At the exchange party, Xu Chuan and Artur Avila chatted for a while about automorphic forms and automorphic l-functions. After listening to Xu Chuan’s ideas, Professor Avila suddenly became interested and pulled him to talk about it.
These ideas are tried and tested.
However, the result is predictable. Neither of them are experts in number theory, and the calculation got stuck soon after they started.
But neither Xu Chuan nor Avila cared about it, which is normal.
In the world of mathematics, when solving a difficult problem, especially a world-class mathematical problem like this, even if an idea is feasible, it will take a long time to complete the verification.
Mo Kun, who had followed along, stared at the preliminary calculations and the mathematical formulas on the manuscript paper and fell into deep thought. He didn't know what he was thinking.
As for Hu Xingjian, although he also came with him, besides looking confused, he could only act as the atmosphere team.
Tonight's exchange was a bit too profound for a graduate student like him. Even if this was the direction of his study and research, he couldn't keep up with the pace.
But tonight's exchange is a good opportunity for him, if he is interested in making further academic progress.
Even if you don’t understand or understand these verification processes, it doesn’t matter. In this kind of communication with the Fields Medal experts, what you hear is the thoughts and ideas of the experts.
Just like using the regularity of the boundary points of the Dirichlet function to construct a function domain with regularity boundaries, and then introducing curve equations by expanding the domain to restrict the concept of dual reduction groups... to Langlan
This is the same as the breakthrough of the functority conjecture in this program.
This is a complete train of thought, something that cannot be learned in school. Being able to hear this kind of thing is far more valuable than holding a book and chewing slowly by yourself.
Basic knowledge is always there and can be learned at any time, but such boundary-breaking theories and ideas are very rare.
Not everyone has the ability to explore the boundaries of knowledge and expand it. Most people do not have this ability.
Human knowledge is like an ocean. It was the narrowest in ancient times. Those Homo sapiens might only watch the sun rise and set every day.
But people's natural curiosity will prompt people to explore.
From the phenomenon of lightning striking fire, to the process of drilling wood to make fire, to the principle of friction and heat...
Pieces of knowledge and principles are continuously filled into this ocean, becoming bit by bit of sea water, expanding it bit by bit, expanding its boundaries, and eventually evolving into a vast ocean of knowledge.
And every boundary expansion, no matter how big or small, has great significance.
........
After receiving the Morning Star Mathematics Award, I went on stage to give a report on the proof process of the Weyl-berry conjecture. This Morning Star Mathematics Award is basically over.
For Xu Chuan, this World Congress of Chinese Mathematicians has gained a lot.
Not only did I receive a Morning Star Mathematics Gold Medal and rice gold, but I also received inspiration and gains from the exchange with Professor Artur Avila.
Communicating mathematics with top mathematicians is a very pleasant and rewarding thing.
This is why Xu Chuan would rather take some risks and go to Princeton to study mathematics after his rebirth.
It is true that mathematics relies on talent, but talent cannot solve all your problems.
If it hadn't been for Professor Avila's communication and discovery this time, it would have taken him who knows how long it would have taken him to think of this. It might have been years, it might have been decades, or it might have been a lifetime.
.........
After cashing the check at the bank, Xu Chuan sent an email to Professor Deligne at Princeton, saying that he would go to Princeton to study in the near future.
The email received a reply soon, and Professor Deligne expressed his welcome and would be waiting for his arrival at Princeton.
Before leaving, Xu Chuan went to the office of his mentor Chen Zhengping.
After all, I am going to study abroad, so I still have to say hello to the school.
"Mentor, I'm going to Princeton."
In the office, Xu Chuan said goodbye, and Chen Zhengping put down his work and asked, "When will you leave?"
"Tomorrow's air ticket." Xu Chuan replied.
Chen Zhengping nodded and said: "Well, go ahead. You should indeed go to a higher platform to learn more knowledge. I hope you can make more breakthroughs and achieve higher achievements in the future."
After a pause, Chen Zhengping continued: "I have never asked, what direction are you planning to develop after going to Princeton this time? Are you going to continue in-depth research on spectral theory and domain expansion, or are there other study directions?"
Xu Chuan thought for a while and said: "There are still many things I want to learn. In terms of mathematics, I want to try them all, such as turbulence, smooth flow, chaos, analysis, functions, and algebra."
"In terms of physics, particle physics should still be the starting point. I haven't solved the problem of the 'proton radius mystery' last time. I will continue to try to see if I can solve this problem."
"But in the near future, I may focus on number theory and automorphic l functions."
Hearing Xu Chuan's many answers, Chen Zhengping blurted out and wanted to persuade Xu Chuan to concentrate more, but then he held back.
According to common sense, a person's energy is always limited. Wanting to learn everything means that he will not be able to learn anything, or that he will not be able to learn anything profoundly.
