The Science Fiction World of Xueba

When you look at it, you don't know how time flies.

By the time Guo Wenbin and Tao Yongchang finished browsing through the information, more than two hours had passed.

Guo Wenbin raised his head, looked at Pang Xuelin solemnly and said, "Professor Pang, are you sure you can make this electromagnetic space launch system?"

As an expert in aerospace dynamics, if another person presented this project plan in front of him, Guo Wenbin would have thrown him in the other's face long ago.

Electromagnetic space launch systems, although they look beautiful in theory, mostly only exist in the fantasy of science fiction writers.

When actually entering engineering practice, there will be a bunch of problems to be solved.

This is like the steam catapult on an American aircraft carrier. The principle is very simple, but before the Chinese electromagnetic catapult came out, how many people thought it was a super black technology that only Americans mastered.

In particular, the requirements for the sealing of the piston and the machining accuracy of the ejection track are enough to make all countries in the world except the United States sigh.

Not to mention the electromagnetic space launch system, the various technical difficulties involved in it may not necessarily be resolved even if China is given another twenty years.

However, since Pang Xuelin was the one who presented this plan in front of him today, Guo Wenbin hesitated.

In the past two years, this young man has created too many miracles.

Not to mention those achievements in the field of mathematics that are enough to be recorded in the annals of history, a lithium-air battery is enough to establish Pang Xuelin's position in the Chinese scientific community.

Not to mention Pang Xuelin's achievements in the field of carbon nanomaterials.

Industrialized manufacturing of ultra-high-purity electronic-grade single-walled carbon nanotubes, industrialized manufacturing of large-scale single-layer graphene projects, and the just-successful flying edge material project.

Every project, in the eyes of the academic world, is a miracle, but this young man has come up with all of them.

Therefore, for a while, even Guo Wenbin was not sure whether Pang Xuelin could really complete this project.

Pang Xuelin smiled lightly and said, "I'm 80% sure."

Guo Wenbin was silent.

In fact, when I read this document just now,

Guo Wenbin was quite shocked.

The design scheme presented in this document and every technical difficulty listed are extremely detailed.

Although Guo Wenbin doesn't know much about the electromagnetic ejection system.

But for aerospace vehicles, he is a top expert in this field.

As for the design of the aerospace vehicle presented in Pang Xuelin's report, although it involves many advanced technologies that have not yet made breakthroughs in reality, in terms of the overall design layout of the aerospace aircraft, it is faintly compared with Tengyun. The design of the aerospace plane in the project is more than one step higher.

The design of this kind of super-large system engineering is not something that ordinary people can do.

He couldn't understand how Pang Xuelin did this.

After pondering for a moment, Guo Wenbin said, "Professor Pang, can I take this project proposal back for research?"

Pang Xuelin smiled and said: "Yes, and I will submit the same report to the senior management at the same time."

Pang Xuelin is not worried about leaking secrets at all. Even if his plan is sent to the United States, NASA will not be able to produce such an aerospace plane within 20 years.

Without my own participation, this plan is equivalent to a pile of waste paper.

Guo Wenbin nodded, and said to Tao Yongchang beside him, "General Tao, let's go."

Tao Yongchang was taken aback for a moment, and said, "Don't we read the flying blade material?"

Guo Wenbin smiled wryly: "I believe in Professor Pang's level, and more importantly, if the superiors really agree with Professor Pang's plan, there may be no need to continue our Tengyun project."

Pang Xuelin smiled, did not participate in the conversation between Guo Wenbin and Tao Yongchang, but sent them away indifferently.

After returning to the office, Pang Xuelin gave Zuo Yiqiu an encrypted PDF document about the electromagnetic space launch system and the space plane program, and she passed it on to the leadership.

Afterwards, Pang Xuelin was about to deal with the accumulated mail when the knock on the office door rang again.

"Please come in."

Pang Xuelin said loudly.

The offices were pushed away, and Ai Ai, Harke, and Sophie walked in.

"Master, here we come..."

Ai Ai spoke first.

Harke and Sophie also called Pang Xuelin master.

