Although he didn't understand the significance of this matter, Luo Jingrong didn't say anything more. Maybe the genius's ideas are slightly different from those of ordinary people like him.

In fact, Luo Jingrong's worries are not unnecessary.

Indeed, many people have ridiculed the comment section on Weibo.

Of course, as Qiao Yu said, he didn't care, he was even filled with joy to bring a sense of superiority to more people.

He even replied to the netizen who pointed out the mistake for the first time: "So that's it. I haven't read the Chinese language book for a long time, and I actually memorized it..."

If a person is smart enough, he must occasionally expose his stupid side in front of the public. After all, it is very tiring to maintain a high-end personality in front of the public. Only a few people know about the genius side. And it is short-lived. After resting, he really had to work next, and he had no time to pay attention to things like Weibo.

.

Huaqing and Pan Jingyuan have been having a bad time recently, and of course this is mostly due to Qiao Yu.

Think about it, a paper that solved a heavyweight topic was about to be published in a journal, and even the main reviewer gave a positive evaluation. However, just when it was almost time to hold a celebration banquet, he was outed. Here comes a stick. And that person is also a joint training target of his own mathematics research center. Obviously it is difficult to feel good.

What's even more annoying is that Qiao Yu discovered the problem from a very tricky angle.

So these days, the entire research team is desperately searching for relevant information, trying to quickly find a way to patch this vulnerability.

He mainly rediscovered some proof routes that had been temporarily abandoned during the previous research process, and tried to use these methods to repair the damage caused by such special singular points to the high-order category axiom system. The workload in this area is huge, as you can imagine .

There is no other way. When this road fails, you have to find another way. After all, the problem is there, and it is impossible to just give up so many years of hard work.

In fact, Pan Jingyuan suggested whether Qiao Yu could be included in the team to help them fix this vulnerability. In fact, this is a very common thing.

When a mathematician discovers a loophole in a heavyweight paper, the research team will often take the initiative to invite the mathematician who discovered the loophole to join the team and work together to find ways to overcome the problem. However, on this issue, the team has never reached a unified opinion. His supervisor Dennis maintains a positive attitude towards this, but the attitude of the other two main research team members has not been clear, and Pan Jingyuan can only give up temporarily.

To be honest, Pan Jingyuan really didn't have any negative emotions towards Qiao Yu.

Although Pan Jingyuan has not been dealing with Qiao Yu for a long time, he actually has a good impression of Qiao Yu.

Needless to say, being polite is a basic quality for a sixteen-year-old. In addition, Qiao Yu is also very trustworthy in daily life, such as respecting the professor's time. Well, this should actually be a basic quality for students, but

As the saying goes, people are most afraid of comparison...

There are many students who have no concept of time, which shows how good punctual students like Qiao Yu are. Although they are talented, they are also honest and trustworthy, respecting professors and respecting time...

What bad thoughts could such a child have?

He just happened to be interested in the geometric Langlands conjecture, and he happened to read their paper and found a small mistake. And Qiao Yu also promised him that if he thought of a way to solve this loophole, he would be the first to do so.

Time will tell.

Qiao Yu is already so sensible, but if he still resents a sixteen-year-old child, Pan Jingyuan will feel that he is too petty.

He believed Professor Dennis had the same idea.

I just don't know why Professor Sam and Professor Feng seem to have some conflicts with Qiao Yu. Pan Jingyuan suspected that it was because Qiao Yu was too young and the two professors couldn't help but feel embarrassed.

It is precisely for this reason that the recent news from Professor Li next door made his impression of Qiao Yu more complicated. During this period, Qiao Yu actually solved the problems encountered by Lao Li's research team.

It still makes me feel a little bit disgusted. Qiao Yu, this kid, is responsible for killing and not burying him!

For both emotional and rational reasons, we should first help them think about the proposition of the geometric Langlands conjecture. Of course, this cannot be blamed on Qiao Yu.

After all, Qiao Yu is now a member of his research team, and it is natural for him to think about his own research project. In short, his emotions are very complicated and very troublesome.

But there is nothing we can do.

Pan Jingyuan planned to wait until he went to France to attend the World Congress on Algebraic Geometry, and then find time to have a chat with Qiao Yu. After all, he really didn't have time during this period of time. In this way, time simply flew by, and the whole of April and Friday

I worked for most of the month and didn't make much progress.

