After the opening ceremony and awards ceremony on the first day, there was an exchange party.
The exchange party was held at Wenjin International Hotel. Shuimu University, which has the most abundant scientific research funds in the country and has always ranked first in the university funding rankings, is also full of pride.
During the World Conference of Chinese Mathematicians, I directly reserved the right to use Wenjin International Hotel for a week, which can be said to be very wealthy.
After dinner and a short nap, Xu Chuan went downstairs and followed Rong Zhizhuan to the auditorium for the exchange party.
It was only about 7:30 in the evening, half an hour before the exchange party started, but the auditorium was already crowded with people.
As soon as they entered the venue, they bumped into Zhang Weiping and Hu Xingjian from Sun Moon University.
After greeting each other, Zhang Weiping's eyes moved and he threw his student to Xu Chuan, and he followed Rong Zhizhan.
The euphemistic name is to allow young people to communicate more, so that the two bad old men will stop joining in the fun together.
Looking at the two division commanders who disappeared in the vast sea of people in the blink of an eye, and then looking at Hu Xingjian standing aside, the corner of Xu Chuan's mouth twitched.
"Sichuan God, I'm sorry to trouble you."
Hu Xingjian smiled shyly and embarrassedly, probably because he also felt that his tutor was a bit unreliable.
"You're welcome. It would be nice if this kind of communication could be more casual." Xu Chuan said with a smile, leading Hu Xingjian towards the center of the venue.
"Is this the first time for Brother Hu to participate in this kind of exchange party?" Xu Chuan asked as he walked.
Hu Xingjian nodded, looking around and replied: "It is indeed my first time to participate in something so formal. Has Sichuan God participated in it before?"
"I participated once before when I went to Princeton to give a report."
Xu Chuan nodded, took a few grapes from the white table at the venue, stuffed them into his mouth, and gave two to Hu Xingjian.
Hu Xingjian took the grapes with a yearning look in his eyes: "Princeton is the legendary holy land of mathematics. I heard that anyone I bump into there on the road is a top math expert."
Xu Chuan smiled and said: "It's not that exaggerated, but there are still many math experts at Princeton. Brother Hu, do you have any idea to apply for a PhD at Princeton?"
"I must have an idea. After all, I am studying mathematics. Anyone who studies mathematics would not want to go to Princeton, but there is a high probability that I will not have the chance."
Hu Xingjian shrugged and said, for students studying mathematics, Princeton is almost the ultimate goal, and no one wants to go there.
But they can't recruit many students in the entire country of China a year, and the competition is so fierce that it's countless times more difficult to pass 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. Although he won the gold medal in the Qiu Chengtong College Student Mathematics Competition, it was still not enough.
Xu Chuan smiled and was about to say a few polite words to cheer him up when another voice came to his ears.
"Hi, Xu, I finally found you."
A somewhat rough voice sounded, and then a man with a full beard walked over.
Seeing the person coming, Xu Chuan was stunned for a moment, and then a smile appeared on his face.
"Long time no see, Professor Avila."
The visitor was Professor Artur Avila, a Brazilian mathematics professor whom I had met at the Princeton Mathematics Conference before. The two had also chatted about mathematics all morning.
After shaking hands with the Brazilian mathematician enthusiastically, Xu Chuan asked curiously: "Why did you come to this conference of Chinese Mathematicians?"
Although this World Congress of Chinese Mathematicians was held quite grandly, and many foreign mathematicians came to participate in the conference, it was mainly Chinese and Chinese mathematicians who faced it.
Xu Chuan really didn’t expect that Artur Avila would appear at this mathematics exchange meeting.
Artur Avila smiled and said: "I have a cooperative project in mathematical dynamical systems with P University in your country. I happened to be here during this time and received the invitation letter, so I came over to take a look.
Can I meet you?"
Xu Chuan suddenly nodded and said: "That's it, welcome."
On the side, Hu Xingjian watched the two exchanges with curiosity, eagerly waiting 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. He has won top mathematics awards such as the European Mathematical Society Award and the Fields Medal.
