Great Country Academician

After the opening ceremony and awards ceremony on the first day, the exchange party was ushered in.

The exchange party was held at Wenjin International Hotel. As the country with the most abundant scientific research funds, Shuimu University, which has occupied the top ranking of university funding all year round, is also full of pride.

During the World Congress of Chinese Mathematicians, they directly contracted the right to use the Wenjin International Hotel for a week, which can be described as rich and powerful.

After dinner and a short rest, Xu Chuan went downstairs and followed Rong Zhizhuan to the auditorium of the exchange party.

It was only around 7:30 in the evening, half an hour before the exchange party started, but the auditorium was already crowded with people.

As soon as the two entered the venue, they bumped into Zhang Weiping and Hu Xingjian from Sun Moon University.

After greeting each other, Zhang Weiping moved his eyes and threw his student to Xu Chuan, who then followed Rong Zhizhuan.

It's a beautiful name, let the young people communicate more, and the two bad old men won't join in the fun together.

Looking at the two teachers who disappeared into the vast crowd in the blink of an eye, and Hu Xingjian who was standing aside, the corners of Xu Chuan's mouth twitched.

"God Chuan, please excuse me."

Hu Xingjian smiled shyly and embarrassedly, probably because he also felt that his mentor was a bit unreliable.

"You're welcome, this kind of communication will be a little more casual." Xu Chuan said with a smile, and walked towards the center of the venue with Hu Xingjian.

"Is this the first time for Brother Hu to participate in this kind of exchange party?" Xu Chuan asked while walking.

Hu Xingjian nodded, looked around and replied, "It's so formal, it's indeed the first time for me to participate. Has Chuan Shen participated before?"

"I participated in it once when I went to Princeton to give a report."

Xu Chuan nodded, took a few grapes from the white table in the venue, stuffed them into his mouth, and gave Hu Xingjian two by the way.

Hu Xingjian took the grapes, and his eyes showed yearning: "Princeton, the legendary holy land of mathematics, I heard that anyone who bumps into anyone on the road there is a top mathematics expert."

Xu Chuan smiled and said, "It's not so exaggerated, but Princeton still has a lot of masters in mathematics. Does Brother Hu have any idea to apply for a PhD in Princeton?"

"I must have an idea. After all, I study mathematics. If you study mathematics, you don't want to go to Princeton, but I probably won't have a chance."

Hu Xingjian shrugged and said, for mathematics students, Princeton is almost the ultimate goal, and there is no one who does not want to go.

But they can't recruit a few students in the whole of Huaguo a year, and the competition is fierce, which is countless times more difficult than the college entrance examination in Qingbei.

If you want to apply for Princeton in Huaguo, you have to stand at the top of the pyramid. Although he won the gold medal in Qiu Chengtong's college mathematics competition, it is still far from enough.

Xu Chuan smiled, and was about to say a few polite words to ask him to cheer up, but another voice came from his ear.

"Hi, Xu, I finally found you."

A somewhat rough voice sounded, and immediately, a man with a full beard walked over.

Seeing the person coming, Xu Chuan was taken aback for a moment, then a smile appeared on his face.

"Long time no see, Professor Avila."

The person who came was Professor Artur Avila, a Brazilian mathematics professor whom he had met at the Preston Mathematics Conference, and the two had chatted about mathematics all morning.

After enthusiastically shaking hands with the Brazilian mathematician, Xu Chuan asked curiously, "Why did you come to this Chinese Mathematician Conference?"

Although this World Congress of Chinese Mathematicians was held quite grandly, and many foreign mathematicians came to attend the conference, the main audience was Chinese and Chinese mathematicians.

Xu Chuan really did not expect Artur Avila to appear at this mathematics exchange meeting.

Artur Avila said with a smile: "I have a cooperative project with P University in your country on mathematical dynamical systems. I was here during this time, and I received an invitation letter, so I came to have a look, by the way. Let's see if I can meet you."

Xu Chuan suddenly nodded and said, "So that's the case, welcome."

On the side, Hu Xingjian watched the two exchange with curiosity, and waited anxiously for Xu Chuan's introduction.

After noticing Hu Xingjian's gaze, Xu Chuan introduced with a smile: "Brother Hu, this is Professor Artur Avila, a Brazilian mathematics professor who has won top mathematics awards such as the European Mathematical Society Award and the Fields Medal. Deep research in chaos theory, the field of dynamical systems, and spectral theory."

