby hotels are very tight. The professors from Yanbei University here rely on the organizing committee to successfully check in.

Rooms that will coordinate.

However, this time it is hard to say that it is all Tian Yanzhen’s fault, and it is also related to the fact that many mathematicians are very interested in Qiao Yu. Every time a genius appears in the mathematics world, he always attracts everyone’s attention quickly.

But Tian Yan really didn't expect it to happen so quickly. As soon as they entered the hotel, they heard someone saying hello to him.

"Hi, Professor Tian, ​​you are finally here...well...let me guess, you must be Qiao Yu, right?"

When Tian Yanzhen followed the voice and looked over, Dennis had just stood up from the sofa on the right side of the hotel lobby for guests to rest. In one sentence, he had already walked to the opposite side of him, and his eyes were staring at Qiao Yu beside him. Dennis was

Such an attitude made Tian Yanzhen nervous, especially since this guy's hair was a little messy and his eyes were a little red, and he looked very scary...

So Tian Yanzhen took the initiative to step forward and said, "Well, Qiao Yu, let me introduce to you. This is Professor Dennis, who is also..."

"Director Tian, ​​I know that Professor Pan often talks to me about Professor Dennis, saying that the luckiest thing for him is to meet a mentor like Professor Dennis." After saying that, Qiao Yu said hello to Dennis generously:

"Hello, Professor Dennis."

"Hello, um, you know, Professor Tian, ​​I just arrived at the hotel. Damn it, there are only economy class tickets left. Hey, anyway, you should understand that I need to talk to Qiao Yu now." Dennis

Said somewhat incoherently.

This made the professors at Yanbei University who followed Tian Yanzhen feel very strange.

Even if I have never met Dennis, mathematics professors from such well-known universities are very stable most of the time. Obviously, Dennis at this time is different from the famous Harvard professor in terms of image and attitude.

Match. "So what is the issue you need to discuss with Qiao Yu?" Tian Yanzhen couldn't help but ask.

If it's about the theory of conjugate ridged singular points, there's really no need to come to Qiao Yu to discuss it. The paper is about to be released. Tian Yan really doesn't believe that Dennis hasn't discussed it in depth with Pan Jingyuan. "Don't you know? Qiao Yu.

Yu said that the problem he raised has been solved!" Dennis looked at Tian Yanzhen in surprise and said.

Does the tutor not know the results of his students at all?

"No, no, it should be said that I just have an idea for the time being, and it has not been completely solved yet. In fact, I also hope to solve the problem in these two days. So I haven't mentioned it to my instructor yet. I told him before getting on the plane

Professor Pan said the same thing, it’s just an idea..."

Qiao Yu quickly emphasized from the side.

The professors from Yanbei probably understand why Dennis looks like this today.

I really didn't care about anything else, so I kept guarding the door of the hotel after arriving in Paris.

But then again, if it were them, and the proposition that had been studied for more than ten years had such twists and turns, it would probably be the same. After all, it involved so many years of hard work.

"That's it, then you and Professor Dennis can chat first, and we'll check in first. But you're here? Why not go directly to the room." "No, there is a special conference room upstairs. I just asked

It’s ready to use.”

Tian Yanzhen glanced at Qiao Yu, who nodded and said generously: "No problem, Director Tian. Anyway, I slept well on the plane. I just want to talk to Professor Dennis about my thoughts first." Tian Yanzhen glanced at Qiao Yu.

Yan Zhen nodded. On one side was the energetic young man, and on the other side was the bad old man with red eyes. Obviously, the person facing him would not be able to survive Qiao Yu...

"Okay, let me collect the room card for you first. After talking to Professor Dennis, call me. By the way, we also have several professors here who are interested in the proof of the Langlands conjecture in geometry. You can go and listen together.

?Professor Dennis?"

Dennis glanced at Tian Yanzhen, and it took him a while to realize: "Of course, but we're going up now." "It doesn't matter." After saying that, Tian Yanzhen looked at the other professors behind him.

After a few brief explanations, two professors from Yanbei University quickly walked out and stood together with Qiao Yu, saying hello to Dennis.