He has profound research in chaos theory, the field of dynamical systems and spectral theory."
"Professor Avila, this is the student of one of my teachers, Hu Xingjian. His research areas are also spectral theory and Hilbert space."
After listening to Xu Chuan's introduction, Hu Xingjian was dumbfounded.
He didn't expect that Xu Chuan actually knew such a super boss and could chat and laugh with him.
As a graduate student studying spectral theory, he had naturally heard of the name Artur Avila.
This is one of the most famous mathematicians in Brazil, a Fields Medal winner, a top expert in chaos theory, dynamical systems and spectral theory. I didn’t expect to see him here today.
"Hello, nice to meet you." Artur Avila smiled and stretched out his hand.
After Hu Xingjian was stunned for a moment, he came to his senses and quickly clasped his hands: "Hello, Professor Avila, I have heard your name for a long time. I have read your work on spectral theory "Spectral Fractal Region Reconstruction"
study"."
Artur Avila smiled and said: "Xu is the real expert in spectral theory and spectral fractals. My achievements are completely insignificant in front of him."
Hearing this, Hu Xingjian couldn't help but swallow his saliva.
Good guy, I knew Xu Chuan was awesome, but I didn’t expect him to be so awesome.
A Fields Medalist personally said that the area in which he is good at is far inferior to him. Even if there is an element of mutual flattery, that is not a big deal.
He's got this thigh!
........
After shaking hands with Hu Xingjian and saying hello, Artur Avila turned his attention back to Xu Chuan.
This chapter is not over, please click on the next page to continue reading! "Xu, when we met last time at Princeton, 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: "In what respect?"
Artur Avila: "Non-commutative harmonic analysis and the theory of automorphic forms in the Langlands program. I wonder if you are familiar with or have some understanding of 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 specific aspect you are referring to."
"Also, why did you suddenly start studying number theory and harmonic analysis?"
Xu Chuan looked curiously at Artur Avila. This Fields Medal winner is most famous for his research in the fields of chaos theory and dynamic systems. Spectral theory is also involved, but number theory and harmonic analysis.
He seemed to have never heard of this professor's research.
Artur Avila smiled and said: "I am not familiar with number theory and harmonic analysis, but I have some research on spectral theory and the Laplacian operator."
"After chatting with you last time, I looked through your proof of the Weyl-berry conjecture."
"In your paper, there is a very essential method, which is to convert the Laplace operator and the Laplace hyperbolic equation in the Dirichlet function field, as well as the expansion of the field and how to convert the function into a subgroup and
Make connections to intermediate domains and collections.”
"I am studying this method and it seems that it can be applied to some issues in the Langlands Programme."
"For example, some conjectures derived from the automorphic l function."
"As you know, automorphic functions are generalizations from circular functions, hyperbolic functions, elliptic functions, and other functions in elementary analysis, while automorphic l functions are defined through automorphic group representations."
"In the Langlands conjecture, the automorphic l functions satisfy certain harmonious relationships, and there is a unique factorization, which is reflected in the automorphic group representation. This is the functority between the automorphic group representations."
"And this functority conjecture can be completely determined by the mapping between l groups. Given a linear algebra group, the relationship between its automorphic group representation on the base domain and the group representation on an extended domain
It is called a basis transformation and is a special case of functority..."
"... Can the method in your paper also be applied to basic automorphic functions? Or, in some way, to conduct a deeper study of the Gaussian reciprocity law.
Promotion?”
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 watching the whole process, looked at Xu Chuan and then at Professor Artur Avila with a confused look on his face.
Damn it, what are these things talking about?
He knows the Weyl-berry conjecture, he also knows the Dirichlet function, and he has also heard of the famous Langlands conjecture.
But after these nouns are connected together, why can't he understand a sentence?
Is it because he doesn't speak English well?
But it is clear that he has a score of 7.9 in IELTS Category A.
Suddenly, Hu Xingjian felt a surge of despair in his heart. He had previously thought about standing on that stage like Xu Chuan, but now it seems that the gap between the two is really not that big.
Chasing? Why did he chase? He began to not understand what they were saying.
