Great Country Academician

". Make the coefficient before the right-hand side of the estimated formula (4.5) enter 6/2 greater than 0."

"Therefore, the connected fractal area proves that the Weyl-Berry conjecture is valid in the weakened form!"

Xu Chuan was very precise in controlling the time. He said that after explaining the key points in ten minutes, he would never exceed it. At the ninth and a half minutes of the report meeting, he bowed slightly to the audience.

Following his report, there was warm applause from the audience.

Mathematics professors who can come to listen to the report, even if they are interested because of Xu Chuan's age, have researched in the fields of Weyl-Berry conjecture, spectral asymptotics, inverse spectral problems, fractal drum theory, etc.

Moreover, when participating in an academic report, it is an unspoken rule in the academic world to read the speaker's paper at least once, and it is also a necessary etiquette.

Therefore, the professors who participated in this report meeting basically understood Xu Chuan's explanation, or at least understood part of it.

As for those students who follow the teacher to expand their horizons, who cares what they think?

Unless they can come up with the killer question in the ensuing questioning session, few people care if they really understand it.

Waiting for the applause from the audience to slow down, Xu Chuan said again: "Thank you for listening, the above is the key point process of the weakened form proof of the Weyl-Berry conjecture."

"Next will be a question and exchange session."

Hearing this, a resolute and powerful hand was raised in the front row of the auditorium.

After seeing who raised their hands to ask questions, there was a slight commotion in the auditorium.

"It's actually Professor Fellman? Does he have any doubts? Or did he not understand the reporter's explanation?"

"Impossible. Professor Fellman is the top expert in partial differential equations. I understand the explanation. It is impossible for him not to understand."

"Perhaps, he discovered some fatal loophole during the explanation?"

"It's unlikely, right? Isn't the Weyl-Berry conjecture weakening form proof paper already publicly published on Advances in Mathematics? This has been personally verified by Professor Gowers."

"What if, what if it's a loophole that Professor Gowers didn't notice?"

"That's really bad news for the young reporter."

On the stage, Xu Chuan was also a little surprised to see that it was Professor Fellman who raised his hand.

After all, in his opinion, there shouldn't be any problems with this boss.

But since the other party raised his hand to ask a question, he couldn't ignore it. After signaling the other party to ask a question, Professor Fellman stood up.

"I just noticed that in the course of the report, you mentioned that the fractal dimension of Ω and the spectrum of fractal measures can be restricted by the Dirichlet field, but this seems to be consistent with the weakened form of the Weyl-Berry conjecture you published. The paper seems to be unrelated, can the reporter please explain it?"

Professor Fairman stood up, looked at Xu Chuan on the stage and asked.

In the report meeting, the questions raised by the questioners generally revolve around the contents of the report.

Although this supplementary theorem is a bit out of scope, it still belongs to the category of questions.

Hearing this, Xu Chuan's eyes flashed with surprise, and he briefly mentioned it as a supplement to the proof of the weak Weyl-Berry conjecture, but he did not expect to be caught by this big guy.

After thinking about it for a while, and sorting out the ideas in his mind, Xu Chuan said: "Using the Dirichlet field to limit the fractal dimension of Ω and the spectrum of the fractal measure is not a weakened form of the Weyl-Berry conjecture. middle."

"In the previous reports and the papers published in "New Advances in Mathematics", I have described that in the Weyl-Berry conjecture, it also includes the assumption that the region Ω itself is a fractal region."

"In the Weyl-Berry conjecture, it is assumed that the differential operator cannot be directly defined on the area Ω itself, but the Laplacian operator can be defined by the differential method or the Dirichlet form to calculate its eigenvalues."

"If it can be proved that the fractal dimension and fractal measure of Ω are spectrally invariant, then the Weyl-Berry conjecture can become a theorem."

"The fractal dimension of Ω and the spectrum of fractal measures are restricted by the Dirichlet field. This is my continued research on the Weyl-Berry conjecture after proving the weakened form of the Weyl-Berry conjecture."

"So it actually has nothing to do with the weakened Weyl-Berry conjecture, but a supplement to the Weyl-Berry conjecture."

As he said that, Xu Chuan looked at the staff standing beside the stage, and said, "Can I trouble you to fetch a blackboard and a box of chalk for me?"

Under the stage, the staff of the Princeton conference affairs group nodded without any hesitation, turned and left.

