Just turned over a new leaf and became a wise and intelligent student

Chapter 329: Unexpected Visitors and Hodge's Theory

Leave Longjiang and return to the capital.

These two girls are just like they are starting to take acting classes at Beijing Film Academy or the Central Academy of Drama, focusing on releasing their nature.

The rivalry and jealousy that they had suppressed in front of the elders could no longer be suppressed at this moment. What's more, Qiu Jing had leaned so close to Xu Qingshan when she was talking to him just now, and she was a completely different type from the two of them. Even though there was nothing between them, they still felt an inexplicable sense of crisis.

Fortunately, Xu Qingshan still has Wang Chuan to rely on.

A copper stove hotpot dinner for young people passed by in a lively and noisy manner. It was lively and nice.

The next day, there were only two days left until the start of school at Kyoto University.

Some students have started to return to school one after another.

Tong Tong needs to register with the training group first and collect the new study materials, while Jiang Huanxi needs to go to the dormitory in advance to clean and tidy up, as she will officially move out of the dormitory this semester.

I arrived early just in time to go to the institute office to submit my application and go through the formalities.

If this was an ordinary student from an ordinary school or college, the counselor would definitely not be able to release him and would have to resort to illegal means.

But the relationship between Jiang Huanxi and Xu Qingshan is no secret.

Students at Yuanpei College have always had more freedom. When they found out that the place Jiang Huanxi moved to was actually Yandong Garden, the counselor, who was only a few years older than Jiang Huanxi, pulled Jiang Huanxi into a small dark room and earnestly explained a bunch of safety precautions before letting Jiang Huanxi leave with a red face.

Looking at Jiang Huanxi's back as he quickly left the school office in small steps, the counselor couldn't help but sigh and said with emotion.

"What kind of world is this? I, a young girl, am telling a little girl who has already tasted meat about these safety awareness? Will she think I am being redundant?"

Everyone is busy with their own things.

Xu Qingshan also went to the office of the Institute of Mathematics and Computer Science and took a look.

Xiao Xue and Xiao Wang have been staying in the office for a long time. Judging from the appearance of their desks, they have been in school for at least a week or two.

Yes, doctoral students start school earlier than undergraduate students.

Professors generally live near the school, and they do not have a specific start time for school because they never have holidays. It is common for them to take students and assistants to continue doing scientific research and experiments during summer and winter holidays.

Only a special case like Xu Qingshan could create a bug.

He has the functions of a professor, but his identity card shows that he is an undergraduate.

"Why, are you not having a happy Spring Festival?"

As soon as Xu Qingshan entered the office, he saw two girls with sad faces. When Xue Xueqing saw Xu Qingshan, she stood up first, but her soul was still sitting at the table. Her originally yellow hair had turned peach pink, but the dry hair ends and messy hair showed that she had not been doing well recently.

Wang Wei on the other side moved his mouth first, but no one reacted.

She called out "Teacher" first, and three seconds after she finished speaking, she slowly stood up, rubbing the chair against the ground with a sizzling sound.

"The Spring Festival was fine. It's about our thesis. I want to work on Diophantine's problems, but I have no idea how to solve several of them. Now I'm looking at the tenth question of Hilbert's 1900 problems in 23, but I found that I didn't understand Matiajevic's thesis."

"I am happy for the Spring Festival. But what is worse than the snow is that I am trying to replicate your whole process. But I am stuck. There are several steps that I found I have not been able to fully understand, but I dare not call you during the holidays."

Looking at the two young girls complaining in front of him, Xu Qingshan shook his head helplessly.

It's just a matter of a phone call, it's not that big of a deal. In the end, we still became estranged.

"That's easy, Xiao Xue. You're talking about the tenth question, 'Can a polynomial equation with any number of unknowns be determined through a feasible evolution in a finite number of operations to determine whether the equation has integer solutions?' In Matiajevic's doctoral thesis, it was proved that there is no general algorithm that can solve all Diophantine equations, right?"

"Yes, that's it. I read a lot of classic literature and research history. I looked through everything I could find. I also looked at Turing's Turing machine theory and Gödel's."

“Don’t look forward, look backward.”

Xu Qingshan reached out to interrupt Xiao Xue's performance and said.

