After the opening ceremony and award ceremony on the first day, it was ushered in the networking evening.

The exchange party was held at the Wenjin International Hotel, and as the most abundant scientific research funding in China, Mizuki University, which occupies the first place in the list of university funding all year round, is also full of pride.

During the World Congress of Chinese Mathematicians, he directly contracted the right to use Wenjin International Hotel for one week, which can be described as wealthy.

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

It was only about half past seven in the evening, and it was still half an hour before the exchange party began, but the auditorium was already crowded.

As soon as the two entered the venue, they bumped into Zhang Weiping and Hu Xingjian of Riyue University.

After saying hello to each other, Zhang Weiping's eyes moved, and he threw his student to Xu Chuan, and he followed Rong Zhi to specialize.

In the name of beauty, let the young people communicate more, and the two of them will not join in the fun together.

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

"Kawajin, I'm sorry for you."

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

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

"Is it the first time for Brother Hu to participate in this kind of exchange party?" As he walked, Xu Chuan asked.

Hu Xingjian nodded, and replied while looking around: "This kind of formal, I am indeed the first time to participate, and Chuanshen has participated before?" ”

"I attended it once before when I went to Princeton to give a presentation."

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

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

Xu Chuan smiled and said, "How can it be so exaggerated, but there are still a lot of math masters in Princeton, does Brother Hu have the idea to apply for a PhD at Princeton?" ”

"There must be an idea, after all, I studied mathematics, and I don't want to go to Princeton if I study mathematics, but I probably don't have a chance."

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

However, people can't recruit a few students in the whole of China in 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 China, you have to stand at the top of the pyramid, and although he won the gold medal in the Qiu Chengtong Collegiate Mathematics Competition, it is still far from enough.

Xu Chuan smiled, and was about to politely say a few words like cheering him, but another voice came from his ear.

"Hey Xu, I've finally found you."

A somewhat gruff voice sounded, and then a man with a full beard walked up.

Seeing the visitor, Xu Chuan was stunned for a moment, and then a smile appeared on his face.

"Long time no see, Professor Avila."

The person who came was Professor Artur Ávila, a Brazilian mathematics professor whom he had met at the Prereston Mathematical Society, and the two had a morning chatting about mathematics.

After shaking hands with the Brazilian mathematician enthusiastically, Xu Chuan asked curiously, "Why did you come to this conference of Chinese mathematicians?" ”

Although the World Congress of Chinese Mathematicians was held quite grandly, and many foreign mathematicians came to participate, it was mainly faced with Chinese mathematicians and Chinese mathematicians.

Artur Ávila will appear at this mathematics exchange meeting, Xu Chuan really didn't expect it.

Artur Avila smiled: "I have a collaborative project with your country's University of Science and Technology on mathematical dynamical systems, and I happened to be here during this time, and I received an invitation, so I came over to have a look, and by the way, I can see if I can meet you." ”

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

On the side, Hu Xingjian watched the two communicate with curiosity, waiting for Xu Chuan's introduction.

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

"Professor Avila, this is a student of one of my teachers, Hu Xingjian, and his research field is also spectrum 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 elder and still be able to talk and laugh with him.

As a graduate student in the theory of genealogy, it was natural that he had heard the name Artur Avila.

This is one of the most famous mathematicians in Brazil, a Fields Medal winner, and a top expert in the field of chaos theory, dynamical systems and spectral theory.

"Hello, nice to meet you." Artur Ávila smiled and held out his hand.

Hu Xingjian was stunned for a moment, then quickly clasped his hands after coming back to his senses: "Hello, Professor Avila, I have heard your name for a long time, I have read your work on spectral theory, "Spectral Fractal Region Reconstruction". ”

Artur Avila smiled and said, "In terms of spectral theory and spectral fractals, Xu is a real expert, and my achievements are not worth mentioning in front of him. ”

Hearing this, Hu Xingjian couldn't help but swallow his saliva.

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

A Fields Medal said that his area of expertise was far inferior to him, even if there was an element of mutual praise, it would be terrible.

This thigh, he holds it!

........

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

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

"Inspired by you, I have something new to talk to you about recently, I wonder if you have time, is it inconvenient?"

Xu Chuan asked curiously, "Which one?" ”

Artur Avila: "I don't know if you are familiar with or understand these two fields of noncommutative harmonic analysis and self-defending form theory in the Langlands Program. ”

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 study number theory and harmonic analysis?"

Xu Chuan looked at Artur Ávila curiously, the most famous research of this Fields Medal winner is in the field of chaos theory and dynamical systems, and spectral theory is also involved, but he seems to have never heard of this professor in number theory and harmonic analysis.

Artur Avila laughs: "I'm not familiar with number theory and harmonic analysis, but I have some research in spectral theory and the Laplace operator. ”

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

"In your paper, there is a rather quintessential approach to the transformation of the Laplace operator and the Laplace hyperbolic equation by the Dirichlet function domain, as well as the expansion of the domain and how to transform the function into subgroups and establish connections between intermediate fields and ensembles."

