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

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

Guo Wenbin raised his head, looked at Pang Xuelin with a solemn face, and said, "Professor Pang, are you sure that you can get this electromagnetic space launch system out?" ”

As an expert in aerospace dynamics, if someone else put this project plan in front of him, Guo Wenbin would have thrown it in the other party's face.

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

When you actually get into engineering practice, there are a bunch of problems that need to be solved.

This is like the steam catapult on the US aircraft carrier, the principle is very simple, but before China's electromagnetic catapult came out, how many people thought that this was a super black technology that only Americans mastered.

In particular, the requirements for piston tightness and ejection track machining accuracy are enough to amaze all countries in the world except the United States.

Not to mention the electromagnetic space launch system, which involves various technical difficulties, even if China is given another 20 years, it may not be able to solve them.

However, the person who brought this plan to him today was Pang Xuelin, and Guo Wenbin was a little hesitant.

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

Not to mention those achievements in the field of mathematics that are enough to go down in 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.

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

Every project, in the eyes of the academic community, is a miracle, but this young man has done it all.

Therefore, for a while, even Guo Wenbin was not sure whether Pang Xuelin would really be able to complete the project.

Pang Xuelin smiled faintly and said, "Eighty or ninety percent sure." ”

Guo Wenbin was silent.

In fact, when he first read this information, Guo Wenbin was quite shocked.

The design scheme presented in this document, and each of the technical difficulties listed in this document, is extremely detailed.

Although Guo Wenbin does not know much about the electromagnetic catapult system.

But when it comes to aerospace vehicles, he is a top expert in this field.

As far as the design scheme of the aerospace aircraft 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 more than a step higher than the design scheme of the aerospace aircraft in the Tengyun Project.

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 a moment of silence, Guo Wenbin said, "Professor Pang, can I take this project plan back for research?" ”

Pang Xuelin smiled: "Yes, 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 in its original form, NASA will not be able to produce such an aerospace plane within 20 years.

Without their own participation, this proposal is equivalent to a pile of waste paper.

Guo Wenbin nodded and said to Tao Yongchang on the side: "General Tao, let's go." ”

Tao Yongchang was slightly stunned and said, "Haven't we looked at the flying blade material?" ”

Guo Wenbin smiled bitterly: "I believe in Professor Pang's level, and more importantly, if the superiors really agree to Professor Pang's plan, our Tengyun project, I'm afraid there is no need to continue." ”

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

After returning to the office, Pang Xuelin handed over an encrypted PDF document about the electromagnetic space launch system and the aerospace aircraft program to Zuo Yiqiu, who forwarded it to the leadership.

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

"Please come in."

Pang Xuelin said loudly.

The offices were pushed open, and Ai, Halq, and Sophie walked in.

"Master, we're here......"

Ai Ai was the first to speak.

Halke and Sophie also called Pang Xuelin a master.

According to her, in China, the teacher and the master are not the same thing, the traditional sense of the master and the apprentice are relatives, the heaven and earth are the teacher, the real sense of the master-apprentice relationship is far closer than the relationship between the teacher and the student.

So she insisted on calling Pang Xuelin her master, and Halke and Sophie also learned from her.

Pang Xuelin doesn't care, these three people are the three mantle disciples he selected in the field of mathematics, and the five math problems he gave to the three of them last semester turned out to be a little unexpected by Pang Xuelin, and they all successfully completed them before the final exam, which can be regarded as passing Pang Xuelin's first wave of tests for them.

"Hello, Halk, Sophie."

Pang Xuelin said with a smile.

At the beginning of the new semester, he had made an appointment with his three disciples by 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 so long last time, are you okay?" ”

When Pang Xuelin was in a coma, it was summer vacation, and after Ai Ai and they learned the news, they also left a message for Pang Xuelin through WeChat, and Pang Xuelin replied a few words after waking up, but he didn't say anything in detail.

Pang Xuelin smiled: "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, which you all read during the summer vacation, right? ”

Sophie said, "Master, we've all finished reading it." ”

Pang Xuelin said with a smile: "That's good, just as the new semester is coming, I have prepared a few meeting gifts for you." ”

As Pang Xuelin spoke, he took out three pieces of printed white paper from the drawer and handed them to the three of them.

"Ai Ai, it's yours, Halq, yours, and Sophie, this one is yours."

"Master, what is this?"

Pang Xuelin smiled: "To be honest, the questions I gave you last semester can be regarded as a thorough investigation of your mathematical level, and on the whole, I am quite satisfied." And you've basically completed the foundational stage, and you're going to need to really get in touch with some of the most cutting-edge research. What I am giving you today is the problem that you need to study in the future, and these problems are currently hot research areas in the mathematical community, and many of them have not yet been solved. I don't expect you to be able to solve these problems completely, but I hope that you will be able to complete a high-level doctoral dissertation by studying these problems before you graduate...... I'm talking about the high level, at the level of the big four journals, and if you can't do it, then I'm sorry, you can't graduate from me. Of course, if you are interested, you can take on some of the more difficult and well-known puzzles yourself, and I will not stop you......"

Ai Ai, Halk, and Sophie couldn't help but look at each other one by one.