A hammer here and there a stick, doing a little of this and a little of that. Doing everything is the biggest taboo in academic research.
But judging from current observations, this taboo seems to have failed for his disciple.
Not to mention mathematics, the proof of the Weyl-Berry conjecture and the application of the Xu-Weyl-Berr theorem were all completed in just one year.
In the eyes of ordinary people, this may be a genius.
But in the eyes of insiders like them, this is simply a miracle.
It takes an extremely long time for a world-class mathematical conjecture to be proven and become a mathematical theorem.
For example, it took Professor Andrew Wiles 7 years to prove Fermat's Last Theorem, and it also took a long time to apply Fermat's Last Theorem to other aspects of mathematics.
After all, it takes a long time to fully understand the proof process of Fermat's Last Theorem, then turn it into your own thing and use it flexibly.
Even for mathematicians in the same field, or even Professor Wiles himself, it would take at least one or two years.
However, this theorem also failed in Xu Chuan's case. After he completed the proof of the Weyl-berry conjecture, he skillfully applied it to other fields in more than three months, which was simply beyond everyone's imagination.
In addition to his achievements in mathematics, his disciple also showed his talent in physics.
This does not refer to ipho's gold medal, but to the issue of the 'proton radius mystery'.
Chen Zhengping knew that Xu Chuan was studying the 'mystery of the proton radius'. The two had exchanged and discussed it, and he had also read some of Xu Chuan's later data analysis.
He dared not say that those things were definitely correct, but at least he could see his disciple's physics skills in those data.
Although it is not as good as the achievements in mathematics, to be honest, it is not bad. It is better than ordinary college students, graduate students, and even doctoral students.
This made Chen Zhengping very confused.
How did his disciple do it?
In less than a year, he not only solved a world-class mathematical problem, but also improved in physics, even exceeding his original expectations.
In addition, there are some achievements in the astronomical world. Although they mainly rely on mathematical calculations, if you don't understand astronomical knowledge, it will be useless no matter how good you are at mathematics.
Mathematics, physics, and astronomy blossom in three areas.
How is this done?
Perhaps, people are really different, and there are indeed all-round geniuses in this world who can break common sense.
Thinking of this, Chen Zhengping swallowed back the words that had popped up in his throat.
"As long as you have study goals, take good care of yourself when you go out this time. If you have any questions, you can go to Lin Feng. Don't worry about trouble."
Xu Chuan nodded and didn't care about this.
As long as the United States does not take action, he is still very safe in Princeton.
"Oh, by the way, there is something else I forgot to tell you."
Chen Zhengping explained a few words, then patted his head and said: "I will have an experiment and meeting at CERN in July this year. Do you want to go and have a look?"
"The experiment you were talking about last year?"
Xu Chuan suddenly remembered that Chen Zhengping told him last year that this year he seemed to be going to the European LHC to do experiments. He also said that if he could study well, he could take him there with him to learn more.
"Well, it was originally supposed to be this month, but there was an accident later, which caused the subsequent experiments to be delayed for two months. For me, it was delayed until mid-July."
"If you want to go, I will add your name to the project team. After you have an experimental experience, you can apply to be an intern or summer job at LHC later, and you can have access to first-hand collision data.
It will be of great help to you.”
"Including you are researching the 'mystery of the proton radius'. With the working experience of the LHC, it will be much easier to apply for the use of the proton collider."
Chen Zhengping nodded. Although his research direction has shifted from condensed matter physics and high energy physics to materials physics in recent years, it does not mean that he has given up his original scientific research direction.
Since his disciple still doesn't want to give up physics and is talented in particle physics, it would be good for him to gain some knowledge through this experiment.
And regarding the 'mystery of the proton radius', maybe you can take this opportunity to apply for a collider at the Atomic Energy Laboratory.
The Large Strong Particle Collider LHC has little hope, but the European Atomic Energy Experiment has more than just this collider, there are also small and medium-sized ones, and their performance should be enough for Xu Chuan to complete experiments in this area.
Even if I can't jump in line this time, with this experimental work experience, subsequent applications will be much easier.
There are still many benefits.
.......
"Teacher, please bring me one. You can send me the specific time when the time comes, and I will go directly from Princeton."
Xu Chuan agreed. If there was a chance to observe the European Atomic Energy Laboratory, he would definitely go.
It is the world's largest large strong particle collider. More than half of the world's high-energy physics results come from the LHC. His high-energy physics results in his previous life are basically related to the LHC.
And if we go this time, we might be able to find an opportunity to apply for a proton collision facility and conduct two experiments to collect data on the 'proton radius mystery'.
He didn't expect to solve this problem in one experiment, but at least there had to be progress, right?
Only when progress and results are achieved can we continue to apply for the use of other people's collider.
I have to say that he and Chen Zhengping wanted to go together.