Chapter 110: That Touch of Inspiration White Dove (Third update, please subscribe for a monthly ticket)
".Making the coefficient before entering 6/2 on the right side of the estimated equation (4.5) greater than 0."
"Therefore, this connected fractal area proves that the Weyl-Berry conjecture is true in the 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 understand all the explanations. There's no way he doesn't understand."
"Perhaps he discovered some fatal loopholes during the explanation?"
"It's unlikely, right? Hasn't the paper on the weakened formal 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 to be unrelated. Can the reporter please explain 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 fractal measures 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."< br>
"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."
"Limiting the fractal dimension and the spectrum of fractal measures of Ω through the Dirichlet domain is the research I continued to do on the Weyl-Berry conjecture after proving the weakened form of the Weyl-Berry conjecture."
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"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 around 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 methods to take the lead.
However, Xu Chuan did not mind revealing that the Dirichlet field can be used to limit the fractal dimension of Ω and the spectrum of the fractal measure.
Because this is just a small piece in the process of proving the Weyl-Berry conjecture.
Moreover, you don’t have to worry about being plagiarized when writing your ideas and inspirations on the blackboard at mathematics exchange meetings.
Whether it is a mathematics conference held by the International Mathematical Union, a mathematics exchange meeting held by Princeton, or a mathematics meeting held by other schools or organizations, the video recordings and information texts of the lectures will be retained.
These things are a fatal blow to plagiarists.
Unless it's some entertainment program that doesn't have a bottom line.
Soon, the staff of the conference team dragged the blackboard over. Xu Chuan took the chalk and said thank you.
".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"
So when λ→infinity, we have.
On the blackboard, pure white chalk outlines rows of calculations. This is the essence of how the Dirichlet field can be used to limit the fractal dimension of Ω and the spectrum of fractal measures.
As Xu Chuan wrote, Professor Fellman's pupils, who were still standing in the audience, suddenly shrank.
Professor Deligne, who was sitting next to Professor Fellman, narrowed his eyes slightly and stared sharply at the blackboard on the stage.
At the same time, sitting with Professor Zhang Weiping on the other side, Professor Tao Zhexuan, who had chatted with Xu Chuan just the day before, also sat up straight, wiped his lenses with the corner of his clothes and put them on again.
After Xu Chuan's blackboard writing began, 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 are having a hard time.
Although the young man on the stage had already explained what he wanted to write on the blackboard before, there were still a large number of mathematics professors who couldn't keep up with the rhythm or couldn't understand what was being written.
The method used by Xu Chuan's Dirichlet field to limit the fractal dimension and spectrum of fractal measures of Ω is excerpted from the proof process of the Weyl-Berry conjecture. Not everyone can be as omnipotent as Terence Tao. of.
These mathematics professors are like this, and the students who come with their tutors to see the world are even worse.
Although they have good eyesight that allows them to see clearly the strokes of the speaker on the stage, they are at a loss when facing the content written on the blackboard.
"Expanding the domain, transforming the function, what does he want 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 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 domain expansion, and then limited the fractal dimension of Ω and the spectrum of the fractal measure, so that the numbers in these two pieces can be calculated. .”
On the side, Zhang Weiping replied without turning around after hearing the disciple's inquiry. He had studied the basis of the Weyl-Berry conjecture weakened form proof paper before, and it was not difficult for him to understand these things.
Suddenly, Zhang Weiping suddenly shook his head and sighed: "This guy is really talented in mathematics. It's a pity that he went to Nanjing University for physics."
On the stage, Xu Chuan did not pay attention to the discussion in the audience. His attention was on the blackboard in front of him.
Once again writing about the method of Dirichlet domain to limit the fractal dimension of Ω and the spectrum of fractal measure, he felt a strange feeling in his heart that he didn't know where to come from, like the figure of an inspired white dove crossing his head. In my mind, but not very clear.
In order to understand it, Xu Chuan filled the blackboard in front of him with calculations, but in the end he still failed to capture the sudden and wonderful feeling.
With a slight sigh in his heart, Xu Chuan prepared to finish the 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 The person just stood there stunned, not moving for a long time.
(End of chapter)