"Professor Avila, this is a student of one of my teachers, Hu Xingjian. His field of study is also spectral theory and Hilbert space."

After listening to Xu Chuan's introduction, Hu Xingjian was already stupid.

He didn't expect Xu Chuan to know such a super boss, and he could chat and laugh happily with him.

As a graduate student studying spectral theory, he had naturally heard the name Artur Avila.

This is one of the most famous mathematicians in Brazil, a winner of the Fields Medal, and a top expert in chaos theory, dynamical systems and spectrum theory. I did not expect to see him here today.

"Hi, nice to meet you." Arthur Avila smiled and held out his hand.

After Hu Xingjian was stunned for a moment, he shook his hands quickly after recovering: "Hello, Professor Avila, I have heard of your name for a long time. I have read your book "Spectral Fractal Region Reconstruction" on spectral theory. "."

Artur Avila smiled and said: "In terms of spectral theory and spectral fractals, Xu is the real expert. My achievements are completely worthless in front of him."

Hearing this, Hu Xingjian swallowed involuntarily.

Good guy, I know that Xu Chuan is awesome, but I didn't expect to be so awesome.

A Fields Medalist personally said that he is far inferior to him in the area he is good at, even if there is mutual praise, that is incredible.

This thigh, he hugged it!

After shaking hands with Hu Xingjian and saying hello, Arthur Avila turned his gaze back to Xu Chuan.

"Xu, when we met at Princeton last time, we talked about spectral theory and the spectrum of fractal dimensions and fractal measures, which gave me a lot of inspiration."

"Inspired by you, I have some new things I want to talk to you about recently, I wonder if you have time, is it convenient?"

Xu Chuan asked curiously, "Which aspect?"

Artur Avila: "The non-commutative harmonic analysis and automorphic form theory in the Langlands program, I don't know if you are familiar with or understand these two fields."

Hearing this, Xu Chuan frowned slightly, and said, "There are too many things in these two fields. I don't know which aspect you are referring to."

"Also, why did you suddenly start studying number theory and harmonic analysis?"

Xu Chuan looked curiously at Artur Avila. The Fields Medal winner is most famous for his research in the fields of chaos theory and dynamical systems. Spectrum theory is also involved, but number theory and harmonic analysis, he It seems that I have never heard of this professor doing research.

Arthur Avila laughs: "I'm not familiar with number theory and harmonic analysis, but I have some research in spectral theory and Laplacian operators."

"After chatting with you last time, I went through your proof of the Weyl-Berry conjecture."

"In your thesis, there is a rather quintessential approach in the field of Dirichlet functions to convert Laplacian and Laplacian hyperbolic equations, and the extension of the field and how to convert functions into subgroups and Links to intermediate domains and collections."

"I've been working on a method that seems to apply to some of the Langlands program problems."

"For example, some conjectures derived from the self-defense L function."

"You know, automorphic functions are generalized from circular functions, hyperbolic functions, elliptic functions, and other functions in elementary analysis, and automorphic L functions are defined by automorphic group representations."

"In the Langlands conjecture, automorphic L functions satisfy certain harmonious relations, and there is a unique factorization, which is reflected in the automorphic group representation, which is the functor property between automorphic group representations."

"And this functor conjecture can be fully determined by the mapping between L groups, given a linear algebraic group, the relationship between its automorphic group representation on the base field and the group representation on a certain extension field is called a basis transformation, and is a special case of functorality."

".Can the method in your thesis also be applied to basic automorphic functions? Or, in some way, to make a deeper generalization of the Gaussian reciprocity law?"

After listening to Professor Artur Avila's words, Xu Chuan frowned and pondered, vaguely, as if he had captured something from these words.

On the side, Hu Xingjian, who was listening the whole time, looked at Xu Chuan and then at Professor Artur Avila with a dazed expression.

Meow, what are these things talking about?

He knows the Weyl-Berry conjecture, he also knows the Dirichlet function, and he has heard of the famous Langlands conjecture.

But after these nouns are connected together, why can't he understand a word?

Is it because he can't speak English?

But obviously he has a score of 7.9 in IELTS A class.

Suddenly, Hu Xingjian felt a wave of despair in his heart. Before that, he wanted to stand on the stage like Xu Chuan, but now it seems that the gap between the two is really not ordinary.

catch up? What did he use to catch up? He couldn't understand what they were saying.

Xu Chuan pondered, Hu Xingjian was in despair, and Professor Avila looked at Xu Chuan expectantly.

