Great Country Academician

In the auditorium, Xu Chuan was a little surprised when he heard Tao Zhexuan handing over the invitation.

After all, the gap between the two is too great.

Tao Terence is 41 years old this year, and has already won various top mathematics awards such as the Fields Medal, the Cray Research Award, the MacArthur Award, the Waterman Award, and the Mathematical Breakthrough Award.

In addition, he also holds various academic honors such as academician of the Royal Society where the sun never sets, foreign academician of the National Academy of Sciences of the United States, academician of the American Academy of Arts and Sciences, and national academician of Australia.

And now, he is just a college student who has proved the conjecture of world-class final difficulty.

The status gap between the two is too great.

Of course, mathematics does not pay much attention to these things. In the field of mathematics, strength is the most respected. As long as you are truly capable, let alone college students, even high school students and junior high school students can be respected by others.

As for the invitation, Xu Chuan's heartbeat was average.

Although Professor Tao Terence is the winner of the Fields Medal, Princeton has more Fields Medal winners. Although the University of California is very good, it can be said to be one of the top three existences in the United States after Pujaye. Under the circumstances, Princeton is undoubtedly stronger.

So he directly declined Professor Tao's invitation.

Hearing Xu Chuan's refusal, Tao Zhexuan gave a moment of regret, but he also knew that the most suitable school for the boy in front of him was not the University of California, Berkeley, but the one under their feet.

In terms of mathematics alone, Princeton can beat all other colleges and universities in the United States.

After listening to Professor Schultz's report, Xu Chuan also returned to his hotel room.

After making a phone call to ask the hotel waiter to deliver a dinner, he took out his notebook and pen from his schoolbag and began to sort out today's harvest.

Whether it is the "P·S Advancement-Geometric Theory" explained by Professor Schultz at the report meeting, or the communication between the two when he met Professor Terence Tao, he has brought him a lot of feelings and mathematical knowledge.

Taking advantage of the clearest memory in his mind, recording these things again will help him deepen his understanding of these knowledge.

"The main conjecture of Iwasawa's theory: ch(A)=ch(E/C), A is an ideal group of number fields, and is a pure algebraic object. The centroidal unit is essentially an analytic object."

"In fact, let ζ(p, s)=ζ(s)·(1 ps)=∑p|n*1/n^s, this function is called p-advance ζ function, it is a continuous function on Zp, And its value at negative integers can be represented by a first polynomial interpolation of Zp[T]"

"."

After sorting out the gains in his mind, Xu Chuan pondered over and over whether these gains could be applied to certain aspects.

This is his unique habit.

It is true that mathematics needs inspiration, but inspiration is based on knowledge reserves.

There is a saying that "opportunities are only reserved for those who are prepared". If you are not prepared, you will not be able to catch inspiration when it comes.

"Take a suitable Garrod field as a finite commutative group, equating algebraic objects to p-adic."

When the black signature pen in his hand recorded a string of characters in the white notebook, a flash of lightning flashed in Xu Chuan's mind.

"Wait. The elements of the Galois field can be generated by the primitive polynomials on the field. The fields obtained by the primitive polynomials all have 0 for addition and 1 for multiplication. The primitive polynomial is a prime polynomial."

"Although it is a finite field, the Dirichlet field can be expanded to infinity. Is it possible to construct a field value through the expansion of the number field, and then turn it to a high latitude, and then use the Dirichlet field to adjust the value of Ω Spectrum of fractal dimension and fractal measure?"

"The ultimate requirement of the Weyl-Berry conjecture is to prove that it is a spectral invariant of any fractal dimension and fractal measure. If the boundary points can be given, then the spectrum of Ω's fractal dimension and fractal measure should be determined."

"This idea was indeed my inspiration at the beginning, but I didn't have enough basic knowledge to allow me to check it. Now it seems that this inspiration is still a little flawed, but it doesn't matter, I can try it first."

Staring at the information recorded on the manuscript paper, Xu Chuan fell into deep thought.

When he had a cold last year, he had been inspired to prove the Weyl-Berry conjecture, but he couldn't check it because he didn't have enough basic mathematics.

But today, after listening to Professor Schultz's lecture on "P·S Advancement-Geometric Theory" and the discussion with Professor Terence Tao, this opportunity seems to have arrived.

After realizing this, Xu Chuan got up and picked up the landline next to the bed to call the waiter in the lobby on the first floor and asked them to bring up a stack of manuscript paper or printing paper.

This is a free and must-have service in any hotel in Princeton.

Because this is a sacred place for mathematics, no one knows whether a certain mathematician is staying in the hotel, or whether he suddenly has an inspiration one night.

Therefore, for the sake of academics, Princeton has done its best in all services.

Soon, the hotel waiter brought over a thick plate of manuscript paper, along with a word of blessing.

"Good luck, sir."

But Xu Chuan didn't pay attention to it. He was still immersed in the idea in his mind at the moment. After Wushen took the manuscript paper from his brother, he closed the door with a bang.