"You can read Jones's 1982 paper in the Journal of Symbolic Logic, which details the argument that there is no algorithm to determine whether any polynomial equation with 9 unknowns has natural number solutions. That paper has a detailed explanation of the tenth question. If you still have questions after reading that paper, you can read Sun Zhiwei's 1989 paper "Necessary and Sufficient Conditions for Two Linear Diophantine Equations to Have Common Solutions" in the Journal of Jinling University and "Reduction of Unknowns in Diophantine Representations" in the 91 issue of Chinese Science Series A. If you still don't understand after reading them, come back and find me."

After Xu Qingshan finished speaking, he saw Xue Xueqing feeling somewhat guilty, so he reached out and knocked on her head.

"Also, sometimes you don't just think about looking for answers to certain questions in foreign journals. Sometimes there are good insights in China, too. Although there is indeed a gap in terms of proportion, when doing scientific research, if you are interested, you should be comprehensive enough. Don't say there is no way out before you have tried your best. Remember?"

"remember"

Xue Xueqing sat down feeling aggrieved, and obediently went to look for the paper that Xu Qingshan mentioned.

Wang Wei on the other side was slow to react this time.

She immediately sat down as well, staring intently at her computer screen, even though it was displaying Spider Solitaire.

"It's Xiao Wang's turn next."

Xu Qingshan looked at Wang Wei.

"Teacher, I don't need to ask anymore. I'll take another look and maybe I'll understand."

No wonder Wang Wei didn’t even dare to make a phone call during the New Year.

Xu Qingshan thought to himself that he didn't seem to have taught her a lesson. What made her look so fierce? Could she stop a baby from crying and a doctor from asking questions?
"Stop talking nonsense and show me what you don't understand. You're working on a project with me, but your teammates don't understand it. If someone asks you a question and you get stumped, wouldn't that be a disgrace to me?"

Xu Qingshan patted Wang Wei's shoulder gently and said jokingly.

As a result, Wang Wei's whole body suddenly trembled, and his voice became tearful.

"Teacher, I really didn't fail to work hard. I just am, I just am."

"Okay, okay, I didn't say you didn't work hard. Show me the problem first and I'll explain it to you briefly. Just kidding, you are already much better than others."

Xu Qingshan withdrew his hand and comforted him helplessly.

Fortunately, Wang Wei's questions were indeed rather tricky, and there were indeed some small skips in some places. Jiang Huanxi had the basics, but he still didn't master some parts deeply enough. Without Wang Wei's review, Xu Qingshan might not have cared about it.

After explaining his ideas, Wang Wei seemed to be more clear-headed. "Then you should work on these problems next, integrate them, and publish as the first author. It should be easy to publish in SCI zone 1. See if you can submit new progress. After all, these are still hot fields before you win the award. I recommend them to you."

Xu Qingshan patted Wang Wei's shoulder again and was about to return to his seat to organize his ideas for the next research.

Xue Xueqing, who was jealous at the side, threw away her grievances and panic in the blink of an eye, and raised her hands and yelled like a primary school student.

"Teacher, I want one too!"

"Show me the paper first. After you finish reading it, I'll find you a topic in the same field as Diophantus. Then follow me and do it."

Xu Qingshan simply ignored the lively girl who was trying her best to act cute and sat back in his seat.

Xue Xueqing could only pout and sit back in her seat and continue looking up information, but she couldn't hide the joy on her face. Although Director Xu had made a promise, how could Director Xu's promise be comparable to that of others?
This is a real cake! You can eat it until you are full!
Xu Qingshan found a piece of paper, thought about it, and simply wrote down the basic ideas he had just discussed with Xue Xueqing.

The fact that he was able to master so many papers related to Diophantus and could talk about the development history of various issues in the field of Diophantus at will was not something he was born with.

My buddy was just reborn, he wasn’t caught in the rain, and he won’t become a god who knows everything.

It was just that after finishing it, Xu Qingshan consciously wanted to look at the Diophantine connection, because in the process of proving the twin prime conjecture, Xu Qingshan used similar ideas many times to find a way.

Duffin-Schaeffer conjecture

Xu Qingshan wrote a line of black words, and then wrote [Dirichlet Theorem].

He quickly organized his thoughts.

In the field of mathematics, especially in the field of pure numbers, there are many various important conjectures. Many of these conjectures seem quite simple at first glance, but they have not been solved for a long time.

