Chapter 110 That Touch of Inspiration

Chapter 110 That touch of inspiration~

".Making the coefficient before the right-hand side of estimated equation (4.5) enters 6/2 is greater than 0."

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

Xu Chuan controlled time very accurately. If he could explain the key points in ten minutes, he would never exceed it. At the ninth and a half minutes into the report meeting, he bowed slightly to the audience.

Following his report, the audience burst into warm applause.

Mathematics professors who were able to attend the lecture, even those who were interested because of Xu Chuan's age, also conducted research in the fields of Weyl-Berry conjecture, spectral asymptotics, inverse spectral problems, and fractal drum theory.

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

Therefore, the professors who participated in this lecture basically understood Xu Chuan's explanation, or at least partially understood it.

As for the students who come with their teachers to expand their horizons, who cares what they think?

Unless they can ask the killer question in the following Q&A session, almost no one cares whether they really understand.

After waiting for the applause from the audience to subside, Xu Chuan spoke again: "Thank you everyone for listening. The above is the key point process of the weakened formal proof of the Weyl-Berry conjecture."

"The next step will be a question and answer session."

Hearing this, a firm and powerful hand was raised in the front row of the audience.

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

"It's actually Professor Fellman? Is he confused? Or does he still not understand the speaker's explanation?"

"It's impossible. Professor Fehrman is a top expert in partial differential equations. I understood all the explanations. There's no way he didn't understand."

"Perhaps he discovered some fatal flaw during the explanation?"

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

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

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

On the stage, Xu Chuan was also a little surprised when he saw Professor Fellman raising his hand.

After all, in his opinion, there should be no problems with this big boss.

However, since the other party raised his hand to ask a question, he could not turn a blind eye. After signaling the other party to ask a question, Professor Fellman stood up.

"I just noticed that during the report, you mentioned that the fractal dimension and the spectrum of the fractal measure of Ω can be limited by the Dirichlet domain, but this seems to be consistent with the weakened form of the Weyl-Berry conjecture you published. The paper seems unrelated. Can you please tell me about it?”

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

At the report meeting, the questions raised by the questioner generally revolve around the content of the reporter's report.

Although this supplementary theorem is a bit out of scope, it still falls within the scope of the question.

Hearing this, Xu Chuan's eyes flashed with surprise, and he briefly mentioned it once as a supplement to the proof of the weak Weyl-Berry conjecture. Unexpectedly, the big boss caught his attention.

After thinking for a while and sorting out the ideas in his mind, Xu Chuan said: "Limiting the fractal dimension and the spectrum of Ω through the Dirichlet domain is not a weakened form of the Weyl-Berry conjecture. Proof paper "

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

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

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

"The Dirichlet domain is used to limit the fractal dimension and the spectrum of fractal measures of Ω. This is the research I continued to do 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 form of the Weyl-Berry conjecture, but a supplement to the Weyl-Berry conjecture."

With that said, Xu Chuan looked at the staff standing beside the stage and said, "Can you please bring me a blackboard and a box of chalk?"

In the audience, the staff of the Princeton conference team nodded without any hesitation and turned to leave.

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

This boy's request for a blackboard and chalk has happened countless times in Princeton's history.

On the stage, Xu Chuan waited quietly.

Generally speaking, if a mathematician is researching a certain conjecture, he will basically not disclose his research methods to the outside world.

Because this may lead to other scholars using your research method to get ahead.

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

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

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

".C≤2γμ*n（n1+o（1）））∑p|n*1/n^s"

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

So when λ→infinity, we have.

On the blackboard, pure white chalk outlined lines of formulas on it. This is the essence of how Dirichlet fields can be used to limit the spectrum of fractal dimensions and fractal measures of Ω.

As Xu Chuan wrote, Professor Feldman, who was still standing on the stage, suddenly contracted his pupils.

Professor Deligne, who was sitting next to Professor Feldman, narrowed his eyes slightly and stared at the blackboard on the stage with sharp eyes.

At the same time, Professor Terence Tao, who was sitting with Professor Zhang Weiping and had talked with Xu Chuan the day before, also sat up straight, wiped his glasses with the corner of his clothes and put them on again.

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

Behind these people, other mathematics professors were having a hard time.

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

The method of using Dirichlet fields to limit the fractal dimension and spectrum of fractal measure of Ω written on the blackboard by Xu Chuan was copied from the proof of the Weyl-Berry conjecture. Not everyone can be as omnipotent as Terence Tao.

These mathematics professors are like this, and the students who followed their mentors to see the world are even worse.

Although they have good eyesight that allows them to see every stroke of the reporter on the stage, they are at a loss when facing the content written on the blackboard.

"Expand the domain, transform the 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 paper, his study direction was not in the field of domain theory, so he was a little confused at the moment.

"Simply put, he constructed a new fractal framework by expanding the domain, and then limited the fractal dimension of Ω and the spectrum of fractal measure, so that the numbers in these two areas can be calculated. "

On the side, Zhang Weiping heard the disciple's question and replied without turning his head. He had studied the weakened form of the Weyl-Berry conjecture before, so it was 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 to study physics. "

On the stage, Xu Chuan didn't pay attention to the discussion below the stage, his attention was on the blackboard in front of him.

Writing once again the method of limiting the fractal dimension and spectrum of fractal measure of Ω by Dirichlet field, he felt a strange feeling in his heart, like the figure of a white dove of inspiration passing through his mind, but it was not very clear.

In order to understand, Xu Chuan covered the blackboard in front of him with formulas in one breath, but in the end he still failed to successfully capture the sudden strange feeling.

With a slight sigh in his heart, Xu Chuan was ready to finish this blackboard writing. His eyes fell on the data he had just written, and the white chalk in his hand stayed less than one centimeter away from the blackboard. Then the whole person just stood there, motionless for a long time.