Great Country Academician

After writing a paper on the miniaturization of tokamak devices, Xu Chuan threw it into the folder and picked up a mathematics journal from the table to read.

After not having to worry about research work for the time being, he felt quite relaxed.

I go to NTU every week to give classes to the undergraduate students, and then I give guidance to a few of the students I teach, and then I go to the Xinghai Research Institute to preside over daily work and research.

The rest of the time is basically spent reading books and following some of the current popular research and related papers in the fields of mathematics, physics and materials.

Although his daily schedule is still full, for him, reading is not considered work.

Even those mathematics textbooks and journals that are boring to ordinary people are also things that interest him.

For him, knowledge is like wealth for ordinary people, there is never too much.

The days passed like this day by day,

At NTU, after finishing a mathematics class, Xu Chuan closed the textbook on the desk, tucked it under his arm and walked out of the classroom.

In the lecture theater, the students who were full of seats also began to disperse.

During this period of time, he was basically a regular NPC at Nanjing University. Although every class was still packed with people, at least things like asking for autographs and asking questions were much better than before.

After returning to the office, Xu Chuan opened the computer and checked his mailbox.

At this moment, the office door was pushed open.

Xu Chuan glanced casually and saw that his student Cai Peng walked in, holding a pile of books or papers.

He didn't care. During this period of time, when he was tutoring these students at Nanda, he would often point out some books for them to read. It was normal for Cai Peng and others to come back from outside with books in their hands.

After putting down the books he was holding, Cai Peng took out a stack of manuscript paper from his desk drawer and walked over: "Well, professor, I may have some ideas about the calculation of the minimum differential dimension polynomial of differential equations." . "

Hearing this, Xu Chuan turned his head and glanced, then took the manuscript paper from his hand with interest: "Let me take a look."

The calculation of the minimum differential dimension polynomial of a differential equation is Cai Peng’s chosen graduation topic.

This is a world-class mathematical problem, with difficulty ranging from the end of T3 to the top of T4.

To solve such a difficult problem may take a lifetime for many mathematicians, and may not even be possible.

Xu Chuan did not expect Cai Peng to solve this problem before graduation. As long as he made a breakthrough in this field, could produce phased results, and the paper passed the review of the journal, that would be enough.

On the one hand, Cai Peng's talent is not among the top ones. His talent is about the same as Gu Bing's, not as good as Amelia's, or even as good as his new fanboy student Rong Xinji. After all, The latter has won a perfect individual gold medal at IMO.

On the other hand, Cai Peng did not study differential equations at the earliest. He did not find a path that suited him until his PhD. His accumulation in the field of study was far less than that of Gu Bing and Amelia who solved Bloch's conjecture. deep.

In addition, he was almost thirty years old, so Xu Chuan didn't really think about the fact that he wouldn't be able to graduate unless he solved a problem.

As long as you can make a breakthrough in the chosen goal and write a top-ranked SCI paper in the first area, you are almost ready to graduate.

What surprised him was that this day came so quickly.

Originally, he thought it would take about half a year to a year.

Taking the manuscript paper from Cai Peng, Xu Chuan began to read it carefully, focusing his eyes on the marked difficult calculations.

".Suppose K is a zero-characteristic differential field, ={δ1,···,δm} is its differential operator, let L = Khη1,···, ηni be K and a finite number of elements η={η1,·· The differential extension field generated by ·, etan}. Let Θ represent the free commutative semigroup generated by δ1, ···, δm. If r is any non-zero integer, let Θ(r)={δ^ k1, 1 ···δ^km, m∈Θ|∑m_i=1, Ki≤ r”

After carefully reading Cai Peng's calculations, he thought about it with interest.

The concept of differential dimension polynomial is not just in the mathematical sense, it is closely related to the concept of strength of the system of partial differential equations that determine the physical field.

The concept of strength was pioneered and researched by Einstein. He once raised the question of how to determine the strongest group of differential equations that define a physical field.

It's just that Einstein didn't solve this problem at the time. After all, he didn't even have the corresponding mathematical tools at that time.

Later in the late 20th century and 1980s, two mathematicians, Mikhalev and Pankratev, collaborated to explain the strength of differential algebraic equations and defined them as a differential extension related to a system of equations. Differential dimension polynomial.

This problem derives from the problem involving finding the minimum differential dimension polynomial of a certain differential extension field.

To this day, this problem is still a well-known problem in differential equations and differential dimension polynomials, and the final two algorithms still have no answer.

Putting the manuscript paper on the table, Xu Chuan thought for a while and then said: "Not bad. It seems that you have worked harder than I thought during this period, but your knowledge in physics is not enough to use calculation skills. There is still room for improvement.”

After a pause, he stood up, pulled out a blackboard from the corner, picked up a piece of chalk, and started explaining.

"For example, in the application of linear bounded operators and metric projection operators, you obviously have a problem here, it should be"

In the office, Xu Chuan stood on the blackboard and wrote down rows of equations, explaining to the student some essentials in the calculation process of differential equations.

On the side, Cai Peng listened carefully, with some thoughts on his face.

Obviously, no matter how many books and papers he read, he could not learn these technical things.

After finishing the explanation, Xu Chuan paused for a moment and continued: "There are two known methods for calculating differential dimension polynomials."

"The first is based on the characteristic set of differential ideals that determine the extended domain, and the second is to use the free decomposition of the K¨ahler differential module related to the extended domain. These are two methods commonly used in mathematics."

"However, neither method has an algorithm for calculating the minimum differential dimension polynomial. Even in the special case where the determining ideal of the generating set is generated by a linear differential equation, this problem has not been solved."

"If you want to delve deeper into this area, I think you can try to solve the problem of algorithmic tools first."

As he spoke, Xu Chuan threw the chalk in his hand into the chalk box. After patting the dust on his hands, he seemed to remember something.

"By the way, regarding this problem, maybe you can try to build a new fractal framework through domain expansion, just like the method I used to solve the Weyl-Berry conjecture."

"You should have read those two papers. You can review them. Combined with your current research, it may bring you some other gains."

On the side, Cai Peng stood in front of the blackboard and thought, without replying or making any movement.

Obviously, Xu Chuan's words gave him full inspiration and ideas.

On the other side, Yin Shi, who was studying by himself in the office, felt his scalp numb as he listened to the exchange between his instructor and the senior brother. He couldn't help but glance at Xu Chuan secretly.

Is this the world of the boss?

If she has to solve a world-class problem to graduate, does she still have any hope of graduating in this life?

What's going on in this world? It's too scary!

Xu Chuan keenly noticed the student's little movements, turned his head to look at her, and asked curiously: "Do you have any questions too?"

Yin Shi quickly shook his head and said: "No, no, not yet."

This kind of world-class conjecture. What problems can she, a weak, pitiful graduate student who cannot eat, have?

There is no such thing as a good method that I dare not have at all!