One, Professor Tan Zhiqing from the Mathematics Research Center, has been doing research on the P-Langlands program over the years, and the other is Professor Su Changhe from Yanbei Institute of Mathematics, who mainly does research on L invariant theory. In fact, it is true

Speaking of which, both of them knew Dennis.

Our research directions are similar, and we occasionally meet at some academic conferences, and we even have the experience of discussing via email. It’s just that the number of meetings may not be that many, and the impression may not be that deep.

"Then let's go." Dennis looked at Qiao Yu and said. "Oh, okay."

"Qiao Yu, can you briefly introduce your thoughts first?"

As the four of them walked towards the elevator, Dennis couldn't help but ask.

"Didn't Professor Pan tell you?"

"I talked a little bit, but he said your explanation was very rough. I only roughly understood your idea, but it wasn't very detailed."

"Actually, my idea is quite simple. Since the problem lies in singular points, why not bypass this problem? So it is better to introduce a new paradigm and construct a fine reconstruction tool of local-global interaction to re-examine the geometry. Langlands conjecture."

The two professors Tan Zhiqing and Su Changhe who were following Qiao Yu looked at each other.

When Qiao Yu found the loophole in the conjugate ridge singularity, the two of them actually discussed in private how to fix the loophole. This was indeed one of the methods, but obviously this method was not as simple as Qiao Yu said. .

But before they could speak, Dennis said: "Actually, I have had this idea before. Pan and I have constructed a fractional homology deformation method to deal with the problem of singular points.

Define a new homology layer near a singular point, such as Fxα, α represents fractional order. In this way, their growth rate can be controlled by fractional order values ​​to reflect the complex geometric structure at the singular point. But then this method Failed. Because this method mainly relies on approximation, complex singular points cannot provide sufficient proof of convergence through this approximation. This problem has troubled us for a long time.

It wasn't until Sam and Frank used their method to connect the feature layer with the white noise that they got the final answer. Are you sure that the method you provided can effectively avoid this situation?" "Oh... Third floor, thank you. "

At this time, the four of them had already gotten on the elevator. Dennis told the waiter in the hotel elevator what floor he was in, and then turned to look at Qiao Yu.

"Well, my method is different from your previous method. But your idea is definitely not feasible. The fractional homology layer is not a true integer-order homology. There will definitely be errors in the details, and the more complex the singular points, the greater the error. will be larger. In the end, it will still lead to local-global mismatch.

My idea is more direct, to directly identify and filter out the white noise components introduced by the feature layer, so that the structure of the local system maintains a very clean reflection globally. And this method is not complicated, the main thing is to introduce a denoising Fuzzy operator, it’s too troublesome to talk about. I’ll show you an example later and you should understand.”

Dennis nodded.

The collision of mathematical ideas is indeed sometimes difficult to explain clearly with words. Fortunately, the conference room is right in front of us.

"Lemma 1: Local reconstruction of conjugate ridge-like complex singular points."

"Let X be an algebraic variety, x∈X represents a conjugate ridge singular point."

"At the conjugate ridge singular point x, a local reconstruction object Fx, LGIR and a lossy power ladder operator DLGIRD can be constructed to deal with the non-convergence of the traditional local system at the singular point. The definition is as follows:" "

Under the LGIR framework, define a destructive curtain ladder operator DLGIRD. The result of acting on Fx and LGIR is: "

In the conference room, Qiao Yu wrote down some of his recent research results on the manuscript paper provided by the hotel, and then handed it to Dennis.

This is not all Qiao Yu's thoughts. Lao Xue has taught him that the academic circle is not as pure as outsiders seem, and he must be on guard at all times. So he decided to announce the remaining key solution process only at the conference. But Qiao Yu

Yu believes that mathematicians who have studied this proposition for more than ten years can see the value of his idea.

After all, the limit structure he designed can ensure that the local reconstruction object is still well defined under the high-order homology group. Traditional methods may cause divergence due to high-order perturbations, but through this limit structure, it ensures that the local reconstruction object has
To be continued...