Just like the conjecture in his hand now, which sounds completely unknown at first glance, it actually belongs to the level of phonetic vowels in the field of Diophantine approximation.

Xu Qingshan did not stop writing, but clarified the whole issue.

First assume a continuous function, and the question is whether there are infinite continuous functions of the real number x that are approximately rational numbers p/q (q>0, (p, q)=1) such that the absolute value of x minus the absolute value of p/q is less than q.

When the continuous function of q is equal to q to the power of -2, it is actually Dirichlet's theorem: for any real number x, there are infinite rational numbers that satisfy the inequality.
only.

Xu Qingshan's thoughts were obviously more jumpy.

He did not stop at the Duffin-Schaeffer conjecture. After writing a lot of dense text, he turned to another page and wrote the Wirsing-Schmidt conjecture.

Just when he forgot to tidy up the table and documents, his butt touched this long-missed yet familiar ergonomic chair and he began to enter a mysterious state.

The knock at the office door attracted the attention of the three people in the office.

Xu Qingshan looked up in surprise.

Tong Tong and Jiang Huanxi should not have finished their work at this time, so it is impossible for them to come here.

Even if she came to the office, given how familiar they were with each other, did she need to knock on the door?
But when he looked up, Xu Qingshan saw an old friend who was as long-lost and familiar as the ergonomic chair under his butt.

Actually, it’s not entirely true to say that we are old friends, we just had some in-depth chats.

Looking at the handsome Senior Brother Liu Ruochuan in front of him, who was wearing a very stylish brown suit, Xu Qingshan blinked. His first words were not to welcome him or greet him, but
"Brother, aren't you really cold outside dressed like this?"

Liu Ruchuan, who was holding a briefcase in one hand and a beautiful gift box in the other, was stunned, but kept smiling. He shook his head, walked in, put his things on Xu Qingshan's desk very familiarly, and pulled a chair over to sit down.

"What's so cold? I just came back from France. But France is really warm, much warmer than Beijing."

"Warm? Really? Doesn't Paris have a Mediterranean climate? Wouldn't it be even colder in the winter when it rains?"

Xu Qingshan moved the exquisite gift box brought by Liu Ruochuan. It was full of foreign languages. He had never learned it. It looked like English, but there seemed to be a big difference. From the composition of the letters and the word order, it looked like French.

When Liu Ruchuan heard Xu Qingshan's question, his reaction was much stronger than before. He looked at Xu Qingshan with disbelief.

"Huh?!! Didn't you get full marks in the college entrance exam? Isn't this in the geography book? How come you don't even know this? Paris has a temperate maritime climate. It's in the north of France."

Xu Qingshan blinked and lowered his head to open the gift.

"I am the top student in science, I got full marks in science, not in liberal arts. The geography exam will be completed in my second year of high school. I didn't start to work hard in my second year of high school."

"I see. I thought you were really good at the decathlon. Hey, hey, hey, I didn't even tell you it was a gift for you. You are so shameless that you just tore it apart."

Liu Ruochuan took off his suit jacket.

It was warmer once I entered the house. The heating in the house was not installed for nothing.

"It's already on my desk. It's a gift to me even if it's not. But you came here without even saying hello, brother. What's wrong? Do you love me so much? Why did you come to see me right after you came back from France?"

Xu Qingshan took a look at the contents of the gift box. It was a set of exquisite-looking enamel porcelain. However, the more he looked at it, the more it looked like it was made in China.
Xu Qingshan took the gift box and looked at it over and over again, hoping to find some clues.

"You're overthinking. I went to see the teacher first, and the teacher told me that it would be okay to ask you for help, so I came to see you."

Upon hearing this, Xu Qingshan put the porcelain in his hand back into the gift box and quickly closed the lid of the gift box.

"Go out, turn left, walk slowly, I won't see you off."

He continued to calmly read the manuscript he had just written.

"Hey, Qingshan, don't be so distant. I brought this back specially for you. I think you young people who are in love will definitely like this. How great is it to coax girls?"

Liu Ruchuan raised his eyebrows and looked at Xu Qingshan in a flattering manner.

"Tell me what you want to do first."

Xu Qingshan had a blank expression on his face.

"Hodge theory. I've been working on applications related to p-entry Hodge theory recently. Isn't it a disadvantage to have strong computing power, good ideas, and awesome people as your thighs? Look, isn't this tailor-made for me?"

(End of this chapter)