Xu Chuan was deep in thought, Hu Xingjian was confused and desperate, and Professor Avila looked at Xu Chuan expectantly.
The three of them stood like this in the venue until another voice came.
"Professor Avila, you are here."
At the same time, a thin middle-aged man came over.
"Professor Mo." Seeing the person coming, Professor Artur Avila smiled and nodded in greeting.
"Professor Avila, what's going on?"
Seeing Xu Chuan meditating beside him, Professor Mo asked doubtfully. Xu Chuan had just received the Morning Star Mathematics Award in the auditorium of Shuimu University in the afternoon. There was no way he didn't recognize him.
Artur Avila smiled and said: "We just talked about mathematics. He may have some ideas? He is thinking about it."
"Oh? Can I hear what you guys were talking about?" Hearing this, Professor Mo raised his eyebrows in interest and asked.
"Of course, mainly the non-commutative harmonic analysis and the theory of automorphic forms in Langlands' program..."
Avila would naturally not refuse someone to share mathematics with, and since Professor Mo was a researcher in number theory, they might be able to communicate with him, so he smiled and simply repeated the theory and problem just now.
"Langlands program, automorphic formal theory, any ideas?"
Upon hearing this, Mo Kun's eyes lit up and he quickly asked, this happened to be one of the academic areas he studied.
Avila shook his head, looked at Xu Chuan and said: "I'm not very familiar with this area. 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 deep thoughts, opened his mouth and was about to speak, when his eyes fell on Mo Kun beside him.
"Who is this?"
Xu Chuan looked curiously at the fourth person who suddenly appeared. The person who appeared here should be a mathematician, but this math parent is quite special. His face is very distinctive. He has a horse face, and the bridge of his nose is exactly where his head is.
There are still some protrusions, and the appearance is indeed average.
"This is Professor Mo Kun from P University. He is an expert in number theory and number fields. He is also a member of the project I am cooperating with P University."
"This is Xu Chuan, my good friend."
On the side, Artur Avila introduced each other with a smile.
"Oh, hello, Professor Mo." Xu Chuan reached out his hand and said hello.
Mo Kun shook hands with a smile and said: "Hello, classmate Xu Chuan, I have heard of you a while ago. When I saw you today, you are indeed well-deserved. You are young and promising."
This chapter is not finished yet, please click the next page to continue reading the exciting content! "I just heard Professor Avila say that you are talking about non-commutative harmonic analysis and automorphic formal theory? Do you have any ideas? Let's exchange ideas together?"
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 will work."
Hearing this, Mo Kun quickly asked: "What do you think?"
Xu Chuan: “I just 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 two are closely related. According to Robert Langlands's conjecture, all meaningful l-functions come from automorphic l-functions."
"The so-called automorphic form is a special type of complex variable function that 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 of the global Heckian algebra.”
"When I was studying the Weyl-berry conjecture before, I took advantage of the fact that every boundary point in the Dirichlet function domain is regular and is a type of boundary point, and used it to complete the transformation of the Laplacian operator
and Laplace’s hyperbolic equation.”
"If we can use this to build a group domain, we might be able to discover something."
"For example, the study of functor properties can provide a driving force for the Langlands program. Such studies can generally be unified under a framework called howe duality or theta correspondence."
"But now it seems that we can construct a number field to transform the Laplace operator by studying the Dirichlet function, and then use its curve equation to restrict it to the dual reduction group to achieve partial functority."
"This may be a feasible path."
Xu Chuan simply stated some of the ideas he had just conceived.
Under normal circumstances, unless they are in the same project team or have a very friendly relationship, ordinary researchers will not tell their inner thoughts and research in detail to other colleagues, especially unfamiliar colleagues.
Because this may cause your ideas to be used by others first, or published first.
But since Professor Mo knew Avila and was a member of his project team, there was no harm in chatting.
I have to say that Artur Avila really brought him a huge surprise this time. He had never thought of applying this method to the fields of number theory and group theory before.
But now, it seems that I can give it a try.
The Dirichlet function is indeed a super treasure among functions, and there are too many things that can be mined in it.