The research projects of miniaturized and controllable nuclear fusion and aerospace engines are progressing in an orderly manner, and after focusing on these two projects, he learned about the work of the other two research institutes of the Xinghai Research Institute.

At present, there are not many independent scientific research projects in the work of the Institute of Information Science and the Institute of Materials, which are mainly in conjunction with the research projects of miniaturized and controllable nuclear fusion and aerospace engines.

As for management, Xu Chuan doesn't particularly want to spend time on it, after all, people's energy is limited.

Fortunately, there are people arranged by the state to help, but he doesn't need to worry too much.

In mid-to-late June, after several rounds of testing and collecting enough data, the Huaxing fusion device started the first round of deuterium-tritium raw material fusion ignition experiments.

The experiment went quite smoothly, and after several rounds of adjustments to the numerical control model of the plasma turbulence, the control of the high-temperature plasma in the internal chamber of the stellar simulator became more and more complete.

After two hours of operation, the Huaxing fusion device successfully drove a group of ferrofluid engine units to transmit a small amount of power to the local power grid.

This news is undoubtedly encouraging, as it represents the potential of stellarators to enable controlled nuclear fusion technology as well.

Of course, there are many problems found in this experiment.

For example, the internal chamber space of the stellarator is small, and the shape orbit is complex, which is easy to form unrestricted particle orbits, which will lead to the loss of high-energy particles and hot particles, and the relative difficulty of plasma temperature increase.

These problems affect the Q value and efficiency of the stellarator, and they are all problems that need to be solved.

However, compared to the problems faced by the first research of the Daybreak fusion device, these problems are far less difficult to solve.

Although Xu Chuan cares, these problems are not impossible to solve when handed over to the Xinghai Research Institute.

And he's got to give the others some exercise, doesn't he?

If all the problems were solved by him, what would be needed from the other researchers and engineers.

The days passed like this, and at the beginning of July, as usual, Xu Chuan stepped on the dot and came to Nanda.

In the office, as soon as he entered the door, an excited voice came over, almost startling him.

"Professor, I've got it done!"

The excited voice came from his ears, Xu Chuan looked at it, and in the office, Cai Peng was standing in his position excitedly, with a red and excited expression on his face.

Looking at his excited student, he was slightly stunned for a moment, then remembered something, and said with a smile: "What about the paper?" Let me see. ”

Hearing this, Cai Peng quickly handed over the paper in his hand.

Xu Chuan took the paper and read it carefully.

Phased Proof of Minimum Differential Computation of Dimensional Polynomials of Differential Equations! 》

Let K be a zero-feature differential domain, ={δ1,···,δm} as its differential operator. Let L = Khη1,····,ηni be the differential expansion domain generated by K and a finite number of elements η={η1,····,ηn}. Θ denotes the freely commutative semigroups generated by δ1, ···, δm. If r is any non-zero integer, let .

"(i) If r is any sufficiently large integer, then there is ωη|K(r)= trdegKLr; ”

“(ii) degωη|K 6 m, and ωη|K(t) can be written as ωη|K(t)=mXi=0ait + ii, where a0, ···, am is an integer. ”

“(iii) d = degωη|K、am”

The paper in his hand was flipped through little by little, and Xu Chuan looked at it seriously.

The calculation of the minimum differential dimension polynomial of differential equations was the graduation topic chosen by his student.

Before this year, he didn't expect Cai Peng to solve this problem before graduation.

After all, this is a world-class math problem, and the difficulty is probably around the end of T3 to the top of T4.

Solving such a problem can take a lifetime for many mathematicians, or they may not be able to do it.

For Cai Peng, as long as there is a breakthrough in this field, phased results can be made, and the paper passes the review of the journal.

However, at the beginning of this year, Cai Peng made great progress and breakthroughs on this issue, and at that time he looked at what was made and pointed out some directions.

Now a few more months have passed, and now, it is his turn to reap the abundant fruits.

Turning over the pages of the paper, Xu Chuan's eyes carried some praise.

With his ability, it is not very difficult to understand these things when it is proved that the paper has been made.

After reading the last page of the paper, Xu Chuan raised his head with a smile and praised: "Very beautiful proof process, by expanding the field to construct a fractal framework, so as to make a judgment on the minimum differential dimension polynomial of the differential dimension polynomial, in recent months, you have not wasted your time." ”

In the paper in his hand, he saw some shadows of the methods he used in his previous solution to the Weyl-Berry conjecture, and also saw something that belonged to Cai Peng himself.

Although it is only a phased achievement, it is already very, very good for a PhD student.

"Thanks to your guidance, Professor, without your teaching, I might never have found my way."

Cai Peng thanked him from the bottom of his heart, this is indeed what he said in his heart.

It was only now that he realized how important a good mentor really is.

Before he followed Xu Chuan, to be honest, the upper limit of his life was probably like that.

Go to Princeton, then go back to your home country and get a job, and do a little more math to see if you can make something.

If he's lucky, maybe he can make something and publish a big four journals, mix up a good youth or a distinguished young man or something, but this is almost as good as he can imagine, and he has to have full luck.

Like now, being able to solve a world-class problem before graduating from his Ph.D., although it is really a phased achievement, although it has not yet passed the journal review, it is still something he never dreamed of before.

There are a lot of talented people, but there are few who can get ahead, one percent? Not even one in a thousand.

There are too many buried talents in this world, Maxima often has, but Bole does not often have them.

Although this mentor was a bit 'unreliable' most of the time, he still taught him countless things, especially those experiences and methods in academic research, which he would not necessarily learn when he went to Princeton.

After all, Princeton doesn't have the first person in math either, does it?

