Chapter 367 Proof of Bloch’s conjecture!
While the researchers of Planck Plasma Physics were conducting investigations in the Western Superconducting Group's factory, the Qixia Controlled Nuclear Fusion Engineering Base also selected a team of about thirty people and sent them to the Germanic country. .
For transactions between ASDEX devices 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. In about half a month, Planck Plasma Physics Research and Xu Chuan communicated again and began to conduct transactions.
Xu Chuan did not go there personally. Gao Hongming would arrange a special team to negotiate and handle related matters.
At this point, there was nothing else left to do, and Xu Chuan also focused on the Qixia Mountain controllable nuclear fusion project.
In addition to the nuclear fusion project, Nanjing University also welcomed the big boss classes again, which surprised many students in the School of Mathematics.
The days passed like this day by day, and time soon came to May.
Working in three shifts, with people resting and machines not resting, and using several times the manpower to fill the project, the controllable nuclear fusion project base in Qixia Mountain has completed the construction of the main building, and it is expected to take about another month and a half. The overall construction can be completed.
The ASDEX device that Xu Chuan is concerned about has also departed from the Germanic country and is being sent across the ocean.
In order to ensure that there will be no errors in the transportation of this kind of large precision equipment, the ships that sail and transport will choose a more reliable route.
And you need to always pay attention to weather changes when sailing, so the delivery time will be longer, and it will arrive around early July.
In addition, large-scale supercomputing centers for running plasma turbulence numerical control models are also being built in full swing.
According to the plan, its completion time is similar to that of the base research institute. It will remain in mid-June, just in time, leaving half a month for acceptance, and then after receiving the ASDEX device, the test will be started simultaneously.
On the other side, NTU.
After celebrating the 20th New Year, Gu Bing and Amelia, who had returned to school, were staying up late together.
Without him, their graduation thesis seems to have a promising breakthrough.
Following a mentor like Xu Chuan can be said to be a great blessing or a great misfortune.
Because from the beginning, this instructor had very high requirements for them.
Using a world-class mathematical problem as a goal to graduate from him is simply terrifying.
Although there are algebraic variety and group mapping tools that have reduced the difficulty, for a doctoral student, this requirement is still ridiculously high.
However, it is precisely because of this high demand that they gained more knowledge while studying with this instructor.
Although there may be many times when the mentor may be busy with his own business, he never holds back when it comes to teaching them.
Whether it's mathematics or physics, or some questions that interest them, as long as they are serious, he can give the answer.
And this learning experience is extremely valuable for both of them.
Time flies to early June.
In the Qixia Mountain Controlled Nuclear Fusion Research Institute, Xu Chuan is processing documents in his office.
As the project was gradually completed, he had more things to do. There were meetings and reports to be held and read every day.
Since the completion of the institute in May, the team that originally rented offices at the Xianlin campus has also moved here collectively, and he is no exception. Most of the work on the project is now handled here.
The black pen in his hand was used to sign his name on a business document. Xu Chuan was about to open the next document when the cell phone on the table rang.
He picked up the phone and took a look at it. The caller was his student Amelia.
He answered the call casually, clicked the speakerphone and put the phone on the table. Xu Chuan continued to flip through the files on the table.
On the other end of the phone, Amelia's voice sounded with some joy and excitement: "Professor, are you free to come to school now?"
Xu Chuan asked casually: "What's wrong? What's the matter?"
"We would like to ask you to read a paper."
Hearing this, Xu Chuan stopped flipping through the documents and looked at his phone. After thinking for a moment, he smiled and said, "Then wait for me for a while."
"No problem!"
After hanging up the phone, Xu Chuan held the signature pen in his hand and stared at the white wall opposite for a moment, then put down the pen and stood up to leave the office.
It didn't take long to rush back to Nanda from Qixia Mountain. In less than twenty minutes, Xu Chuan stood at the door of his office. Glancing at the half-opened door, he stopped and paused for two seconds before opening the door and walking in.
In the office, three students, Gu Bing, Amelia and Cai Peng, were present. They were discussing something happily but they quickly became nervous after seeing Xu Chuan's arrival.
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 manuscript paper from the two men's hands, and then combined it into one.
"If p is a property, and non-constant integral 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 tightened.
Just as he expected, his two students may be graduating.
His eyes fell on the manuscript paper in his hand. Xu Chuan was immersed in it and reviewed it carefully.
A specific family of holomorphic functions is a theory proposed by the mathematician P. Montel in 1912 and has been widely used in complex variable function theory.
Bloch's conjecture is not actually a conjecture in the strict sense. It is a problem derived from the normal family of holomorphic functions and the normal family of meromorphic functions.
The normal family refers to a family of functions with certain convergence properties, which is defined as: "A holomorphic function family F in a region D is said to be normal within D. If from each function sequence fn(z)( n=1, 2,...) can select a subsequence such that it uniformly converges to a holomorphic function or uniformly diverges to ∞ within D. ”
Nowadays, the theory of the normal family of holomorphic functions and the normal family of meromorphic functions has been developed to a very complete stage, but an important research issue in this theory is to seek new regularity rules.
Mathematicians have actually done a lot of work on this issue.
For example, corresponding to Liouville's theorem about integral functions is Montel's theorem above about a family of uniformly bounded holomorphic functions; or corresponding to Picard's theorem about integral functions is Montel's theorem about two A regular theorem for a family of holomorphic functions with exceptions.
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 a family of holomorphic functions 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 the manuscript paper in his hand, and beside him, Gu Bing, Amelia and Cai Peng were waiting quietly.
The tense atmosphere filled the whole room, and the three of them didn't even dare to take a breath for fear of affecting something.
Half an hour passed in the blink of an eye, and the last two pages of manuscript 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 It is holomorphic within △-(Z, δ/2) = {z: |z-z|≤δ/2}, and has max0≤θ≤2π (1/Fn(z+δ/2eiθ)<2/A). ”
".In this small circle, there are {Fn} inner closures that uniformly converge to 0, so F is normal at Z, then F is on the right track in area D!"
"It is not difficult to deduce from the above expression that Bloch's conjecture is established!"
After quietly flipping through the last two pages of the manuscript, Xu Chuan raised his head with a pleased smile on his face: "It is excellent proof that the work you have done is quite excellent. You have expanded the scope of regular family functions and surpassed the predecessors." limits and made a great result! ”
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 20, for two and a half years, they studied mathematics with themselves, learning algebraic varieties and group mapping tools; then they expanded on this basis, extended their own ideas, and created their own knowledge.
Now, it's 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 to see that the theory of "algebraic varieties and group mapping tools" he constructed for the Hodge conjecture was showing its tenacious life in the new generation.
It did not stop at Hodge's conjecture, nor was it limited to itself, but was passed on.
A single spark can start a prairie fire.
Xu Chuan believes that one day, the theory of "algebraic varieties and group mapping tools" will blossom into the most dazzling life in the world of mathematics.
PS: Second update, please vote for me!
(End of chapter)