“..... The coefficient before the right end of the estimation equation (4.5) enters 6/2 is greater than 0. ”

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

Xu Chuan is very accurate in time control, saying that after ten minutes to explain the key points, it will definitely not be exceeded, and in the ninth and a half minutes of the beginning of the report meeting, he bowed slightly to the audience.

With his report, the audience also burst into warm applause.

The mathematics professors who were able to attend the lecture were interested in Xu Chuan's age, and they also studied the Weyl-Berry conjecture, spectrum asymptostic, inverse spectrum problems, and fractal drum theory.

Moreover, when participating in an academic presentation, it is an unspoken rule in the academic world to read the presenter'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 partially understood.

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

Unless they can pick out the fatal questions in the next questioning session, little one cares if they actually understand it.

......

Waiting for the applause from the audience to slow down a little, Xu Chuan re-spoke: "Thank you for listening, the above is the key point process of the Weyl-Berry conjecture to weaken the proof of form. ”

"This will be followed by a Q&A session."

Hearing this, in the front row of the audience, a resolute and powerful palm was raised.

After seeing who it was who raised his hand to ask questions, there was a slight commotion in the auditorium.

"Professor Fairman? Did he have any doubts? Still don't understand what this reporter is saying? ”

"No way, Professor Feuerman is the top expert in partial differential equations, I understand the explanation, it is impossible that he did not understand."

"Perhaps, he found some fatal loophole in the course of the explanation?"

"It's unlikely, right? Isn't the Weyl-Berry conjecture weakened form proof paper published in New Advances in Mathematics? This has been verified by Professor Gowers himself. ”

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

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

.......

On the stage, after seeing that it was Professor Fairman who raised his hand, Xu Chuan was also a little surprised.

After all, in his opinion, there should be no problem with this elder.

However, since the other party raised his hand to ask a question, he could not take it as a blind eye, and after motioning for the other party to ask a question, Professor Fehrman stood up.

"I just noticed that in the course of the presentation, you mentioned that you can use the Dirichley field to limit the fractal dimension and the spectra of the fractal measure of the Ω, but this does not seem to be related to your paper on the weakened form proof of the Weyl-Berry conjecture, could you please tell us about it?"

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

In the briefing, the questions raised by the questioners are generally based on the content of the reporter's report.

And this complementary theorem, although a bit out of scope, is still in the category of questioning.

Hearing this, a trace of surprise flashed in Xu Chuan's eyes, and he briefly mentioned it once, which was regarded as a supplement to the proof of the weak Weyl-Berry conjecture, but he didn't expect to be caught by the elder.

After thinking for a while and sorting out the thoughts in his mind, Xu Chuan spoke: "Limiting the fractal dimension and fractal measure spectrum of Ω through the Dirichley domain is not a weakened form of the Weyl-Berry conjecture in the proof paper. ”

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

"In the Weyl-Berry conjecture, it is assumed that the region Ω itself cannot directly define the differential operator, but the Laplace operator can be defined in the form of a difference method or a Dirichlet form to calculate its eigenvalues."

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

"The use of the Dirichley field to limit the fractal dimension of the Ω and the spectra of the fractal measure is a study I continued to do on the Weyl-Berry conjecture after proving the weakened form of the Weyl-Berry conjecture."

"So it's actually not related to the weakened form of the Weyl-Berry conjecture, but rather a supplement to the Weyl-Berry conjecture."

As he spoke, Xu Chuan looked at the staff standing on the side of the stage and said, "Can you please help me get a blackboard and a box of chalk?" ”

In the audience, the staff of the Princeton conference team did not hesitate, nodded and turned to leave.

For them, serving the mathematicians on stage is the only job, and they will do whatever it takes, as long as it is not too excessive or impossible to do.

Requests for chalkboards and chalk like the teenager's have happened many times in Princeton's history.

On the stage, Xu Chuan waited quietly.

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

Because this may lead other scholars to use your research methods to get ahead of the curve.

However, Xu Chuan did not mind revealing that the Dirichlet domain could be used to limit the fractal dimension of the Ω and the spectrum of the fractal measure.

Because this is only a small part of the process of proving the Weyl-Berry conjecture.

And in the math exchange meeting, you don't have to worry about being plagiarized by others by writing your own ideas and inspirations.

Whether it is a mathematics conference organized by the International Mathematical Union, a mathematics exchange held by Princeton, or a mathematics conference organized by other schools or organizations, there will be video recordings and information texts of the lectures.

These things are a fatal blow to plagiarists.

Unless it's some kind of entertainment that doesn't have a bottom line.

.......

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

“......-6/2）a^δ-n（1+o（1）））∑p|n*1/n^s.....”

"Definition: w(λ,j)=max|k-k(λ)|≤j",k≥0........"

So when λ → infinity, we have .......

On the blackboard, lines of arithmetic are outlined in pure white chalk, which is the essence of the spectrum that Dirichlet fields can use to define the fractal dimension of Ω and the spectra of fractal measures.

As Xu Chuan wrote, Professor Fairman, 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 table.

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

After Xu Chuan's board book began, the top mathematics professors behaved almost the same, and they saw something new from Xu Chuan's board book.

Behind these people, the other math professors are a little struggling.

Although the young man on the stage had already explained what he was going to write on, there was still a large percentage of math professors who couldn't keep up with the pace or couldn't understand what was written.

The method used by the Dirichlet domain of Xu Chuan's board book to limit the fractal dimension of the Ω and the spectrum of the fractal measure is extracted from the proof process of the Weyl-Berry conjecture, and not everyone can be as versatile as Tao Zhexuan.

This is true of these math professors, and even more so of the students who follow their mentors to see the world.

Although they have good eyesight that allows them to see the marks of the presenter on the stage, they are at a loss when confronted with the contents of the board on the blackboard.

"Expansion domain, transformation function, what is he trying to do?"

Following Zhang Weiping's side, Miao Pingbo frowned and stared at the blackboard on the stage, although he had read Xu Chuan's paper, his learning direction was not domain theory, so he was a little confused at the moment.

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

On the side, Zhang Weiping didn't turn his head after hearing the disciple's inquiry, and he had studied the basis of the Weyl-Berry conjecture to weaken the form proof paper, and it was not difficult for him to understand these things.

Suddenly, Zhang Weiping suddenly shook his head and sighed: "This kid's talent in mathematics is really strong, but it's a pity that he went to physics at South University." ”

......

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

Writing once again about the way Dirichlet limits the fractal dimension of the Ω and the spectra of fractal measures made him feel a little strange in his heart, like the figure of an inspired white dove crossing his mind, but it was not very clear.

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

With a slight sigh in his heart, Xu Chuan was about to finish the board book, his eyes fell on the data he had just written, and the white chalk in his hand stayed at a distance of less than one centimeter from the blackboard, and then the whole person was stunned for a long time.

........。