The tutors Dennis, Professor Sam and Professor Feng are also very similar.

Of course, this is normal. For an extremely complex topic, a problem is raised. To solve the problem and maintain the integrity of the framework, it is not that simple. All links need to be reorganized.

, of course it is not completely without gain.

After communicating with Professor Dennis via email, he proposed a previously abandoned method at yesterday's group meeting, which was to reconstruct a topological perturbation category, the Topological Perturbation Category, or TPC for short, and analyze local areas at the conjugate ridge singular points.

system.

The core idea is to re-harmonize the geometric structure near the singular point by introducing small topological perturbations to make it suitable for the global needs of the geometric Langlands conjecture.

The mathematical explanation is that for each singular point x on the algebraic variety

The first-order singularities are smoothed at a very small scale ∈, making the local geometry topologically similar to smooth points.

This was actually a previous idea. The reason why it was abandoned at that time was that the limit process of topological perturbation E→0 is not necessarily consistent at different singular points. Especially in complex singular point networks, the limit of HnTPC(x) may not be stable enough.

But there is no way. This is currently the best solution to fix the problem raised by Qiao Yu, but it is technically more troublesome.

As long as the problem of the failure of the Ambidexterity theorem in the limit process can be solved, the paper can be re-generated without major revisions.

In short, at least we can determine the direction of our next efforts.

There is no way, Pan Jingyuan has felt that the emotions of the other two people in the research team have become unstable recently. This can be seen from the frequency of email exchanges between everyone recently. It is not that there is less communication, but too much.

.

Once someone in the research team puts forward too many unreasonable ideas in a short period of time, it will inevitably waste a lot of everyone's time. Especially Professor Feng, who makes Pan Jingyuan very uncomfortable. Some of his recent ideas are obviously outrageous.

Fortunately, at the group meeting, he and Dennis convinced the two of them to accept the plan.

However, Pan Jingyuan has no time to pay attention to this proposition in the past two days. He will leave for France the day after tomorrow to attend the World Congress on Algebraic Geometry. Although he will not speak at the conference this time, he is also one of the mathematicians invited to participate. Okay

, he originally had the opportunity to give a report at the branch venue.

But before the correct solution to this problem was found, neither he nor Dennis had the intention to make a report.

It's not that Pan Jingyuan never thought of going there with Qiao Yu, but this time Qiao Yu went with several mathematics professors from Yanbei University, and Yanbei University said that Ling Zhan would leave tomorrow and take a China Airlines flight directly to Charles de Gaulle.

Airport. Although the departure time is a bit unsuitable, this is the shortest flight. The whole journey only takes less than twelve hours, which is equivalent to arriving at the venue three days in advance.

This is probably Tian Yanzhen's decision. But there is nothing wrong with it.

If Qiao Yu was his student, Pan Jingyuan would also choose to go in advance and take Qiao Yu to get acquainted with the world's leading professors in related research fields who were attending the conference. Sometimes things are just such a coincidence, Pan Jingyuan just thought of it

When Qiao Yu was waiting, the phone suddenly rang, and it was this little guy calling.

Speaking of Cao Cao, Cao Cao is like this. There are many more ways to interpret it in modern times.

Okay, this is before going to France to attend a meeting. Do you still remember to say goodbye to him? Then this guy is pretty good... It was so late at night, how did Qiao Yu know that he was still awake?

Pan Jingyuan thought mockingly to himself, and then connected the phone. As a result, Qiao Yu's first words made him stunned.

"Hey, Professor Pan, didn't I promise you before that if I think of a solution to the geometric Langlands conjecture, I would inform you as soon as possible?" Pan Jingyuan immediately asked, "Huh? You have already thought of a solution?"

"Well, yes, I have some rough ideas, but there is another problem. I don't know how to deal with it." Pan Jingyuan was stunned and asked subconsciously: "What problem?"

"I read those papers. The work of Professor Sam and Professor Frank mainly focused on proving that each feature layer contributes to white noise in some way to prove the local-global proof. But the way I thought of is The LGIR tool was introduced to solve this problem.

