Two billion to buy a relatively short-term license for laboratory preparation methods. Even if the purchase object is room temperature superconducting materials, the price is indeed a bit exaggerated.

However, Xu Chuan and Fan Pengyue both knew that the two billion yuan was not only a subsidy to the Sichuan-Hai Materials Research Institute, but also an investment in subsequent optimization and industrialization of room temperature superconducting materials.

Room-temperature superconducting materials are too important for the development of cutting-edge technology and national defense weapons for a country.

It's so important that two billion is not even a drop in the bucket.

As long as the industrialization problem of room temperature superconducting materials can be solved, China's scientific and technological development can rise to at least another level.

This kind of income, let alone 2 billion, is worth 20 billion, 200 billion.

Therefore, Xu Chuan and Fan Pengyue did not mention returning part of the money. Since they gave it, they can just accept it.

What they have to do is to try their best to speed up and invest money to solve the optimization and industrial production problems of temperature superconducting materials.

...

After arranging the work at the Sichuan-Hai Institute of Materials, Xu Chuan returned to Nanda.

Room-temperature superconducting materials are still firmly occupying the hot spots of discussion on major platforms these days, but this matter no longer has much to do with him.

Yuan Zhouli from the science and technology side took over the relevant work and sent some of the world's top materials research institutes to China to conduct superconducting testing experiments.

Although he was a little puzzled by the short-term secrecy and the practice of preventing room temperature superconducting materials from flowing out in a short period of time, Xu Chuan didn't think much about it and asked the Chuanhai Institute of Materials to cooperate with the above work.

Probably there are some other ideas of his own, but to him, these are just trivial matters.

In the office, while Xu Chuan was thinking about arranging work in the aerospace field, a clear and sweet voice sounded in his ears.

"Professor, are you free now?"

Xu Chuan turned around and saw that his youngest student Liu Jiaying was standing at the door looking at him.

Smiling, he asked: "What's wrong?"

Walking over quickly, Liu Jiaying handed over the notebook in his hand and asked: "I have a question that I don't understand. Can you explain it to me?"

"Let me see."

Xu Chuan smiled and nodded, taking the notebook.

"In terms of submanifolds and codimensions."

His eyes fell on the delicate handwriting, Xu Chuan glanced at the questions written down with a ballpoint pen, and said with a smile.

"This question involves multiple theories such as differential geometry, differential topology and algebraic topology, differential equations and nonlinear analysis. Where did you find it?"

Liu Jiaying thought for a moment and replied: "I encountered it when I was studying Lagrangian manifolds and inferring smooth functions."

Hearing this, Xu Chuan glanced at her in surprise and asked curiously: "Does that mean you didn't find this question from other places, but derived it yourself during the learning process?"

Liu Jiaying nodded and said: "It seems that I have never seen this problem in relevant textbooks."

After a pause, her eyes fell on the notebook held in Xu Chuan's hand, and then said: "When learning compact (boundless) symplectic manifolds, the number of critical points of any smooth function on M should not be less than M.

The domain number of , and the latter is not less than the cup product length of the cohomology group of M."

"These quantities are all topological invariants of M, but the number of fixed points of non-degenerate Hamilton diffeomorphisms does not seem to be above them."

Xu Chuan smiled and said: "Non-degenerate Hamilton diffeomorphism? Of course it is not above the critical point, because this is not the content of undergraduate students."

Standing up, he walked to the corner and dragged out the mobile blackboard, picked up the marker from the pen basket, and wrote on the blackboard:

"A 2n-dimensional manifold M is called a symplectic manifold if it has a 2-form w that is non-degenerately closed everywhere. Its n-dimensional submanifold L is called a Lagrangian manifold."

"If w|L = 0, you can set: H : R/Zx M→ R is a smooth function, which defines a vector field XH that satisfies w(·, XH)= dH."

".....Diffeomorphisms have two cases: degenerate and non-degenerate. The number of fixed points of Hamilton's diffeomorphism depends on..."

The basics and ideas about this issue in his mind were written on the blackboard like a trickle of water. When the last stroke was written, Xu Chuan turned around with a smile, looked at Liu Jiaying who was staring at the blackboard and asked with a smile.

"How much did you understand?"

"About half?"

Liu Jiaying thought for a while and then quickly changed his mind and said weakly: "One third?"

"Maybe one in five..."

Xu Chuan smiled and said: "It's okay, this problem is beyond your current stage of study. This is something that only doctoral students will deal with. You are an undergraduate now, so you are already very good."

After a pause, he continued: "To solve this problem, you need to first know how to use the domain number of M and the cup product length of the cohomology class of M to determine the lower bound on the number of fixed points of?"