The three stood in the venue like this until another voice came.

"Professor Avila, you are here."

At the same time, a thin middle-aged man walked over.

"Professor Mo." Seeing the person coming, Professor Artur Avila nodded and greeted with a smile.

"Professor Avila, what's the matter?"

Seeing Xu Chuan who was contemplating at the side, Professor Mo asked suspiciously. Xu Chuan won the Morning Star Mathematics Award in the auditorium of Shuimu University in the afternoon, so it is impossible for him not to know him.

Artur Avila said with a smile: "I just talked about mathematics, maybe he has some ideas? He is thinking."

"Oh? Can I hear what you guys are talking about?" Hearing this, Professor Mo raised his eyebrows with interest and asked.

"Of course, mainly non-commutative harmonic analysis and automorphic form theory in the Langlands program"

Naturally, Avila would not refuse someone to exchange mathematics, and this Professor Mo is a researcher in number theory, so he might be able to communicate with him, so he simply repeated the theory and questions just now with a smile.

"Langlands Program, Automorphic Form Theory, what do you think?"

Hearing this, Mo Kun's eyes lit up, and he quickly asked, this happened to be one of the academic fields he studied.

Avila shook his head, looked at Xu Chuan and said, "I'm not very familiar with this aspect. If you have any ideas, I'm afraid you have to ask him. Maybe you can talk about it?"

It just so happened that Xu Chuan recovered from his contemplation, opened his mouth and was about to speak, when his eyes fell on Mo Kun who was beside him.

"Who is this?"

Xu Chuan looked curiously at the fourth person who appeared suddenly. The person who appeared here should be a mathematician, but this mathematician parent is quite special, with a very characteristic face. Not to mention a horse face, the bridge of the nose is close to the head There are still some protrusions, and the appearance is indeed ordinary.

"This is Professor Mo Kun from P University. He is an expert in number theory and number fields, and he is also a member of the project I have cooperated with P University this time."

"This is Xu Chuan, my good friend."

On the side, Arthur Avila introduced each other with a smile.

"Oh, Professor Mo, hello." Xu Chuan stretched out his hand and said hello.

Mo Kun shook hands with a smile, and said, "Hello, student Xu Chuan, I've heard of you before, and I saw you today, and you really deserve your reputation, young and promising."

"I just heard from Professor Avila that you are talking about non-commutative harmonic analysis and automorphic theory? Do you have any ideas, let's exchange ideas together?"

Xu Chuan didn't think too much, and said with a smile: "I have a little idea, but I don't know if it will work."

Hearing this, Mo Kun quickly asked, "What do you think?"

Xu Chuan: "Just now I talked with Professor Avila about automorphic forms and automorphic L-functions. Generally speaking, the sources of L-functions are composed of two types, arithmetic L-functions and automorphic L-functions. These two The latter are closely related, and according to Robert Langlands' conjecture, all meaningful L-functions come from automorphic L-functions."

"And the so-called automorphic form is a special kind of complex variable function, which satisfies the transformation law described by the automorphic factor under a certain discrete transformation group. Strictly speaking, the automorphic representation is not a group representation in the ordinary sense, but is the modulus on the overall Hecke algebra."

"When I was studying the Weyl-Berry conjecture before, I made good use of the fact that each boundary point of the Dirichlet function domain is regular, and it is a kind of boundary point, and I used it to complete the conversion Laplacian and Laplace hyperbolic equations."

"If we can use this to construct a group domain, we may be able to discover something."

"For example, the study of functors can provide a driving force for the Langlands program, and this type of research can generally be carried out under a framework called Howe duality or Theta correspondence."

"But now it seems possible to transform the Laplace operator by constructing a number field by studying the Dirichlet function, and then using its curvilinear equations to restrict to the dual reduction group to achieve partial functoriality."

"That might be a viable path."

Xu Chuan simply expressed some of the ideas he had just conceived.

Under normal circumstances, unless it is with the project team or a very friendly relationship, ordinary research scholars will not tell other colleagues, especially strangers, their thoughts and research in detail.

Because this may lead to your ideas being used by others or published first.

But since Professor Mo knew Avila and was a member of his project team, it would be fine to chat.

I have to say that Arthur Avila really brought him a huge surprise this time. He had never thought of applying this method to the field of number theory and group theory before.

But now, it seems like you can give it a try.

The Dirichlet function is indeed a super treasure in the function, and there are too many things that can be excavated.