The title of master was brought up by Ai Ai. According to her, in China, a teacher and a master are not the same thing. In the traditional sense, a master and an apprentice are a family relationship. The relationship is far closer than the relationship between teachers and students.

So she insisted on calling Pang Xuelin her master, and Harke and Sophie followed her example.

It doesn't matter to Pang Xuelin, these three people can be regarded as the three mantle disciples he selected in the field of mathematics. The five math problems he gave them last semester turned out to be somewhat beyond Pang Xuelin's expectations, and they all passed the final exam. It's done, and it can be regarded as passing Pang Xuelin's first wave of tests for them.

"Ai Ai, Harke, Sophie, hello."

Pang Xuelin laughed.

The new semester started, and he had already made an appointment with his three disciples via email two days ago, and met in the office today to make a study plan for this semester.

Ai Ai said: "Master, you were in a coma for such a long time last time, are you okay?"

When Pang Xuelin was in a coma, it was the summer vacation. Ai Ai and the others also left a message to Pang Xuelin through WeChat after they heard the news. Pang Xuelin replied a few words after waking up, but did not elaborate.

Pang Xuelin smiled and said: "It's nothing, I'm in good health now. By the way, at the end of last semester, I gave you some list of papers. Have you read them during the summer vacation?"

Sophie said, "Master, we've finished watching."

Pang Xuelin said with a smile: "That's good. It just so happens that the new semester is here. I've prepared some greetings for you."

While talking, Pang Xuelin took out three printed sheets of white paper from the drawer and handed them to the three of them.

"Ai Ai, this is yours, Harke, yours, and Sophie, this one is yours."

"Master, this is?"

Pang Xuelin smiled and said: "To be honest, the few questions I gave you last semester can be regarded as a thorough investigation of your mathematics level. Generally speaking, you are quite satisfied. And you have basically completed the basic stage of study. Next, you need to get in touch with some cutting-edge research. What I have listed for you today are the problems that you need to study in the future. These problems are currently regarded as hot research areas in the mathematics world, and many of them have not yet been solved. I don’t I hope that you can completely solve these problems, but I hope that you can complete a high-level doctoral thesis before graduation by studying these problems... The high-level I mean is at the level of the four major journals. If you do No, then I'm sorry, you can't graduate from me. Of course, if you are interested, you can challenge some more difficult and well-known problems by yourself, I will not stop this..."

Ai Ai, Harke, Sophie couldn't help but look at each other.

Ai Ai briefly glanced at her white paper, frowned and said, "Master, my research field is the Dirac operator in unitary representation?"

Pang Xuelin nodded and said with a smile: "The Dirac operator is a first-order differential operator. It was introduced by the famous physicist and Nobel Prize winner Paul Dirac in 1928 as the square root of the Laplacian operator. Using this operator, Dirac explained the spin of electrons and predicted the existence of positrons, thus laying the foundation of relativity quantum mechanics. At present, Dirac operators with various backgrounds are widely used in many fields of physics branch, and is extended to differential manifolds, is a very important research object in mathematics”

Pang Xuelin paused, and continued: "The Dirac inequality derived from the unitary representation derived from the Dirac operator is also a powerful tool for studying the classification of unitary representations. For the connected real semisimple Lie group G, Worgan uses the general envelope algebra and Clifford algebra Defined a fully algebraic Dirac operator and the Dirac cohomology of (g, K) modulo X. A very important invariant of Lie group representations is its infinitesimal character. Wogan conjectures that if the semisimple Lie The irreducible (g, K) module X of the group G has non-zero Dirac cohomology, then the infinitesimal characteristics of X are completely determined by its Dirac cohomology. This conjecture has been proved by Huang Jinsong and Pandzic. In fact, the above result It can be extended to the more general homogeneous space G/H, and there are similar conclusions for the cubicDirac cohomology defined by Kostant."

"Worgan's conjecture about Dirac cohomology characterizes a deep algebraic property of the Dirac operator, which further characterizes the infinitesimal characteristics of the representation, which provides a new tool for the study of unitary representations. For example, it can be derived from The more refined Dirac inequality, the geometric structure of irreducible unitary representation can also be simplified. At the same time, Dirac cohomology is closely related to Lie algebra cohomology. In many cases, Dirac cohomology can simplify the calculation of Lie algebra cohomology .At present, the application of Dirac cohomology is becoming more and more extensive, even beyond the range of semi-simple Lie group representations.”