While talking, he erased some formulas and wrote on the blackboard again: "Birkhoff-Lewis fixed point theorem and a conjecture of Arnold", "Non-regularized gradient flow of symplectic action", D. Huss

You can check out these papers and textbooks such as "Symmetric Bilinear Forms" written by Mohler and "Applications of Gauge Theory in Four-Dimensional Topological Structures" written by Professor Donaldson."

Hearing this, Liu Jiaying quickly took out his mobile phone from his pocket and took a picture of the blackboard: "I understand, professor."

Xu Chuan smiled and said, "Go ahead. After reading these textbooks and papers, you should be able to solve this problem."

"Thank you, Professor."

"Wait a minute." Looking at the formula on the blackboard, Xu Chuan suddenly remembered something and called out to Liu Jiaying who was about to leave.

This chapter is not over yet, please click on the next page to continue reading! "What's wrong, Professor."

Xu Chuan said with a smile: "Being able to study the issues of diffeomorphisms and topological invariants means that your knowledge has gone beyond the scope of undergraduate studies, and you can consider graduating from undergraduate studies."

"But I'm only a junior, is this appropriate?" Liu Jiaying thought for a while and asked.

Xu Chuan smiled and said: "It doesn't matter, no one stipulates that you have to wait until your senior year to graduate. With your current knowledge, the knowledge at the undergraduate level no longer has much value to you."

After thinking for a while, he continued: "Let's use the question you asked today as a graduation thesis."

"As for whether you want to study for a master's degree or a direct doctoral degree after graduating from an undergraduate degree, it all depends on your own thoughts. Think about it after you go back."

It is not uncommon to graduate early as an undergraduate, and it is even less rare to get a direct PhD.

He himself is a direct Ph.D. After solving the weak Werberg conjecture, he went directly to Princeton University.

Issues regarding diffeomorphisms and topological invariants are somewhat difficult even for a doctoral student, but as an undergraduate thesis, it is already very good.

As for his kind of taking the proof of a world-class problem as his undergraduate thesis, we cannot compare it with him.

According to Xu Chuan's estimation, it would take the primary school student about four or five months to read the papers and books he divided and solve this problem.

"Professor, can I still apply for your graduate degree after graduation?" Liu Jiaying thought for a moment, then looked at Xu Chuan and asked, with hope in his eyes.

Putting aside other factors, purely from an academic point of view, she didn't want to leave.

Although this tutor doesn't have time to guide these students most of the time, what you can learn from him is unmatched by other tutors.

Xu Chuan smiled and nodded, saying: "Of course."

"Thank you, Professor."

Hearing the affirmative answer, Liu Jiaying's face suddenly showed a joyful smile: "I'm leaving first, bye, professor."

"Um."

...

Looking at Liu Jiaying's back as he walked out, Xu Chuan smiled happily.

Unknowingly, this primary school student has been following him for more than a year, reaching the moment of graduation.

Although I only graduated with a bachelor's degree, my foundation is really good, my talent is also very good, and I am hardworking and have a promising future.

Smiling, Xu Chuan turned his attention to the aerospace engineering on his desk.

According to the solar calendar, a full week has passed in 2024, and it is now 2025.

As time goes by, and as their aerospace technology matures, the time has come to land on Mars.

With the documents in hand, Xu Chuan sent a message to Zheng Hai and came to Xinghai Research Institute.

In a quiet office in the southwest corner of the Aerospace Research Institute, Academician Chang Huaxiang, who serves as the technical director of aerospace engineering, is arranging and handling the aerospace work at hand.

At this moment, the office door was knocked twice, and a young figure opened the door and walked in.

"Hey, rare guest, what kind of wind is blowing to you?"

Academician Chang Huaxiang looked up when he heard the noise. He was stunned for a moment and then put a smile on his face.

After asking with a smile, he put down his pen and stood up and walked towards the cabinet, took out a box of tea leaves and prepared to make tea.

For the Institute of Aeronautics and Astronautics, Xu Chuan is really a "rare guest". Apart from his frequent appearances during the Xinghai manned space flight and moon landings, he is rarely seen in the future.

Xu Chuan looked at the old academician and said with a smile: "Mr. Chang, please pay attention to your health and get more rest. You have a lot more gray hair."

He hadn't seen Academician Chang for a while. When he met again, his hair was obviously much grayer.

Chang Huaxiang said with a smile: "Our aerospace industry has just started. There is still a lot to be busy with. There is no time to rest."

Xu Chuan smiled and said: "Then you should also pay attention to your health and balance work with rest."

Academician Chang Huaxiang smiled and nodded. He responded and was about to say something when his eyes fell on Xu Chuan. After looking at him for a moment, he said curiously.

"Come to think of it, you don't seem to have changed much in the past few years."

There is really nothing wrong with what he said. More than three years have passed since the two first met in 2010, but the Xu Chuan standing in front of him seems not to be much like the one he remembered three years ago.

changes.
To be continued...