Chapter 122 I Understood Everything
Xu Yuan was somewhat surprised to see the Fields Medal winner being so polite. He quickly extended both hands to shake hands with the other party while humbly responding to the greeting with the mentality of a junior.

"Hello, Professor Qiu."

“I’m currently studying for my doctorate, and I still have a lot to learn.”

“I really don’t deserve the title of Prince of Mathematics.”

"You don't have to be modest." Hearing this, Qiu Chengtong waved his hand to interrupt.

"I read your paper on the proof of optimal transmission theory. Both the method and the process are very sophisticated."

"Since Professor Deligne gave you such a high evaluation, it means that your talent is worthy of the title of Prince of Mathematics. I hope this exchange activity will be helpful to you."

Only after he finished his last sentence did Qiu Chengtong let go of Xu Yuan's hand, with the smile on his face never fading.

Liu Yang, Zhang Jundong and others behind him saw this scene, and there was a hint of excitement on their faces.

A lot of thoughts flashed through my mind quickly.

"God Xu is so highly regarded by Professor Qiu. It's really a blessing for us to be able to participate in the exchange meeting."

Zhang Jundong was now more certain of his analysis. It could be said that if it weren't for Xu Yuan, there would probably not have been this exchange meeting at all.

But at the same time, his admiration and respect for Xu Yuan rose again.

Even Professor Qiu Chengtong, an internationally renowned mathematician, attached great importance to it and specially organized an exchange meeting.

It can be seen that Xu Yuan's future development in the field of mathematics is limitless.

Because Liu Yang was very familiar with Xu Yuan, he was not surprised at all when he saw the situation in front of him, except that he was happy for Xu Yuan.

All I can say is that for him, no matter what kind of achievements Xu Yuan made, he felt it was normal.

As for the graduate students who were traveling with him, although they didn't say anything, they were all extremely envious of Xu Yuan.

After Qiu Chengtong finished chatting with Xu Yuan, he did not show any intention of shaking hands with other students. He withdrew his gaze and looked at Liao Fangyi again to talk about the arrangements later.

"Director Liao."

"You must have had a hard journey. Go to your accommodation and have a rest first. I'll send someone to accompany you. If you have any questions, just let me know."

"Then I'll trouble you, Professor Qiu." Liao Fangyi nodded without objection.

The formal exchange activities will start tomorrow. The first thing they must do is to solve the accommodation problem and get familiar with the campus environment. After all, they will be here for almost seven days.

After that, under the guidance of relevant teachers from Hong Kong Chinese University, Xu Yuan and his friends quickly arrived at the dormitory.

Although we live on campus, the graduate student dormitories here accommodate two people per room, and the overall environment is no worse than that of the newly built Bauhinia Apartments.

After everyone was assigned their assigned areas, they unpacked their luggage and made their beds. Everyone seemed very satisfied.

Xu Yuan naturally lived in the same dormitory with Liu Yang. After everything was done, the twenty of them went downstairs together and strolled around the campus.

After all, it is the first time for everyone to come to the Chinese University of Hong Kong, so it is normal to be curious about the environment and culture here.

Liao Fangyi did not stop them, but he did not choose to go with everyone. Instead, he locked himself in the room to continue to perfect the next lecture.

In addition to academic exchanges, cultural exchanges, and discussions on educational methods, the most important arrangement of the entire exchange activity is the mathematics lecture reports.

Professor Qiu Chengtong from the Chinese University of Hong Kong will be giving a lecture at that time, and he certainly doesn't want Qinghua to be at a disadvantage.

Fortunately, with Xu Yuan, the prince of mathematics, we don’t have to worry too much about this matter.

that's it.

Eight o'clock the next morning.

As personnel from both sides completed the opening ceremony in the lecture hall, the exchange between the mathematics departments of the two universities officially began.

Compared to the morning session, the most anticipated event is the first academic lecture in the afternoon.

In addition to students from Qinghua, there were also many graduate students from the Department of Mathematics at the Chinese University of Hong Kong. The lecture hall that could accommodate more than a hundred people was almost full.

The news that Qinghua Mathematics Department was coming for exchanges was no secret, so many people at Hong Kong Chinese University were looking forward to Xu Yuan.

I want to see the real abilities of this mathematical genius who is praised by many famous mathematicians.

So much so that when Xu Yuan walked into the classroom, he immediately attracted many students from the Department of Mathematics of the Chinese University, causing a commotion and whispers.

"He is Xu Yuan who proved the smoothness of the solution of Monge-Ampere equation?"

“He does look young.”

"I published two papers in Annals of Mathematics during my undergraduate studies. No wonder Professor Qiu values ​​me so much."

"I haven't read his paper. Is it really that awesome?"

"No matter how you look at it, this achievement is not as good as Gauss's. How can he be called the Prince of Mathematics?"

"It's a pity that I still can't beat Terence Tao, who is a hot candidate for the Fields Medal at the International Congress of Mathematicians next year."

……

Xu Yuan basically heard all the comments, but his expression remained calm and was not affected.

However, Liu Yang and Zhang Jundong who were sitting next to them were indignant.

"These people actually dare to doubt the level of Xu Shen. I'm afraid they can't even write a paper in the Annals of Mathematics, yet they have the nerve to criticize him."

