Chapter 367 Proof of Bloch's Conjecture!

While the researchers of Planck Plasma Physics Research were investigating in the factory of Western Superconducting Group, the Qixia Controlled Nuclear Fusion Engineering Base also selected a team of about 30 people and sent them to the Germanic country.

For the transaction of ASDEX device and superconducting materials, both parties must fully confirm the qualifications and situation of the other party before proceeding to the next step.

However, this time did not take long. About half a month later, Planck Plasma Physics Research and Xu Chuan communicated again and began to work on the transaction.

Xu Chuan did not go there in person for this matter. Gao Hongming would arrange a special team to negotiate and deal with related matters.

At this point, there was no other work left to do, and Xu Chuan also focused on the Qixia Mountain Controlled Nuclear Fusion Project.

In addition to the nuclear fusion project, Nanjing University also ushered in the days when the big guys taught classes again, which surprised many students in the School of Mathematics.

The days passed one by one, and time soon came to May.

In three shifts, people resting but machines not resting, and using several times the manpower to fill the project, the controlled nuclear fusion project base in Qixia Mountain has completed the construction of the main building. It is expected that the overall construction will be completed in about one and a half months.

The ASDEX device that Xu Chuan is concerned about has also departed from the Germanic country and is being sent across the ocean.

For the transportation of such large precision equipment, in order to ensure that there will be no mistakes, the ships will choose a more stable route.

And it is necessary to pay attention to weather changes at all times during the voyage, so the transportation time will be longer, and it will arrive around early July.

In addition, the large supercomputing center for running plasma turbulence numerical control models is also being built in full swing.

According to the plan, its completion time is about the same as that of the base research institute, which will remain in mid-June. It is just right to leave half a month for acceptance, and then start testing synchronously after receiving the ASDEX device.

On the other side, Nanjing University.

Since the New Year of 20 years, Gu Bing and Amelia, who returned to school, are staying up late together.

Without him, their graduation thesis seems to have a chance to make a breakthrough.

Following a mentor like Xu Chuan can be said to be a great fortune, or a great misfortune.

Because from the beginning, this mentor had very high requirements for them.

Using a world-class mathematical problem as the goal requirement for graduating from him is simply terrible.

Although the algebraic cluster and group mapping tools have reduced the difficulty, this requirement is still ridiculously high for a doctoral student.

However, it is precisely because of this high requirement that they have gained more knowledge while studying with this mentor.

Although this mentor may be busy with his own things many times, he has never been reserved about teaching them.

Whether it is mathematics or physics, or some questions they are interested in, as long as they are serious, he can give answers.

And this learning experience is extremely valuable for both of them.

Time flies and it is early June.

In the Qixia Mountain Controlled Nuclear Fusion Research Institute, Xu Chuan is processing documents in his office.

As the project is gradually completed, he has more things to do, and there are meetings and reports to attend and read every day.

Since the completion of the institute in May, the team that originally rented the Xianlin campus for office space has also moved here collectively, and he is no exception. Most of the work on the project is now handled here.

Xu Chuan signed his name on a business document with a black signature pen in his hand. Just as he was about to open the next document, the phone on the table rang.

He picked up the phone and took a look. The caller was his student Amelia.

He answered the call casually, clicked the speaker, and put the phone on the table. Xu Chuan continued to look through the documents on the table.

Amelia's voice sounded with some excitement on the other end of the phone: "Professor, are you free to come to school now?"

Xu Chuan asked casually: "What's wrong? Is there anything?"

"We want to ask you to read a paper."

Hearing this, Xu Chuan stopped flipping through the documents, looked at the phone, thought for a while and smiled: "Then wait for me."

"No problem!"

After hanging up the phone, Xu Chuan stared at the white wall opposite with the pen in his hand for a while, then put down the pen and stood up and left the office.

It didn't take long to rush back to Nanjing University from Qixia Mountain. In less than 20 minutes, Xu Chuan stood at the door of his office.

Looking at the half-open door, he stopped and paused for two seconds before pushing the door open and walking in.

