Chapter 136 I underestimated your talent
Deligne's main research areas are number theory and algebraic geometry, which is why he knows the amount of energy required. Xu Yuan is indeed very talented in mathematics, but at this age, being able to master a branch of mathematics is already impressive.

Xu Yuan solved the Carmichael number problem in the branch of number theory and made a major breakthrough in the twin prime conjecture.

The Monge-Ampere equation is also added in the middle.

Logically speaking, it should occupy all the energy and time, making it impossible to study other branches.

At least that's the case now.

When he saw Xu Yuan bring out his problem, he subconsciously thought it was in the field of number theory.

I am looking forward to the next communication with Xu Yuan.

Although he has achieved brilliant results in mathematics, he does not dare to say that he is better than Xu Yuan.

This is absolutely impossible with singular theory.

So they can only be considered to understand each other, and they might even get some inspiration from Xu Yuan in the process.

As it turned out, the actual situation was not what he had imagined, and the problem Xu Yuan brought out was actually algebraic geometry.

After listening to Xu Yuan's words, Deligne learned that the other party was also studying Qiu Chengtong's conjecture. He couldn't help but frown slightly and feel regretful.

We have just made a breakthrough in the twin prime conjecture, and we should press on with our victory.

Continue to dig deeper in the field of number theory.

If you suddenly switch to algebraic geometry and have to devote all your energy to it again, there is a high probability that even number theory will be neglected.

Perhaps because he was worried that Xu Yuan's talent was wasted, he moved his lips slightly and finally spoke.

"Why did you suddenly switch to studying algebraic geometry, and even chose the difficult problems in algebraic geometry?"

"Although Qiu Chengtong's conjecture is a problem of algebraic geometry stability, it actually belongs to the first positive case of the remaining Chern class of the Calabi conjecture, which involves many branches of mathematics."

"I suggest that you focus on number theory at this stage and continue to study the problems in number theory."

"In a few years, you will hopefully become a master in the field of number theory in the mathematical world."

Having said this, Deligne put the question handed by Xu Yuan on the table, his eyes full of anticipation.

Xu Yuan naturally understood that the other party was considering him, but Deligne didn't know that he could enter a deep learning state at any time. This allowed him to have a learning efficiency and thinking many times higher than that of others. This could be said to be his biggest reliance for studying multiple branches of mathematics at the same time.

The thought stayed here, and he didn't refute anything, but just answered truthfully.

"It was Professor Qiu Chengtong who asked me to try to solve his conjecture. I am also very interested in algebraic geometry."

"Professor Qiu Chengtong?" Deligne repeated.

As a fellow Fields Medal winner, he is naturally no stranger to Qiu Chengtong.

Learning that Qiu Chengtong was also so optimistic about Xu Yuan, he couldn't help but feel a little confused.

After a brief thought, he picked up the question again and said, "In that case, let me tell you about this conjecture."

However, it is worth mentioning that this time he was talking about the topic, not communicating like number theory.

Obviously, in his heart, he didn't think Xu Yuan had much understanding of algebraic geometry.

Xu Yuan didn't care about this and sat opposite him with a serious expression.

"The Calabi conjecture involves string theory, which states that complex high-dimensional space is made up of multiple multi-dimensional spaces glued together, meaning that high-dimensional space can be assembled through simple geometric models."

"Qiu Chengtong solved the Calabi conjecture that the Chern class is zero or negative, but he could only transform the problem of the Chern class being positive into the stability of algebraic geometry."

"The academic community believes that this conjecture should start from the existence of a constant scalar curvature metric on a Kähler manifold and be restricted to the Kähler Einstein metric."

……

Xu Yuan did not just listen to Deligne's explanation, but also added his own thoughts on Qiu Chengtong's conjecture in the process.

Taking advantage of the other party's pause, he immediately continued: "To prove the existence of a constant scalar curvature metric, we need to find a solution to a fourth-order completely nonlinear elliptic equation. In the process of solving the equation, I tried to use algebraic geometry, combined with differential geometry, multi-complex functions and metric geometry." When he spoke of these things, he showed confidence that was no less than that of scholars who had been immersed in it for many years.

Deligne didn't care much at first, but after hearing what Xu Yuan said, his eyes gradually brightened.

He originally thought that Xu Yuan had just started learning algebraic geometry and was trying to prove the Yau Cheng-Tung conjecture.

But now it seems that this is not the case.

Judging from what was said, I'm afraid that even a professor who has studied algebraic geometry for many years would be like this.

The thought stayed here, and Deligne suddenly became interested.

He waved his hands and shouted, "Write out the method you used."

"Okay, Professor Deligne." Xu Yuan took the draft paper and nodded in response.

He has not yet completely proved Qiu Chengtong's conjecture. If he writes down the combined formula, it may be improved under Deligne's guidance. He certainly will not refuse such a thing that will speed up the proof of the conjecture.

Xu Yuan did not waste any time and quickly wrote out the formula he had come up with.

Deligne, whose eyes were fixed on the draft paper the whole time, stood up involuntarily.

After playing it out in his mind, his expression was instantly replaced by surprise.