The little brother at the door didn't mind. Working here, he has seen too many mathematicians, and also seen a lot of 'weirds'.

The customer in this room couldn't even be blamed. He ignored him, which only showed that he was immersed in thinking about a certain problem at the moment.

Although it doesn't look like a mathematician at a young age, there are not no young mathematicians.

For example, Professor Terence Tao stayed in their hotel more than ten years ago, and that Daniel also solved a mathematical conjecture in their hotel.

The back room is reserved as a room with special significance and is rarely opened to the public.

After receiving the manuscript paper from the waiter, Xu Chuan returned to the wooden table again.

The white manuscript paper with a bit of beige was spread on the table, and the black ballpoint pen began to outline mathematical symbols on it.

".Starting from Weyl's theorem 3.2, construct a bounded and connected open set Ω, let Ω be a bounded connected region in R (n≥2) that satisfies the above condition (C), and its boundary has inner Minkowski dimension δ∈ (n-1, n), then there is λ→+∞, and there are:

N(λ)-(λ)≤-Cn, δ(λ/π)δ/2Pn(t+o(1))+o(δλ/π)

"."

"Assuming Ω(a) is a connected area, the side length of each square is Li=a(i+1)-a(i), the function a(x) is strictly monotonically increasing, and limf(x→∞ )=limf(x→∞)(a(x+1)-a(x))=0"

"It is further required that the area of ​​Ω(a) is bounded, namely: |Ω(a)|2=∑∞/f(i=0) li

"Computing bounded inner Minkowski dimension 6 and Minkowski capacity over 6-dimensions"

"."

Starting from the last inspiration, Xu Chuan defined the fractal dimension and the spectral invariant of the fractal measure conjectured by Weyl-Berry to a high-latitude boundary, and then used the Dirichlet function field to convert the Laplacian and Laplacian Plath's hyperbolic equation, and then expand it.

A graceful inspiration erupted in his mind again. Unlike last time, this time, he had enough basic knowledge for him to set up stairs to follow the footsteps of inspiration.

Immersed in the process of solving problems and proving him, he is like a criminal policeman who is collecting evidence bit by bit at the crime scene, finally bringing them together and weaving them into a solid and reliable shackle to arrest the suspect hidden behind the scenes Same.

He is now collecting all kinds of available and reliable mathematical knowledge bit by bit, twisting them into a reliable hemp rope, and then connecting the wooden boards of various mathematical theorems and calculation data to form a pair of reliable stairs leading to The final Weyl-Berry conjecture.

From the evening of the second day to the late night of the third day, for nearly thirty hours, Xu Chuan did not close his eyes.

Except for going downstairs to eat, he never stepped out of this small hotel room.

So much so that after missing the evening party on the second day and the exchange meeting and evening party on the third day, his brother Lin Feng called him on his mobile phone.

Hearing the vibration of the phone, Xu Chuan pressed it without looking at it.

But the other party seemed to be persistent and called one after another, which made Xu Chuan recover from his scattered thoughts.

"Hey, Brother Lin, what can I do for you?"

With a tired voice, he passed along the mobile phone. On the other end of the phone, Lin Feng asked with concern: "Are you okay? Xu Chuan, did you catch a cold or something? You didn't come to today's exchange meeting or party. You missed such an important moment."

"I'm fine. I've been a little inspired these two days, and I'm thinking about things in the room."

Xu Chuan stared at the proof data on the manuscript paper and replied.

For him, if he missed the exchange meeting and evening party on the second and third days, he would just miss it.

Although the exchange meeting is important, it is completely insignificant compared to what he has gained in the past two days.

The busyness of nearly thirty hours without closing eyes was not fruitless. Using the Dicret function field to convert the Laplacian operator and the Laplacian hyperbolic equation, he finally defined a fractal through the differential equation framework, he successfully made the boundary Ω measurable under this fractal framework.

At this point, there is only one last step away from proving the Weyl-Berry conjecture, that is how to prove that the fractal dimension and fractal measure of Ω are spectrally invariant.

As long as this problem is solved, the Weyl-Berry conjecture becomes the Xu-Weyl-Berry theorem.

In comparison, the reports lost at the exchange meeting and the conversations with others at the evening party are insignificant.

"Research question? What research question? Forget it, as long as you have nothing to do, remember to rest early, and don't forget that you have a report meeting tomorrow afternoon."

On the other end of the phone, Lin Feng's voice came over.

He hasn't seen Xu Chuan in the past two days, and he hasn't seen any familiar people around him, so he's a little worried about what happened to this little junior brother here.

After all, this is the first time I have come to the United States, and I am not familiar with the place where I live. In addition, the United States does not prohibit guns, so it is still a bit unsafe.

As for now, since he was only studying the problem in the hotel room, it would be fine.

Although it is a pity to miss the exchange meeting and evening party, it is as long as people are free.