Chapter 123 Qiu Chengtong's Conjecture

Qiu Chengtong was very excited when he heard Xu Yuan's answer, and he had no doubt that Xu Yuan was pretending to know.

The next second he waved his hands and shouted:

"Then come up and try to deduce the rest of the formula."

Xu Yuan naturally had no hesitation when he heard this. He immediately stood up and walked out of the queue to the stage, attracting everyone's attention the whole time.

At this time, students from the Department of Mathematics at the Chinese University of Hong Kong showed some sympathy in their eyes.

Obviously, it is not believed that Xu Yuan can deduce the following formula.

After all, deducing formulas is much more difficult than solving problems.

"I guess I'm going to be embarrassed now."

"I can't even understand what Professor Qiu is saying, let alone deduce this unfinished formula."

"I guess Professor Qiu would have let Xu Yuan go on stage if he hadn't arrived yet."

"Luckily I didn't answer that."

"After all, he has published two papers in the Annals of Mathematics, so he should have some strength, right?"

"Those two papers are in the field of number theory and partial differential equations, but they have little to do with the cross-sectional curvature of Riemann manifolds. I guess he wanted to show off his mathematical genius and deliberately said that he understood them."

……

When I was in school, whenever the teacher finished explaining a question and asked if we understood it, many people would often answer that they understood it.

But in reality, I only understood half of it or didn’t understand it at all, but I was just embarrassed to ask the teacher to explain it again.

As for some teachers who may see that students have not understood, in most cases they will not choose to explain it a second time, because for them it is just completing their teaching tasks.

It is precisely because of this perspective that they do not think Xu Yuan understood, let alone deduce the formula.

However, while they were waiting to watch the fun, Liu Yang, Zhang Jundong and other Qinghua students had calm faces, even smiles on their lips, and they were not worried about Xu Yuan on the stage at all.

joke.

This is their Qinghua’s God Xu.

Prince of Mathematics.

No matter how difficult the math problem is, I can solve it. How can I be stumped by a formula?

Besides, everyone knows that Xu Yuan’s greatest strength is that he tells the truth.

If you understand what I say, then you understand it.

"These people still don't know how terrifying God Xu is. It's time to let them see the level of our Qinghua students."

"Brother Yuan never lets people down." Liu Yang couldn't help but agree when he heard Zhang Jundong's words.

On the stage, Qiu Chengtong looked at Xu Yuan, who had a calm expression, and was very expectant.

He even took the initiative to hand over the chalk.

"Use your own ideas to deduce, it doesn't matter if you are wrong."

"Okay, Professor Qiu."

Xu Yuan took the chalk and nodded, then turned to the blackboard and looked at the formula which only had the first half.

This formula is a verification deduction of the fact that the complete Riemann space has non-negative cross-sectional curvature, which is a concave function.

He combined the mathematical knowledge he had mastered with the content about the cross-sectional curvature of Riemann manifolds he had just heard, and after a little thought, the corresponding ideas emerged in his mind.

And through the automatically generated and growing progress bar on the panel, we can confirm that there is no problem with the calculation idea.

The thought stayed here, and the next second he started calculating immediately. The chalk continued to slide, leaving one mathematical symbol after another on the blackboard.

Finally, a complete and reasonable formula is formed, achieving a logical closed loop.

"fp(x)= dist(p, x)......"

……

Qiu Chengtong watched Xu Yuan's calculation process the whole time, and his eyes became brighter and brighter as new formulas appeared.

The whole person feels like a long-awaited rain, and finally finds what he wants after waiting for a long time.

While he was still thinking about this, a sudden voice in his ear brought him back to his senses.

"Professor Qiu, I have finished calculating the formula."

“Is that all?!”

Qiu Chengtong subconsciously showed a hint of surprise when he heard this, as if he did not expect Xu Yuan's deduction speed to be so fast, much earlier than he predicted.

He became more and more excited and didn't care about anything else. He quickly raised his eyes to look at the formula behind Xu Yuan.

After a pause of nearly two minutes, Qiu Chengtong's face was filled with a joyful smile.

He raised his hand and patted Xu Yuan on the shoulder and said, "You really deserve the reputation of Prince of Mathematics given by Jean Deligne. Xu Yuan, you have a strong talent in mathematics." He did not hide his excitement and joy at all.

After saying that, he looked at Liao Fangyi and said, "You Qinghua really has cultivated a mathematical genius."

"I would also like to thank Professor Qiu for his guidance to Xu Yuan." Liao Fangyi was polite on the surface but he was actually very happy in his heart.

On the other hand, the students from the Department of Mathematics at the Chinese University of Hong Kong looked even more dumbfounded than when they were listening to the lecture just now.

I never expected that Xu Yuan not only deduced the complete formula, but also did it so quickly and received such high praise from Professor Qiu.

“You actually figured it out?”

"With this speed, I would believe it even if you told me to copy it."

"It is truly extraordinary to be able to publish two papers in Annals of Mathematics. No wonder Professor Qiu gave me such a positive evaluation."

"Is the math level of Qinghua students already so high?"

"From this perspective, it seems that Xu Yuan is no worse than Terence Tao. It's still unclear who is the youngest genius in mathematics."

