At least one thing Tian Yanzhen said was right. Regardless of everyone's attitude towards his results, Qiao Yu, a sixteen-year-old child, became the star of this seminar. Even in the lecture the next morning, there was a professor

His absence is deeply regretted, as is Professor Everton.

Those thoughts.

When he attended Professor Felice's lecture in the afternoon, he was surrounded in a physical sense. Many people wanted to discuss with him what he had expressed yesterday. Before the lecture, Professor Felice even

Invited him to stand on the podium and took a photo with him. This caused Professor Everton’s dissatisfaction until he also stood up to speak.

After taking a photo with Qiao Yu on the stage, the lecture officially started.

Qiao Yu also listened more seriously.

In fact, it’s okay if he’s not serious. The professor’s eyes on the stage fall on him from time to time. Well, this is what Director Tian specially emphasized, the so-called most basic respect.

It is actually very simple to offend a mathematician. The most embarrassing way is probably to say to his face that the theorem he proved is meaningless. The second most embarrassing way is to dismiss his lecture. But in fact, the latter means the same thing as the former.

We are both mathematics researchers, and if we think that the other's work is meaningful, we will not fail to take the other's lectures seriously.

Even though Qiao Yu is not yet a mathematician and does not understand the unspoken rules in the mathematics circle, he understands the inexplicable competitiveness of men. Xi

Although these are all great professors from well-known universities and research institutes, I didn’t meet Professor Everton just now because he didn’t take a group photo with him on the first day of his lecture. The result must be

So if he listened carefully to Professor Everton's lecture on the first day, he gained a lot, but today he didn't listen carefully to Professor Felice's lecture, and he unknowingly offended others.

Are you going to take a group photo before letting Professor Felice's lecture officially begin?

Qiao Yu didn't mind offending people.

But considering that Professor Phyllis showed goodwill to him before the lecture began, and he is the kind of big boss who may become an ally of the world's academic community in the future, it is not a bad thing to offend him, and his words are deeply rooted in the hearts of the people. Friends always want to

The more the better.

Come on. This is the simplest calculation problem. It does not require complicated mathematical knowledge. If you can do it after learning addition and subtraction in the first grade of elementary school, then he has already won.

The same is true in the world of mathematics. Based on what Qiao Yu knew about the experiences of Director Tian and Grandpa Shi, when the person opposite raised his head and looked around, he realized that he could not find a friend in the whole world. And Qiao Yu found that young age is really the most perfect.

Amulets are really easy to attract the liking of these uncles.

As soon as the lecture here ended, he was surrounded, and some people even asked him for WhatsApp and email accounts. He had never heard of the former software, and he signed up for a QQ email account, which is a free version.

It was obviously the first time Professor Everton encountered this kind of ten-digit mailbox, and he proofread it several times.

As a result, Yuan Zhengxin taught Qiao Yu a lesson and asked him to go back to Tian Yanzhen to ask for a serious work email address, and also grabbed the professors who asked Qiao Yu for the email address. You can

So Qiao Yu gave the most sufficient reason - to rush back to write a thesis, so he hurriedly "escaped" from Huaqing University back to the Mathematical Research Center of Yanbei University.

He can't really be blown away by sugar-coated bullets. His most important task now is to give the complete proof. Then disseminate it as quickly as possible and be accepted by the mainstream mathematics community.

Although he already has an idea, it still takes time to ensure the rigor of the proof process. But it won’t take much time. Qiao Yu stayed up until two in the morning last night. Now go back and have something to eat. He should be able to finish it all in the evening.

, and then send it to the instructor and Mr. Nang.

Communicate again when you leave.

I got up at 7 o'clock in the morning and finished the most difficult part before coming to attend the lecture.

What he has to do next is to see how his two mentors arrange it.

"In a classical geometric background, the Ambidexterity theorem relies on some kind of equivalence between local and global geometric objects. For example, local homological algebraic objects

However, after research, it was found that a type of singular points with conjugate ridge structures will produce abnormal behavior through high-order categories in the context of nonlinear geometry. This article temporarily names this type of singular points as Qiao points and represents them with P.

It can be globalized through the axioms of higher-order category theory.

Assume that the category C we use is a certain deformation category, in which the object is a module with specific geometric behavior. For the algebraic variety X, the objects in the category C can be expressed as a set of p-adic layers F.

Near the Joe point, the behavior of the local module M is affected by the ridge structure, causing its performance in higher-order category theory to no longer be a conventional object, but needs to be described by adding some complex deformation parameters: Floc=Defjoe

(M).

as follows:

Most of the professors have already arrived, and there is such an article on the table.

Here Def is the functor of the deformation category, which describes how the module M1 at the singular point P1 affects other singular points in the entire geometric space through deformation. The specific proof process

At half past nine in the evening, when Pan Jingyuan was invited to Qiuzhai's small conference room by a phone call from Yuan Zhengxin, he was already more than one person in the conference room. This invitation was not a standard paper, but the proof process was simple.

Clearly.

Pan Jingyuan could tell at a glance that this was probably written by that sixteen-year-old child, and it fit the stereotype he had formed of Qiao Yu.

From yesterday's counterexample that might invalidate their proof process to the public, today they gave a complete proof process, and even attended an academic lecture in the middle. If you are older, your efficiency may not be so high.

However, Pan Jingyuan's mentality was completely relaxed at this time.

