Great Country Academician

Just as Xu Chuan turned around and took two steps, an invitation from Professor Tao Zhexuan came behind him.

Stopping in his tracks, he glanced suspiciously and asked, "Will Professor Schultz's report be at nine o'clock tomorrow morning?"

He had seen the formation arrangement of this mathematics exchange meeting before, and he clearly remembered every report time worth listening to. Professor Schultz's report was one of his key goals this time.

Like Terence Tao, Professor Schultz is a rising star in mathematics, but he is younger, less than 30 years old this year.

The two are hailed as the twin towers by the mathematics community, which shows that they have opened up a big gap with other peers.

"Yes, it was originally ten o'clock in the morning, but Professor W.T Gowers rushed back to Cambridge temporarily, so a copy of this afternoon's report was brought forward, and these things should have been sent to your mailbox." Terence Tao explained with a smile.

"Oh, that's the way it is. I'm going to trouble Professor Tao." Xu Chuan nodded and turned to follow Tao Zhexuan's pace.

"It's just that we can continue to talk about the problem of fractal boundaries, can't we?" Tao Zhexuan pushed the glasses frame and looked at Xu Chuan with a smile.

When the two rushed to Auditorium No. 1 of the report meeting where Professor Schultz was located, they proved that the report had already started.

After finding a seat and sitting down, Xu Chuan looked at the figure with shoulder-length curly hair on the stage, and began to listen carefully.

In this Mathematical Exchange Meeting in Princeton, Peter Schultz unsurprisingly explained his greatest achievement "mathematical concept of quasi-perfect space".

This is a mathematical tool he created during his Ph.D., also known as 'P·S Advancement-Geometric Theory'.

This theory allowed mathematicians to prove many unsolved mysteries in algebraic geometry and other fields, and also combined topology, Galois theory and p-adic numbers to form a new mathematics.

At present, this set of theories is very popular in the field of mathematics, and it is even more unique in the field of number theory.

On the one hand, the inventor Schultz himself used this theory to make many major breakthroughs in the Langlands program, which attracted the attention of many mathematicians.

On the other hand, P-adic numbers are the core of the field of number theory. For example, when Professor Wiles proved Fermat's Last Theorem, almost every step involved the concept of P-adic numbers.

Moreover, the current mathematics community almost agrees that the research on the grand unification of geometry and algebra may be based on P-adic numbers.

Oh, by the way, part of his previous research, the Weyl-Berry conjecture, is also related to P-adic numbers.

Therefore, Xu Chuan will attach great importance to Professor Schultz's report, hoping to get some inspiration from it, and then make a breakthrough in the asymptotic spectrum of the Weyl-Berry conjecture.

"Xu, we all know that the p-adic ζ function is an example of the p-adic L function, which embodies the analytic properties of the corresponding number fields, and the work of Coates-Wiles and Coleman on the law of apparent reciprocity shows that the above polynomials and ch(E/ C) just differ by a fixed polynomial."

"You said that if you choose a suitable Garrod field as a finite commutative group, can you equate algebraic objects with p-adic analytic objects?"

On the side, Tao Zhexuan, who was sitting and listening seriously, came over suddenly and asked in a low voice.

Xu Chuan frowned and asked, "The main conjecture of Yanze's theory?"

Tao Zhexuan nodded and said, "Well, I was inspired when I heard Professor Schultz explain his similar complete space theory. Maybe it's worth trying. What do you think?"

Hearing this, Xu Chuan frowned, thought for a while, and said: "Considering the system composed of the group ring Zp[Gn], since there is a natural limit mapping between Gn and Gn1, this system also has a projective limit Λ, in fact Above, Λ is isomorphic to the power series ring Zp[[T]] with Zp as the coefficient, which is called Iwasawa algebra.”

"Back to the expansion of the subcircle Zp. The ideal group of Kn is a finite commutative group, and its p part is An. On the one hand, because it is a p-order group, it has the function of Zp; on the other hand, the Gamma of Kn/K The Roi group acts on it, so An is the finite module of the ring Zp[Gn]. Since there is a natural mapping from Kn+1 to Kn, we can get the natural mapping from An+1 to An."

"From ch(A) = ch(E/C). It can be seen that A describes the ideal group of number fields, and is a purely algebraic object. The subcircle unit is essentially an analytic object."

"From this point of view, it may be very difficult to use a suitable Garrod field as a finite commutative group, and then equate algebra and p-adic numbers."

Hearing this, Tao Zhexuan fell into contemplation, and said after a while: "But the finite expansion of domain groups should be able to solve this problem, which can use Professor Schultz's similar complete space theory, which can achieve the local domain Arithmetic problems can be simplified as a combination of specific features and feature fields”

Xu Chuan shrugged and said, "Sorry, I'm not clear about this, I'm not familiar with Professor Schultz's 'P·S Advancement-Geometric Theory', otherwise I wouldn't be sitting here today to study .”

He is indeed not familiar with this aspect. P·S Adgressive-geometric theory is about algebra and geometry, while P-adic numbers are purely about number theory. He basically didn't know much about it in his previous life. What he said just now was before the Chinese New Year. Learn some things you learned when you expanded your domain.

Hearing this, Terence Tao woke up suddenly: "Oh, I almost forgot that you are only a freshman this year. Professor Schultz's similar complete space theory is indeed a bit difficult for college students to understand."

"However, your knowledge really surprised me. I didn't expect that in addition to spectral asymptotics and connected regions with fractal boundaries, you also have such a deep understanding of group rings and finite fields."

"Are you really a college student who is still studying for an undergraduate degree? Maybe you can try to learn more about this aspect in the future."

Xu Chuan smiled and said, "I'm doing this."

Hearing this, Tao Zhexuan sighed: "It seems that in the near future, we will welcome another new star in the mathematics world."

After a pause, Tao Zhexuan continued: "Xu, why don't you come to the University of California to study for a Ph. D.? I have some ideas about the main conjecture of the Yanze theory. If you are interested, we can solve this problem together."

"About the group domain, I need someone to help. You are very suitable, and we communicate and have a good time, don't we?"

On the side, a mathematics professor from Argentina looked at Tao Zhexuan and Xu Chuan in confusion.

WTF?

What are these two talking about?

Obviously, the mathematics professor listened to the entire conversation between the two.

Unfortunately, he didn't understand a word.

Well, you can't say that, he understands key words such as group field, Galois field, and Yanze theory.

It's a pity that he didn't know what these two people were talking about when they connected the front and back.

He didn't know Xu Chuan, but he knew Professor Terence Tao.

At the beginning, he thought it was a student brought by Professor Tao. He was glad that he could sit next to the famous Professor Tao, and planned to ask Professor Tao for advice after listening to Professor Schultz's report.

But as time passed, he became confused when the two communicated.

This young man doesn't seem to be Professor Tao's student.

When did the mathematics world produce a newcomer who could talk freely with Professor Tao like this?

He has never heard of it.

Moreover, Professor Tao personally invited him to study for a Ph. D. and to participate in the scientific research project of Yan Ze Theory.

FK, he is so envious, like sitting on a high mountain of lemons, so sour!

I worked my ass off and wrote more than 8,000 words. It is too difficult for me to write more than 10,000 words, ε(┬┬﹏┬┬)3