To put it simply, directly remove the white noise. By creating the "noising fuzziness operator" in LGIR, we can identify and filter out the "white noise" components that may be introduced by the feature layer, thereby ensuring that the structure of the local system is maintained globally. Clean mapping.

This allows us to embed the local singular point system into the global algebraic group representation. How to say? The feature layer equivalent to each singular point will exist in the form of an analytical merged state, so that we can directly avoid Remove the white noise problem caused by the automorphism of the feature layer.

In the same way, this can directly ignore the influence of conjugate ridge singular points and ensure that the behavior of each conjugate ridge singular point is the same as other smooth points on the global scale. Of course, doing so requires a slight modification to the effect of the Ambidexterity theorem. conditions, but allows the theorem to hold in a broader geometric context."

Really, Qiao Yu immediately confused Pan Jingyuan with just a few words.

It took a while to realize the hidden meaning of Qiao Yu's words, and then he subconsciously asked: "Qiao Yu, do you have any objections to Professor Sam and Professor Frank?" This small flaw made me think of your help to me. I feel guilty.

So during this period of time, I have actually been thinking about how to solve this loophole. I just had an idea today, so I will contact you as soon as possible. I think this method is really effective. Maybe I can go to France in the next two days. You can sort out your thoughts.

Just now, Professor Tian was saying that you will also go to Paris to attend the conference this time. Then I will talk to you in detail about my ideas!" Pan Jingyuan only then realized that there was a lot of noise on Qiao Yu's phone at this time, subconsciously asked: "Are you already at the airport?"

"Yes, I came early. Director Tian was coordinating the procedures in front of me. I took the time to call you. Oh, Director Tian called me and I can't talk to you anymore. Professor Pan, let's wait until we meet in Paris. "Wait, hello, hello..." Pan Jingyuan called twice, but unfortunately the person on the other end had hung up the phone. He thought about calling again, but no one answered for a long time.

However, it is understandable. After all, it is a journey abroad, especially for Qiao Yu, who is probably going abroad for the first time. The procedures are relatively complicated. There is really no time to answer the phone at this time. In fact, if Qiao Yu can find the time to make this call to him, he should. Contented.

It's just that, how can he sleep tonight?

Well, this is no longer something that can be solved by an email. Pan Jingyuan thought about it and called Dennis directly. His flight ticket has been booked and it is impossible to change the itinerary. But Dennis has a lot of freedom.

Should be taller than him.

Of course, the most important thing is that he has to discuss this matter with Dennis. To be honest, this matter is a bit too coincidental.

Qiao Yu is going to give a thirty-minute report at the World Congress on Algebraic Geometry.

Of course, for this kind of formal academic conference, the invited speaker needs to provide an abstract or even a detailed speech for the review committee to review. Even at Qiao Yu's age, the reviewer will discuss with Qiao Yu before the report to ensure that

The content is presented reasonably within the 30-minute time frame without timing out or missing key information points.

Pan Jingyuan even knew that Qiao Yu's report this time was focused on conjugate ridge singular points.

After all, Qiao Yu's paper on the prediction of the upper limit point of the curve will not be published on Ann.Math until after the conference. And the video of Qiao Yu's speech questioning the proof of the geometric Langlands conjecture has been circulating in the academic world for a long time.

, and has been recognized by many famous people.

But if Qiao Yu can really find a solution to this problem before he makes his report, Pan Jingyuan believes that the review committee of the conference will definitely agree to Qiao Yu temporarily modifying the content during the report time and allow Qiao Yu to present his complete solution.

Because if Qiao Yu can find a way to solve the conjugate ridge singular point problem before the meeting, it will bring a new breakthrough to the proof of the geometric Langlands conjecture.

It also means that the proof of the geometric Langlands conjecture may be recognized by mainstream academic circles again. It also means that this conference will produce another excellent paper with far-reaching influence on algebraic geometry. Qiao Yu's

This report will definitely become the biggest highlight of this conference.

To be honest, this will have little impact on Pan Jingyuan and Dennis, and they will even be the beneficiaries.

Because the method proposed by Qiao Yu does not deny the core idea proposed by Dennis, it just solves the problem in another way. But the impact on the other two main collaborators is great, which means that the papers they are responsible for will not be
To be continued...