Ai Ai took a cursory look at his blank paper, frowned, and said, "Master, my research field is the Dirac operator in unitary representations?" ”

Pang Xuelin nodded and said with a smile: "The Dirac operator is a first-order differential operator, which was introduced in 1928 by the famous physicist and Nobel laureate Paul Dirac as the square root of the Laplace operator. Using this operator, Dirac explained the spin of electrons and predicted the existence of positrons, thus laying the foundation of relativistic quantum mechanics. At present, Dirac operators of various backgrounds are widely used in many branches of physics, and have been generalized to differential manifolds, which are very important research objects in mathematics."

Pang Xuelin paused and continued: "The Dirac inequality of unitary representations derived from the Dirac operator is also a powerful tool for studying the classification of unitary representations. For connected real semi-monolithic Lie group G, Wolgan uses pan-envelope algebra and Clifford algebra to define a fully algebraic Dirac operator and Dirac cohomology of (g,K) modulo X. A very important invariant represented by Li Qun is its infinitesimal characteristic. Wolgan's conjecture is that if the irreducible (g,K) modulus X of the real semi-monolithic Lie group G has a non-zero Dirac cohomology, then the infinitesimal characteristic of X is completely determined by its Dirac cohomology. This conjecture has been proven by Huang Jinsong and Pandzic. In fact, the above results can be generalized to the more general homogeneity space G/H, and a similar conclusion is made for cohomology on the cubicDirac defined by Kostant. ”

Wolgan's conjecture about cohomology on Dirac describes a profound algebraic property of the Dirac operator, which further characterizes the infinitesimal characteristics of representations, which provides a new tool for the study of unitary representations. This can lead to the derivation of finer Dirac inequalities, for example, and the geometry of irreducible unitary representations can be simplified. At the same time, Dirac cohomology is closely related to Lie algebra cohomology, and in many cases, Dirac cohomology can simplify the calculation of cohomology on Lie algebra. At present, the application of cohomology on Dirac is becoming more and more extensive, even beyond the scope of the half-single Li group representation. ”

"We know that there is an invariant symplectic structure on each coincident orbital of the Lie group, and the orbital method is very effective for studying the representation of the power zero Lie group. In addition, the Weyl algebra in the symplectic space is very similar to the Cillford algebra used in the inner product space in the Dirac operator definition above. 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 Sindilak operator to construct a unitary representation of a real semi-single Lie group? Is there a connection between the Sindirak operator and the coincidence orbit? At present, the research on these problems in the mathematical community is still in its infancy, and in the next two years, I hope that you will achieve something in this field. ”

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

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

She didn't have much research on the Dirac operator at all, and it would probably take more than a week to figure out these problems alone, let alone solve the problems Pang Xuelin said.

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

After saying Ai Ai's mission, Pang Xuelin turned his gaze to Halker and smiled: "Halke, Cherlin-Zilber guesses, you should know, right?" ”

Halker nodded with a wry smile and said, "Master, this conjecture is a conjecture proposed by Boris Zilber 30 years ago about the classification of infinite monogroups: that is, a Morley ω-stable monogroup with finite rank must be an algebraic group on a certain algebraic closed field. This conjecture is a very important problem at the junction of model theory and algebraic group research. ”

Pang Xuelin smiled with satisfaction: "Very good, in the 30 years since the Cherlin-Zilber conjecture was proposed, the research work on ω-stable groups carried out by the mathematical community around this conjecture has made very outstanding progress. This kind of research not only applies many new ideas and methods of model theory, but also uses many ideas from the field of finite group theory, especially in the work of finite monogroup classification. For this study of the conjecture, I recommend that you read a monograph on the Cherlin-Zilber conjecture co-authored by Borovik and Nesin, and I am sure you will find it useful in this book. In addition, although this conjecture has not yet been solved, a similar Cherlin conjecture about o– minimal structures has been proved by Peterzil, Pillay, and Starchenko, and I suggest you take a look at their proof papers, which may be instructive. ”

Harke said: "Master, I will check the information on this as soon as I go back." ”

In the end, Pang Xuelin turned his gaze to Sophie: "Sophie, the Changtian conjecture will be left to you." ”

Sophie pursed her lips and nodded emphatically.

Ai Ai curiously leaned over to Sophie's side, looked at the words on her white paper, and couldn't help but whisper: "P1,...,Pn is the point in the general position on C^2, and m1,...,mn is a set of natural numbers. If there is a d-order curve C, for each 1≤i≤n, the repetition of C at the Pi point is not less than mi, then d^2≥m1^2+......+mn^2. ”

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

Pang Xuelin said with a smile: "Do you think it's simple? Why don't you swap with Sophie? ”。

Ai Ai hurriedly waved his hand and sneered: "No, no, I think my Dirac operation is also very good." ”

Pang Xuelin smiled and said: "In algebraic geometry, the plane algebraic curve is the simplest and most specific algebraic cluster, but there are still some famous problems in this field that have not been solved, and the Nagata conjecture is one of them. Moreover, the Nagata conjecture is one of the few problems in the field of algebraic geometry that can be understood by college students, but it is very difficult. Historically, this conjecture has played a very key role in solving Hilbert's fourteenth question, and in the deeper frontier research of algebraic geometry, the solution of many problems also depends on the solution of Nagata conjecture. Sophie, I hope that research in this area will progress before you graduate. ”