In the office, Gu Bing, Amelia and Cai Peng were all there. They were originally discussing something happily, but they quickly became nervous when they saw Xu Chuan coming.

Xu Chuan smiled and said, "Where is the paper you asked me to read?"

Hearing this, Amelia and Gu Bing stood up at the same time.

Xu Chuan smiled and took a stack of manuscripts from each of them, and then combined them into one.

"If p is a property, non-constant whole functions do not have property p, then the family of holomorphic functions with property p in a region is a formal generalization proof. "

Seeing the title, Xu Chuan's pupils shrank slightly, and the corners of his mouth also showed a slight amplitude.

Just as he expected, his two students may graduate.

Looking down at the manuscript in his hand, Xu Chuan immersed himself in it and began to review it carefully.

A specific family of holomorphic functions is a theory proposed by mathematician P. Montel in 1912, which has been widely used in complex variable function theory.

The Bloch conjecture is not a conjecture in a strict sense. It is a problem derived from the normal family of holomorphic functions and the normal family of meromorphic functions.

A normal family refers to a family of functions with a certain convergence property, which is defined as: "A family of holomorphic functions F in a region D is called normal in D if a subsequence can be selected from each function sequence fn(z) (n=1, 2, ...) of F so that it uniformly converges to a holomorphic function or uniformly diverges to ∞ in D."

Today, the theory of normal families of holomorphic functions and normal families of meromorphic functions has been developed to a very complete level, but an important research issue in this theory is to seek new normality rules.

Mathematicians have actually done a lot of work on this issue.

For example, corresponding to Liouville's theorem on the entire function is Montel's theorem on the uniformly bounded holomorphic function family; or corresponding to Picard's theorem on the entire function is Montel's theorem on the holomorphic function family with two exceptional values.

These are all based on the normal family of holomorphic functions and the normal family of meromorphic functions.

However, the scope of these results is quite limited. How to extend the scope to a region where the holomorphic function family with property p is normal is still a problem that currently plagues the mathematical community.

And now, Gu Bing and Amelia may have done it.

Time passed by minute by minute.

Xu Chuan stood in the office with a manuscript paper. Beside him, Gu Bing, Amelia and Cai Peng were quietly waiting.

The tense atmosphere filled the whole room. The three of them didn't even dare to breathe, for fear of affecting something.

Half an hour passed in the blink of an eye, and the last two pages of manuscript paper came into Xu Chuan's eyes.

".Because fn is a meromorphic function and Fn≠0 in △(Z,δ)={z:|z-z|＜δ}, then 1/Fn is holomorphic in △(Z,δ), so 1/Fn is holomorphic in △﹣(Z,δ/2)={z:|z-z|≤δ/2}, and max0≤θ≤2π(1/Fn(z+δ/2eiθ)＜2/A)."

".In this small circle, {Fn} is closed uniformly and converges to 0, so F is normal at Z, and F is normal in region D!"

"It is not difficult to infer from the above expression that Bloch's conjecture holds!"

After quietly flipping through the last two pages of manuscript, Xu Chuan raised his head with a gratified smile on his face: "Excellent proof, your work is excellent, you have expanded the scope of normal family functions, surpassed the boundaries of predecessors, and made a great achievement!"

Looking at the two students in front of him, he was very pleased, pleased that his students had grown up.

From the beginning of 2018 to June 2020, for two and a half years, they followed me to learn mathematics, algebraic clusters and group mapping tools; then expanded on this basis, extended their own ideas, and created their own knowledge.

Now, it is time for them to reap the fruits.

A world-class problem is enough to prove their talent and hard work.

Of course, at the same time, he was also very happy and happy to see that the theory of "algebraic clusters and group mapping tools" he constructed for the Hodge conjecture showed its tenacious life in the new generation.

It did not stop at the Hodge conjecture, nor was it limited to himself, but was passed on.

A spark can start a prairie fire.

Xu Chuan believes that one day, the theory of "algebraic clusters and group mapping tools" will be able to bloom the most dazzling life in the mathematical world.

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