People are like this. When you have a premonition that something bad is about to happen, the waiting process is actually the most painful. After the result is obtained, even if it is not a good result, the mentality can often be adjusted quickly.

Just like what his mentor Professor Dennis said, since a problem has been picked out, it is nothing more than thinking about how to solve it. It is very difficult, but it will never be more difficult than starting from scratch.

Anyway, even if those five papers are finally published, his next work will continue to think and study the problem of local geometry Langlands. Now he just has to prolong the process.

The proof process given by Qiao Yu is actually not long, and it only lasts for three pages including some cited documents.

Silently reading the proof process reminded him of the time when he first entered this field under the leadership of Dennis many years ago. At that time, he knew almost nothing about geometric representation theory, and most of the

I learned the basic knowledge under Dennis's guidance.

In a blink of an eye, it has been more than six years, almost seven years...

After sighing in his heart, Pan Jingyuan raised his head and looked around the conference room. He didn't find any loopholes. Among the professors who had previously thought Qiao Yu's idea was a bit whimsical, some were still frowning in thought, while others had already started whispering to the people around them.

.

Pan Jingyuan thought for a moment, then simply stood up, walked up to Yuan Zhengxin under the gaze of several people, and asked, "Mr. Yuan, I would like to send a copy of the proof process to Professor Dennis."

In fact, there is no need to ask, even if he sends it, it doesn't matter.

I ask specifically because there are Qiao points in it, which belong to a type of singular points discovered by Qiao Yu. Although it is not a great achievement on a mathematical level, it can be regarded as a new result.

Even out of the most basic courtesy, he still had to ask "Of course." Yuan Zhengxin smiled and nodded.

The minutes of the meeting include original videos, and professors from world-renowned universities participated. There is no possibility that Qiao Yu’s ideas will be plagiarized by anyone.

"Thank you." Pan Jingyuan nodded in greeting, then returned to his seat, took out his mobile phone and opened the commonly used scanning software, entered Qiao Yu's certification process into his mobile phone, and then sent it directly to Dennis's mailbox.

After doing this, Pan Jingyuan began to think about what he would say during the discussion.

As one of the seven members of the team that researched the geometric Langlands conjecture, Pan Jingyuan knew that everyone would be looking forward to him sharing his thoughts later. Even if he didn't want to speak, he couldn't avoid it, so he might as well be more generous.

He couldn't help it. After looking at it carefully, he couldn't find anything wrong with it... On the other side of the ocean, at the University of Berkeley.

Professor Univers Frank is receiving Professor Sam, one of the founders of the research team, in his office.

Apart from the slight discomfort caused by knowing something before, Frank was actually in a good mood during this period.

If nothing else goes wrong, their paper will be published soon. During this period, the promotion of several major partners and the holding of a series of lectures have greatly shortened the review process.

Most of the main reviewers have given agreed review opinions. It is basically impossible to conduct a double-blind review of this kind of results.

As early as thirteen years ago, Professor Dennis, one of the main leaders of the team, had published a paper: "Singular Support of the Coacervate and the Geometrized Langlands Conjecture." The world's mathematical community knows what they are studying.

There are only a few experts who can review papers of this level based on their qualifications and abilities, so there is no way to hide them.

Five years ago, Dennis proposed a series of ideas, such as "white noise".

In the field of classic signal processing, sound waves can be constructed from sine waves, whose frequency corresponds to the pitch in the sound. Anyone who has studied Fourier transform will know that this information can be used to write the sound into a combination of sine waves:

That is, just start with a sine wave with amplitude 1, then multiply the sine wave by the appropriate loudness factor, and then add these sine waves together. The sum of all different sine waves with amplitude 1 is "white noise".

According to the geometric Langlands program, the characteristic layer functions like a sine wave. Dennis identified something named the Poincare layer, which functions like "white noise". However, Dennis does not know whether he can combine each

The feature layers are all represented in the Poincare layer.

He and Sam also joined the team at this time.

They worked together to prove that each feature layer could contribute to "white noise" in some way, and sent the results to Dennis. After gaining approval, they joined Dennis' team and became an important other pole of the team.

Three years later, when it finally came time to bear fruit, Frank was naturally in a happy mood.

He has his own goals and plans, and every step now is making steady progress towards his desired goal.

His next topic has also been selected, which is the connection between a type of number theory problem and Riemann surface objects. It can basically be understood as the application of the geometric Langlands conjecture. This time he will form his own team, with him as the main leader

Overcome this problem.

In fact, research on this proposition has already begun. This is the guarantee for him to win the Fields Medal.

Although Frank has received the Ostrowski Award and the Clay Research Award, these awards are still not convincing enough. As an ambitious person, Frank has many ideas.

The Chinese mathematics community is in a period of drought.

The older generation of mathematicians are almost 70 or 80 years old. Most of the younger generation have taught abroad. Currently, no one of the newly growing generation of mathematicians has any hope of winning the Fields Medal.

At present, he seems to be the most promising one.

The world structure is now very clear. Although China and the United States have their own problems, looking at the world, they have become the two most competitive forces. With awards and honors around them, and many Chinese mathematicians

With the support of everyone, he can even hold up the banner of the Chinese mathematics community in the future.

To be honest, he thinks everything is good here, but being an academician is actually not interesting. If China can develop better in the future, he really doesn't mind returning to China like Mr. Yuan and building a new one named after him.

Mathematics Research Center and became one of the leaders in Chinese mathematics.
To be continued...