Chapter 107 Xu Chuan, what do you think? (Three updates, please subscribe for monthly tickets)
Xu Chuan just turned around and took two steps, when an invitation from Professor Terence Tao came behind him.
Stopping, he glanced with some confusion and asked, "Will Professor Schultz's report be at nine o'clock tomorrow morning?"
He had seen the arrangement of this mathematics exchange meeting before, and clearly remembered every report time that was worth listening to. Professor Schultz's report was one of his key goals this time.
Professor Schultz, like Terence Tao, is a rising star in the world of mathematics, but he is younger, less than 30 years old this year.
The two are hailed as the Twin Towers in the mathematics community, which shows that they have opened up a considerable gap between them and other peers.
"Yes, it was originally supposed to be ten o'clock in the morning, but Professor W.T. Gowers had to rush back to Cambridge because of something unexpected, so one of this afternoon's reports has been brought forward. These things should be sent to your email." Terence Tao explained with a smile.
"Oh, that's it. That's Professor Tao's trouble." Xu Chuan nodded, turned around and followed Tao Zhexuan's pace.
"It just so happens that we can continue to talk about issues with fractal boundaries, right?" Tao Zhexuan pushed up the frames of his glasses and looked at Xu Chuan with a smile.
When the two rushed to Auditorium 1 where Professor Schultz was giving the lecture, they found that the lecture had already begun.
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.
At this Princeton mathematics exchange meeting, Peter Schulz unsurprisingly explained his greatest achievement, the mathematical concept of quasi-perfect spaces.
This is a mathematical tool he created during his Ph.D., also called ‘P·S progressive field-geometric theory’.
This theory allows mathematicians to prove many unsolved mysteries in algebraic geometry and other fields. It also combines topology, Galois theory and p-adic numbers to form a new mathematics.
At present, this theory is very popular in the mathematics community, and it is a unique favorite in the field of number theory.
On the one hand, the inventor Schulz 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 mathematical community almost unanimously believes that the study of 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 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 spectrum asymptotic 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 field, and the work of Coates-Wiles and Coleman on the apparent reciprocity law shows that the above polynomials and ch(E/ C) The difference is just a fixed polynomial. ”
"You said that if we choose a suitable Garrod field as a finite commutative group, can we equate algebraic objects with p-adic analytic objects?"
On the side, Tao Zhexuan, who was sitting seriously and listening to the lecture, suddenly came over and asked in a low voice.
Xu Chuan frowned and asked: "The main conjecture of Iwasawa theory?"
Tao Zhexuan nodded and said, "Well, I was inspired when I just listened to Professor Schultz explaining his similar complete space theory. It might be worth trying. What do you think?"
Hearing this, Xu Chuan frowned and thought for a while before saying: "Consider 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 On, Λ is isomorphic to the power series ring Zp[[T]] with Zp as the coefficient, which is called the Iwasawa algebra."
"Back to the case of the expansion of the cycloid 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 effect of Zp; on the other hand, the gamma of Kn/K The Lois group acts on it, so An is the finite mode of the ring Zp[Gn]. Since Kn+1 to Kn has a natural mapping, and 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 the number field, which is a pure The algebraic object. And the cyclotomic unit is essentially an analytical object. ”
"From this perspective, it is probably very difficult to use a suitable Garrod field as a finite commutative group to equate algebras and p-adic numbers."
Hearing this, Tao Zhexuan fell into deep thought and said after a while: "But the limited expansion of the domain group should be able to solve this problem. This can be done by using Professor Schultz's similar complete space theory. This theory can expand the local domain. Arithmetic problems are simplified and expressed as combinations of specific features and feature domains"
Xu Chuan shrugged and said, "Sorry, I'm not sure about this aspect. I'm not familiar with Professor Schultz's 'P.S. Progressive Geometry Theory', otherwise I wouldn't be sitting here studying today. .”
He is indeed not familiar with this aspect. The theory of P·S agressive field-geometry is about algebra and geometry, while the P-adic number is about pure number theory. He basically didn’t know much about it in his previous life. The things he just talked about were before the Chinese New Year. Learn some knowledge about domain expansion.
Hearing this, Tao Zhexuan suddenly woke up: "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."
"But your knowledge really surprises me. I didn't expect that in addition to spectral asymptotics and connected areas with fractal boundaries, you also have such a profound understanding of group rings and finite fields."
"Are you really a college student 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 am doing this."
Hearing this, Tao Zhexuan sighed: "It seems that in the near future, we will welcome another new star in the world of mathematics."
After a pause, Tao Zhexuan continued: "Xu, how about you come to the University of California to study for a Ph.D.? I have some ideas about Iwasawa's theory. If you are interested, we can solve this problem together."
"I need help from someone regarding the group domain. You are very suitable, and we have a pleasant communication, right?"
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.
But unfortunately, he didn't understand a word.
Well, you can't say that. He understood the keywords group domain, Galois domain, and Iwasawa theory.
Unfortunately, he didn't know what the two people were talking about when they were put together.
He did not know Xu Chuan, but he knew Professor Terence Tao.
At first, he thought this was a student led by Professor Tao. He was just glad that he could sit next to the famous Professor Tao, and was going 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 didn't seem to be Professor Tao's student.
When did a new person appear in the world of mathematics who could communicate freely with Professor Tao like this?
He hasn't heard of it.
Moreover, Professor Tao personally invited him to study for a Ph.D. and to participate in the scientific research project of Iwasawa theory. This treatment
FK, he is so envious, as if he is sitting on a high lemon mountain, so sour!
I worked hard and wrote more than 8,000 words. It is too difficult for me to make 10,000 words per day, ε(┬┬﹏┬┬)3
(End of chapter)