For them, serving the mathematicians on stage is the only job, no matter how outrageous the request is, as long as it is not too excessive or impossible to meet, they will do it.

Requests like this teenager for a blackboard and chalk have occurred countless times in Princeton's past history.

On the stage, Xu Chuan waited quietly.

Generally speaking, if a mathematician is conducting research on a certain conjecture, he will hardly disclose his research methods to the outside world.

Because it may cause other scholars to use your research methods to get ahead of others.

However, Xu Chuan does not mind revealing that the Dirichlet field can be used to limit the fractal dimension of Ω and the spectrum of fractal measures.

Because this is just a small piece in the process of proving the Weyl-Berry conjecture.

And there is no need to worry about being copied when writing your own ideas and inspirations on the blackboard at the mathematics exchange meeting.

Whether it is the mathematics conference held by the International Mathematical Union, the mathematics exchange meeting held by Princeton, or the mathematics meeting held by other schools or organizations, the video recordings and information texts of the reports will be kept.

These things are a fatal blow to plagiarists.

Unless it is some entertainment program that does not have a bottom line.

Soon, the staff of the conference affairs group dragged the blackboard over, and Xu Chuan took the chalk and thanked him.

".C≤2γμ*n(n-6/2)a^δ-n(1+o(1)))∑p|n*1/n^s"

"Definition: ω(λ, J)=Max|k-K(λ)|≤J", k≥0"

Then when λ→infinity, we have.

On the blackboard, pure white chalk outlines lines of calculation formulas, which is the essence of the Dirichlet field can be used to limit the spectrum of fractal dimensions and fractal measures of Ω.

Following Xu Chuan's writing, the pupils of Professor Fellman, who was still standing in the audience, suddenly shrank.

Professor Deligne, who was sitting next to Professor Fellman, narrowed his eyes slightly, staring sharply at the blackboard on the stage.

At the same time, Professor Zhang Weiping was sitting with Professor Zhang Weiping on the other side. Professor Tao Zhexuan, who had chatted with Xu Chuan the day before yesterday, also sat up straight, wiped the lens with the corner of his clothes and put it on again.

After Xu Chuan started writing on the blackboard, the top mathematics professors behaved almost the same. They saw something new from Xu Chuan's writing on the blackboard.

And behind these people, other mathematics professors will struggle.

Even though the young man on the stage had already explained what he was going to write on the blackboard before that, a large part of mathematics professors still couldn't keep up with the rhythm, or couldn't understand what was written on the blackboard.

The method used by Xu Chuan’s Dirichlet field to limit the fractal dimension and fractal measure spectrum of Ω is extracted from the proof process of the Weyl-Berry conjecture. Not everyone can be as versatile as Terence Tao of.

These mathematics professors are like this, and the students who follow their tutors to see the world are even more miserable.

Although they have good eyesight and can see clearly the strokes of the speakers on the stage, they are at a loss when facing the content written on the blackboard.

"Extension, transformation function, what is he trying to do?"

Following Zhang Weiping, Miao Pingbo frowned and stared at the blackboard on the stage. Although he had read Xu Chuan's thesis, he was not studying domain theory, so he was a little confused at the moment.

"To put it simply, he built a new fractal framework through the method of field expansion, and then limited the fractal dimension of Ω and the spectrum of the fractal measure, so that the numbers of these two pieces have a calculation method .”

On the side, Zhang Weiping replied without turning his head after hearing the disciple's question. Having studied the basis of the Weyl-Berry conjecture weakened form proof paper before, it is not difficult for him to understand these things.

Suddenly, Zhang Weiping shook his head and sighed: "This kid is really talented in mathematics, but it's a pity that he went to Nanjing University for physics."

On the stage, Xu Chuan didn't care about the discussion off the stage, his attention was all on the blackboard in front of him.

Once again writing Dirich Rayfield's method of limiting the fractal dimension and fractal measure spectrum of Ω, he felt a little strange feeling in his heart, like the figure of an inspired white dove across his mind In my heart, but not very clear.

In order to figure it out, Xu Chuan filled the blackboard in front of him with calculations in one go, but in the end he still failed to capture the sudden and wonderful feeling.

Sighing slightly in his heart, Xu Chuan was about to finish the writing on the blackboard, his eyes fell on the data he had just written, and the white chalk in his hand stayed at a position less than one centimeter from the blackboard, and then the whole The person just froze there, not moving for a long time.