……

Liu Yang, Zhang Jundong and others listened to the discussions around them and saw the stunned expressions on their faces. They felt extremely happy and proud, thinking that you guys finally know the value of God Xu. As the person involved, Xu Yuan didn't care about other people's reactions, but when he was about to leave, he suddenly heard Professor Qiu Chengtong add a special sentence.

"Xu Yuan, please come to my office later. You don't need to attend the lectures later."

Although Xu Yuan didn't know what it meant when he heard this, he didn't hesitate too much.

He nodded and agreed immediately.

"Okay, Professor Qiu."

Anyway, compared with Professor Qiu Chengtong's difficult content, Liao Fangyi's lectures are more undergraduate-oriented.

It doesn't matter if you don't listen.

What's more, even Liao Fangyi urged him to wait.

Originally, when Professor Qiu Chengtong paused to drink water, the lecture was almost coming to an end.

Just as Xu Yuan finished the subsequent deduction of the formula, the bell for the end of get out of class rang and it was time for a break.

Since it was agreed that he would go to Professor Qiu Chengtong's office, Xu Yuan did not attend Liao Fangyi's lecture, but followed Qiu Chengtong directly to his office at the Chinese University of Hong Kong.

-

"Sit down first."

As soon as he pushed the door open, Qiu Chengtong warmly invited Xu Yuan to sit down, and he put the things in his hand on the table.

Then he walked straight to the water dispenser and got two glasses of water.

"Have a drink of water."

When Xu Yuan saw Professor Qiu Chengtong offering to pour him some water, he quickly stood up and took it with both hands.

"Thank you, Professor Qiu."

He thanked him and then sat down again.

Then Qiu Chengtong sat down next to him, and without keeping anyone in suspense he went straight to the point and asked a question.

"Xu Yuan."

"Do you know anything about the Calabi conjecture?"

When Xu Yuan heard Qiu Chengtong ask this, he was stunned for a moment, then he organized his words and answered in a deep voice.

"The Calabi conjecture originated from algebraic geometry and was proposed by the famous geometer Calabi at the International Congress of Mathematicians."

"Is it possible for a gravitational field to exist in a closed space without any matter distributed?"

"Let M be a compact Kähler manifold, then for any (1, 1) form R of its first Chern class, there exists a unique Kähler metric whose Ricci form is exactly R."

"Then Professor Qiu used the concept of curvature in Kahlabbi geometry to solve the partial differential equation and completed the proof."

Before coming to Hong Kong, Xu Yuan studied Qiu Chengtong's thesis, so he was familiar with the Calabi conjecture.

Qiu Chengtong listened to all of Xu Yuan's answers, nodded affirmatively, and then shook his head to add.

"What you said is all right, but strictly speaking I have not completely completed the proof of the Calabi conjecture."

"I just solved the Calabi conjecture that the first Chern class is negative and zero."

"But the problem of whether the first Chern class is positive has not been solved."

When he said the last sentence, a hint of regret appeared in his eyes.

Xu Yuan knew that the first Chern class of Calabi's conjecture has three forms, namely negative, zero and positive. Qiu Chengtong proved the cases where the first Chern class is negative and positive.

Although the Calabi conjecture that the first Chern class is positive was not solved, it was suggested that it might be possible to transform it into a stability problem in algebraic geometry.

This is the Qiu Chengtong conjecture that has troubled the mathematical community for thirty years.

Thinking of this, Xu Yuan blurted out, "Professor Qiu, are you talking about the Qiu Chengtong conjecture that you proposed many years ago?"

"Yes."

Qiu Chengtong nodded in confirmation: "I want you to prove Qiu Chengtong's conjecture."

When Xu Yuan heard this, a look of surprise suddenly appeared on his face.

"Let me prove Qiu Chengtong's conjecture?" He repeated subconsciously.

He really didn't expect that Qiu Chengtong held an exchange meeting in the hope that he could solve Qiu Chengtong's conjecture.

Qiu Chengtong was obviously very serious about the matter and continued to explain in detail without pausing.

"Transform the existence problem of the Kähler-Einstein metric on a high-dimensional space with a positive first Chern class into a stability problem in algebraic geometry. Although this involves multiple branches of mathematics such as differential geometry and algebraic geometry, with your mathematical talent and level, I believe you may be able to complete the proof and put a perfect end to the Calabi conjecture."

"You don't have to attend the subsequent exchange activities. You can learn relevant mathematical methods in my office."

“I wonder if you have this confidence?”

At this point, Qiu Chengtong smiled and added another sentence.

"I was already 27 years old when I proved the Calabi conjecture, but you published two annual papers when you were only 20 years old."

Xu Yuan listened to Qiu Chengtong's words, and although he knew that the other party was trying to provoke him, he couldn't help but feel a surge of pride in his heart.

If he could successfully solve the Calabi conjecture that the first Chern class is negative zero at the age of 27, why couldn't he thoroughly prove the Calabi conjecture that the first Chern class is positive?

Just as Professor Qiu Chengtong said, this is a perfect ending to this difficult mathematical problem.

The thought stayed here, Xu Yuan quickly made a decision and gave his answer.

"I can try."

This answer also made Qiu Chengtong very happy. He immediately took out many reference books from the bookshelf next to him and piled them all in front of Xu Yuan.

"I will personally teach you in the next few days. I hope you can make up for this regret for me."

……

(End of this chapter)