"So what if the Fields Medal? I believe you will be able to win it in the future, Brother Yuan."

Hearing this, Xu Yuan didn't know whether to laugh or cry. He didn't expect that the two of them were even more arrogant than him.

So he immediately said: "We are here to exchange and learn, so it is a waste of time to care about other people's opinions." As soon as he finished speaking, Liu Yang and Zhang Jundong immediately reacted, spat, and then retracted their attention, waiting to listen carefully to this academic lecture by Professor Qiu Chengtong.

Soon when Qiu Chengtong walked in with a cup, the entire classroom became quiet and there was no sound at all.

As for the department head Liao Fangyi who led the team, he was also sitting in the audience, waiting for his lecture later.

"There are also students from the Department of Mathematics at Qinghua University here today. I hope you can join me in exploring mathematics and discussing various problems in mathematics together."

Qiu Chengtong stood on the podium. He glanced at Xu Yuan who was sitting in the middle seat intentionally or unintentionally, made a brief opening remark, picked up a piece of chalk and turned to write the content of today's lecture on the blackboard.

"L2-integral estimates of the cross-sectional curvature of Riemannian manifolds."

When Xu Yuan saw the content on the blackboard, he was stunned. He didn't expect that Qiu Chengtong's first lecture would be related to Riemann manifolds.

During this period, he read a lot of materials and attended several classes, so he was naturally familiar with Riemann manifolds.

The so-called manifold is a special type of connected Hausdorff-paracompact topological space.

A coordinate system is pre-established near each point in this space, so that the coordinate transformation between any two coordinate systems is continuous.

A Riemann manifold is a differentiable manifold in which the tangent space of each point p defines a dot product, and its value changes smoothly with p.

The cross-sectional curvature is also called the Riemann curvature, which is a way to describe the curvature of a Riemann manifold in Riemannian geometry.

He remembered that Qiu Chengtong had proved the Calabi conjecture by using the concept of curvature in geometry and solving an extremely difficult partial differential equation, and won the Fields Medal for overcoming this world-renowned mathematical problem.

Thinking of this, he couldn't help but become interested, and immediately made himself concentrate and listen carefully.

But this is really hard for Liu Yang, Zhang Jundong and other students sitting in the classroom. They never expected that the first lecture would be so difficult.

It may not be easy to understand.

But since everyone was seated, I had no choice but to listen.

Qiu Chengtong did not pay attention to the situation in the audience, and then started to speak while writing formulas at his own pace.

"K(σ)=(R(u, v)v, u)/|u||v|-(u, v)"

"The simplest type of Riemannian manifold is that of constant cross-sectional curvature, and they are called spatial forms."

“There are three scenarios with scaling metrics.”

……

Qiu Chengtong did not speak very fast in this lecture, but as time passed, most people in the classroom were confused.

Because I couldn't understand the relevant knowledge points at all, I just felt drowsy.

Liu Yang was even more dumbfounded at this moment. He was fortunate to be selected to participate in this exchange between the two schools. He had thought that listening to Professor Qiu Chengtong's lecture would improve his own mathematical level.

As a result, I was hit hard at the first lecture. I couldn't even understand what was being said, let alone improving myself.

It was obviously beyond his current level of mathematical knowledge.

Finally, he sighed helplessly, turned his gaze to Zhang Jundong beside him and asked in a low voice.

"Senior."

"Do you understand?"

Because Zhang Jundong is a fanatical fan of Xu Yuan, the two of them have become much more familiar with each other in the past two days.

Zhang Jundong turned his head away and said in embarrassment: "I haven't learned these yet."

Especially looking around the entire classroom, even the graduate students basically had the same behavior as him.

Only when your eyes fall on Xu Yuan, a face with a serious and focused expression appears in your field of vision, which makes you want to sigh.

"I guess Xu Shen was the only one who understood it in the whole classroom."

Hearing this, Liu Yang glanced at Xu Yuan and nodded in agreement.

The two of them did not disturb Xu Yuan's thoughts until Qiu Chengtong on the stage took the initiative to stop the progress, and then they saw Xu Yuan finally came back to his senses and looked thoughtful.

At this time, Qiu Chengtong picked up the teacup and took a sip of water, then glanced at the students in the classroom and asked.

"Did you all understand the explanation about the cross-sectional curvature problem of Riemann manifolds?"

As the words fell, no one in the entire classroom spoke.

I am too embarrassed to say that I didn’t understand at all, but I also don’t dare to pretend to understand when I don’t.

Qiu Chengtong didn't seem surprised by this result. The next second he directly mentioned Xu Yuan's name and asked.

"Xu Yuan."

"Do you understand?"

Xu Yuan was thinking back over what had just been explained, using his various mathematical abilities to help him understand it quickly, and trying to combine it with other mathematical knowledge in his mind.

When he heard his name, he stood up and answered, "Professor Qiu, I understand everything."

As soon as these words were spoken, they instantly attracted the attention of everyone in the classroom.

Except for Liao Fangyi who looked very pleased, all other students from Hong Kong Chinese University had doubts on their faces.

Most of them were graduate students in the Department of Mathematics, and some of them had even attended Professor Qiu Chengtong's lectures many times. Even they could hardly understand this lecture, let alone Xu Yuan who was still an undergraduate.

(End of this chapter)