"We know that each coadjoint orbit of a Lie group has an invariant symplectic structure, and the orbital method is very effective for studying the representation of the nilpotent Lie group. In addition, the Weyl algebra in the symplectic space is the same as that in the definition of the Dirac operator above Cillford algebras using inner product spaces have a strong similarity. Therefore, in this field, we can ask the following questions, such as if there is an invariant symplectic structure on the homogeneous space G/H, can we also give An algebraic definition of the Sindirac operator? Is it possible to use the Sindirac operator to construct the unitary representation of the real semisimple Lie group? Is there any connection between the Sindirac operator and the coadjoint orbit? At present, in the field of mathematics, these The research on the problem is still in its infancy, Ai Ai, in the next two years, I hope you can achieve something in this field."

Ai Ai nodded with a bitter face. When Pang Xuelin assigned homework to them last semester, she still felt that the difficulty was acceptable, and with a little effort, she could still solve it in one semester.

Unexpectedly, this semester, Pang Xuelin came up and gave them a big move.

She didn't have much research on Dirac operators at all, and it would probably take more than a week just to understand these problems, let alone solve the problems that Pang Xuelin mentioned.

Fortunately, Pang Xuelin only asked them to write a high-level paper by studying this problem, but he did not force them to solve these problems.

After talking about Ai Ai's mission, Pang Xuelin turned his gaze to Harke and said with a smile: "Hark, Cherlin-Zilber guessed, you should know, right?"

Halke nodded with a wry smile, and said: "Master, this conjecture is a conjecture about the classification of infinite simple groups proposed by Boris Zilber and Boris Zilber 30 years ago: that is, an ω-stable simple group with a finite Morley rank must be some An algebraic group on an algebraically closed field. This conjecture is a very important problem in the joint part of the study of model theory and the study of algebraic groups."

Pang Xuelin said with a satisfied smile: "Very well, since the Cherlin-Zilber conjecture was proposed 30 years ago, the research work on ω-stable groups around this conjecture has made outstanding progress. This kind of research not only applies the theory of model theory Many new ideas and methods, but also use many ideas from the field of finite group theory research, especially the work on the classification of finite simple groups. For this conjectural study, I recommend you to read a book by Borovik and Nesin The monograph on the Cherlin-Zilber conjecture, I believe you will find useful materials from this book. In addition, although this conjecture is still unresolved, the similar Cherlin conjecture on o-minimal structures It has been proved by Peterzil and Starchenko, I suggest you read their proof papers, maybe it will inspire you."

Harke said: "Master, I will look up the information on this right away when I go back."

Finally, Pang Xuelin turned his attention to Sophie: "Sophie, I will leave Nagata's conjecture to you."

Sophie pursed her lips and nodded heavily.

Ai Ai leaned over to Sophie curiously, looked at the words on her white paper, and couldn't help but read out in a low voice: "P1, ..., Pn is the point on C^2 in the general position, m1, ..., mn is a group of natural numbers. If there is a curve C of degree d, for each 1≤i≤n, the multiplicity of C at point Pi is not less than mi, then d^2≥m1^2+...+mn ^2."

"Master, isn't Sophie's proposition too simple?"

Pang Xuelin smiled and said, "Do you think it's easy? Why don't you and Sophie change?".

Ai Ai waved her hand quickly, and said with a sneer: "No, no, I think my Dirac operator is pretty good."

Pang Xuelin smiled and said: "In algebraic geometry, the plane algebraic curve is the simplest and most specific algebraic variety. However, there are still some famous unsolved problems in this field, and the Nagata conjecture is one of them. And Nagata The conjecture is one of the very few problems in algebraic geometry that can be understood by college students, but it is very difficult. Historically, this conjecture has played a very critical role in solving Hilbert's fourteenth question, and in deeper algebraic geometry In cutting-edge research, the solution to many problems also depends on the Nagata conjecture. Sophie, I hope that research in this field can make some progress before you graduate."

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