The look he gave Xu Yuan returned to the same as when he first came in, and he couldn't stop talking at all.

“This formula is a wonderful combination!”

"very good."

“There is no loophole in the logic.”

After praising you for several times, he paused for a moment, then said to Xu Yuan excitedly, "No wonder Qiu Chengtong asked you to challenge his conjecture. I didn't expect that you have such a deep understanding of algebraic geometry. I underestimated your talent just now."

"With your current proof ideas and methods, we are only a few steps away from solving a class of fourth-order fully nonlinear elliptic equations."

"Then the Calabi conjecture will be completely fulfilled."

He studied two branches of mathematics in different fields. Whether it was the progress in the twin prime conjecture or the solution to the stability of algebraic geometry, he should be happy and congratulated for it.

Because this represents progress in mathematics.

The importance of mathematics to all walks of life, scientific research and technology is self-evident.

Behind the solution of every difficult mathematical problem lies the progress of human civilization.

Perhaps because he got such a pleasant surprise and was quite excited, he started to study again without waiting for Xu Yuan to speak.

"I know this formula still has room for improvement. Let's study it."

……

Xu Yuan was really moved by Deligne's enthusiasm, and the two of them studied in the office until dark. They even had to ask someone to bring them lunch. Even at the end, Deligne was still reluctant to leave.

However, after communicating and discussing with Deligne, Xu Yuan gained a lot.

At the same time, I have a new idea for the solution to prove Qiu Chengtong's conjecture.

We can try to improve the formula on the original basis in order to solve a class of fourth-order fully nonlinear elliptic equations more quickly.

Since Zhang Yitang arrived at the hotel in the afternoon, Xu Yuan saw him coming after returning from Princeton University.

"If Professor Feng hadn't told me this afternoon that you went to visit Professor Deligne, I would have thought you were out playing."

Zhang Yitang came to Xu Yuan's room and told him what happened in the afternoon.

This time he was invited to give a speech at an academic conference. After all, it was his first time, so he was inevitably a little nervous.

In addition, Xu Yuan improved the sieve method and directly reduced his 4200 million to less than 246 prime number pairs. If Xu Yuan was not there, it would be difficult for him to hold on by himself.

Xu Yuan smiled and explained, "I came to visit Professor Deligne to ask him questions. I didn't expect to talk till so late."

"It's not easy to make Professor Deligne so interested. Is it a problem in number theory?" Zhang Yitang said with some envy.

Xu Yuan shook his head and said, "It's about Qiu Chengtong's conjecture."

After saying that, he took out his draft paper and pen, ready to improve the formula based on the day's discussion.

Zhang Yitang was naturally more envious when he heard this, and the next second he sighed:
"It's better to be young."

"I have to go back and study the report."

The academic conference will officially begin tomorrow, and in the afternoon there will be a report on the proof of the twin prime conjecture.

According to the arrangement, Zhang Yitang will first explain the proof of 4200 million prime number pairs, and then Xu Yuan will come on stage to use the improved sieve method to prove 246 prime number pairs.

As a middle-aged man who achieved success late in life, Lao Zhang naturally could not compare with Xu Yuan in terms of thinking and energy.

Studying number theory alone is difficult enough, not to mention other branches.

After hearing this, Xu Yuan just watched Lao Zhang leave, then sat down at the table in the room and concentrated on his calculations.

The next day.

Eight in the morning.

After having breakfast at the hotel, Xu Yuan and Zhang Yitang went to the venue under the guidance of Feng Zuming.

The academic conference was held in the Auditorium of Princeton University.

Soon after entering the hall, the most eye-catching thing is the hanging posters, which list all the people who will be giving reports and their topics.

Because the twin prime conjecture was the protagonist this time, he quickly found himself and Zhang Yitang.

However, because the content of the paper is so long, only a part of it is included on the poster.

"Let's go over there to get autographs and enter, so as not to delay the opening ceremony." Feng Zuming reminded from the side.

After hearing this, Xu Yuan noticed that there were special personnel nearby who required participants to sign their names before entering.

Xu Yuan naturally had no objection to the conference arrangement, but after signing, he saw that there were free gifts being distributed.

Even though they were all worthless little things, they were printed with the logos of the Annals of Mathematics and Princeton University. When I took them back and gave them to Li Zhenya and the others, they would definitely say "Brother Yuan" to me.

Besides, he hasn't forgotten that he has a little cousin at home, and she will be taking the high school entrance exam next year.

The thought stayed here, so he asked Feng Zuming beside him: "Professor Feng, can I get a few more of these gifts?"

Hearing this, Feng Zuming just sighed and said, "Let's go in first. I'll pack a bag for you and send it to the hotel when the time comes."

"Then I'll have to trouble you, Professor Feng." Xu Yuan replied with a smile.

After arranging the gifts, the three of them went to the main lecture hall upstairs where the opening ceremony was held.

As soon as I walked in, I saw Deligne coming towards me, and next to him was a man wearing half-frame oval lenses. Judging from their hair and faces, the two men should be about the same age.

"Let me introduce you to Xu Yuan. This is Professor Witten from the Institute for Advanced Study in Princeton. His main research is string theory."

……

(End of this chapter)