"I seem to be working on some of the problems of the Langlands Program."

"For example, some conjectures derived from the self-defending l function."

"You know, the automorphic function is generalized from the circular function, the hyperbolic function, the elliptic function, and other functions in elementary analysis, and the automorphic l function is defined by the automorphic group representation."

"In the Langlands conjecture, the self-supporting l functions satisfy certain harmonious relations with each other, and there is a unique factorization, which is reflected in the self-keeping group representations, which is the functivity between the self-respecting group representations."

"And this functivity conjecture can be determined entirely by the mapping between l-groups, given a linear algebraic group, the relationship between its self-respecting group representation on the basis domain and the group representation on an expanded domain is called the basis transformation, which is a special case of functivity........."

“............ Can this approach in your paper be applied to the underlying self-defense function as well? Or, in some way, to promote Gaussian reciprocal law at a deeper level? ”

After listening to Professor Artur Avila's words, Xu Chuan frowned and thought, vaguely, he seemed to have captured something from these words.

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

He's meowing, what is this talking about?

The Weyl-Berry conjecture he knew, the Dirichlet function he knew, and the famous Langlands conjecture.

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

Is he not good at English?

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

Suddenly, Hu Xingjian felt a wave of despair in his heart, he had thought about standing on that stage like Xu Chuan, but now it seems that the gap between the two is really not ordinarily big.

Pursue? What did he chase? He began to understand what people were saying.

Xu Chuan pondered, Hu Xingjian was stunned and desperate, and Professor Avila looked at Xu Chuan expectantly.

The three of them stood in the middle of the hall until another voice was heard.

"Professor Avila, you're here."

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

"Professor Mo." Seeing the visitor, Professor Artur Ávila smiled and nodded in greeting.

"Professor Avila, what's going on?"

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

Artur Ávila laughed: "Just talked about a little math, he might have some ideas?" Thinking about it. ”

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

"Of course, the main thing is the non-commutative harmonic analysis and the theory of self-contained forms in the Langlands program........"

Someone communicates mathematics, Avila naturally will not refuse, and this Professor Mo is a researcher in number theory, maybe they can communicate together, so he smiled and simply repeated the theory and problem just now.

"What do you think about the Langlands program, the theory of self-disciplined form?"

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

Avila shook her 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 communicate?" ”

At this moment, Xu Chuan came back from his contemplation, opened his mouth and was about to speak, when his eyes fell on Mo Kun on the side.

"Who is this?"

Xu Chuan looked curiously at the fourth person who suddenly appeared, who appeared here should be a mathematician, but this mathematician is very special, his face is very distinctive, not to mention a horse face, the bridge of the nose is still a little protruding, and his appearance is indeed average.

"This is Professor Mo Kun of P University, an expert in number theory and number domains, and a member of the project I have collaborated with P University this time."

"This is Xu Chuan, my friend."

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

"Oh, Professor Mo, hello." Xu Chuan took the initiative to stretch out his hand and said hello.

Mo Kun shook his hand with a smile and said, "Hello, classmate Xu Chuan, I have heard of you earlier, and when I saw you today, I really lived up to my reputation, young and promising." ”

"I just heard from Professor Avila that you were talking about noncommutative harmonic analysis and self-contained formal theory? Do you have any ideas to exchange ideas with? ”

Xu Chuan didn't think much about it, and said with a smile: "I have a little idea, but I don't know if it can get through." ”

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

Xu Chuan: "Just now I talked to Professor Avila about the self-defending form and the self-defending L-function, generally speaking, the L-function source is composed of two categories, the arithmetic L-function and the self-defending L-function, which are closely related, according to Robert Langlands's conjecture, all meaningful L-functions come from the self-defending L-function. ”

"The so-called self-defending form is a special class of complex variable functions, and satisfies the transformation law described by the self-defending factor under a certain discrete transformation group, strictly speaking, the self-defending representation is not a group representation in the ordinary sense, but a modulo on the overall Heck algebra."

"When I was studying the Weyl-Berry conjecture, I took advantage of the fact that every boundary point in the Dirichlet function domain is regular and is a class of boundary points, and I used it to complete the transformation of the Laplace operator and the Laplace hyperbolic equation."

"If you can build a group out of this, maybe you can find something."

"The study of functality, for example, can provide a driving force for the Langlands program, and such research can generally be carried out in a unified framework called howe duality or theta correspondence."

"But now it seems that the Laplace operator can be transformed by studying the Dirichlet function to construct a number field, and then using its curve equation to limit to a dual reduction group to achieve partial functivity."

"It might be a viable path."

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

Under normal circumstances, unless they have a good relationship with the project team or have a very friendly relationship, the average research scholar will not tell his thoughts and research in detail to other colleagues, especially unfamiliar colleagues.

This can lead to your idea being used by others first, or being the first to get published.

But since Professor Mo and Avila know each other and are still members of his project team, it doesn't hurt to talk.

I have to say that Artur Ávila 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 it's time to give it a try.

The Dirichlet function is a super treasure among functions, and there is so much more to dig into.

.........。