Listening to Cai Peng's words, Xu Chuan smiled, and after returning the paper in his hand to him, he patted him on the shoulder and said with a smile: "Come on, this is just the beginning, the calculation problem of the smallest differential dimension polynomial, there is still half of it waiting for you." ”

Nodding vigorously, Cai Peng said excitedly: "Hmm! I'll try! ”

Xu Chuan nodded with a smile, looked at the other students in the office, and said, "Your senior brother is also about to graduate, you also have to work hard." ”

In the office, several new students who were admitted last year nodded vigorously and cast envious glances at Cai Peng.

A worldwide problem, this is too enviable!

But then again, the difficulty of this graduation is really high!

In the office, Xu Chuan looked at several students and felt some emotion in his heart.

I have to say that whether it is Gu Bing and Amelia in the past, or Cai Peng now, or a few freshmen who are still studying, watching them grow up step by step and have the ability to take charge of themselves, it is really a kind of old fatherly relief, there is a feeling of annoyance when a child grows up!

Thinking about it, he suddenly remembered something, came back to his senses, looked at several students and said with a smile: "There is still half a month to go, this year's International Mathematical Conference will be held, this afternoon I will give you three questions, if you can solve two of them before the International Mathematical Conference, I will take you to see the world." ”

"Cai Peng can be exempted, the results he made are completely enough for him to give a forty-five-minute report at the mathematics conference."

After a pause, he looked at Cai Peng and said with a smile: "Submit the paper early, maybe this year's International Mathematical Union will send you a reissue invitation letter." ”

It's already early July, and the invitation to the International Mathematical Conference in mid-July has long been sent, but a world conjecture at the end of T3, even if it is a phased achievement, is enough to make the International Mathematical Union pay attention to reissuing an invitation.

Hearing this, the four freshmen immediately threw envious glances at Cai Peng again.

Feeling the gaze of these juniors, Cai Peng grinned, stood up straight with his head held high, and greeted the envious and admiring eyes of the juniors.

He, the elder brother, this will be regarded as a glorious and great, the highlight of a proper life!

"Professor, which journal should I apply to?"

Xu Chuan smiled: "It's good for you to decide this yourself, but I suggest that you publish it on arxiv after submitting to the journal, and send a copy to the International Mathematical Union, after all, the review speed of journals is sometimes very slow." ”

"I'll say hello for you, maybe you can hope that Gu Bing and Amelia will come up and make a report this time."

For mathematics journals, unless it is a top mathematician, such as him, or a problem similar to the Seven Millennial Problems, which deserves a solo presentation, the general review time is as long as several months or even six months to a year.

For such a long time, if Cai Peng is reviewed normally, there will definitely be no hope for him to give a report at this International Mathematical Conference.

However, as his mentor, he can help with a lot of unnecessary things, although the review time of the journal cannot be reduced to half a month, but with his academic reputation, it is enough for the International Mathematical Union to give face.

Of course, more importantly, Cai Peng's paper has enough value to appear on the stage of the International Mathematical Congress.

If not, he wouldn't have been able to open it.

As for Gu Bing and Amelia, they have already received invitations, after all, the two people who solved Bloch's conjecture are fully qualified to give presentations at the International Mathematical Conference.

Looking at the few students who were gearing up, preparing to meet him with math problems, and wanted to go out to meet the world, Xu Chuan shook his head with a smile.

With this year's International Congress of Mathematics just around the corner, it's time for the second half of the Jan Mills existentiality and mass gap puzzle to be sent.

After all, it is a millennial problem, and even at a grand event such as the International Congress of Mathematicians, many mathematicians have to be given some time to prepare in advance.

Thinking about it, Xu Chuan clicked on the arxiv preprint website and submitted the paper that had been prepared for a long time.

For arbitrary, compact single-group G, there is a massive quantum Yang-Mills field with G as the gauge group on R4, and there is a mass gap > 0！ 》

The title of the paper is long, but it is the best response to the problem of Yang-Mills' existential and quality gaps.

After uploading the paper to the arxiv preprint website, Xu Chuan didn't care about it anymore.

He pulled out the paper and pen from the drawer, and looked at the computer screen in front of him, and he fell into deep thought.

The Jan Mills existential and mass gap problem has been solved by him, and the next goal, of course, is to unify the strong electricity.

This is one of the greatest crowns of theoretical physics in the twenty-first century.

It is also the goal that he did not complete in his previous life and hopes to accomplish in this life.

However, he didn't have a complete idea of how to take off the crown, even if the Jan Mills existential and mass gap problem was solved by him.

It's not something that comes naturally.

Although there have been rumors in the physics community that if anyone solves the Yang-Mills existential and mass gap problem, there is hope for the unification of strong electricity, but that is only hopeful.

If someone says that they can easily complete the unification of strong electricity, don't hesitate to go up and give him a big beep directly.

If this problem were so easy to solve, could it be called the greatest crown of theoretical physics in the twenty-first century?

The so-called water comes naturally, then you have to have water first.

For example, gauge symmetry is the cornerstone of the Yang-Mills theory, in which the behavior of a physical system remains constant under some kind of continuous transformation.

Or the gauge symmetry of the electromagnetic field is that under the local transformation of the electromagnetic potential, the interaction and electromagnetic interaction can be described by the Yang-Mills theory.

These are the cornerstones of a theory to help, and they are also the water that comes naturally.

However, there is no such cornerstone for solving the unified theory of strong electricity mathematically, and he needs to find a coupling constant to determine that under the mathematical system, the particles corresponding to these fields can interact.

When faced with this problem, the existence of Young-Mills and the existence of the mass gap can provide some help, but it is not enough to completely solve the problem.