"Congratulations, Professor Li." When Xu Dajiang said this, he couldn't help but have a hint of envy in his tone.
Today is the day when Qiao Ze graduates, and it is also the day when Qiao Ze officially takes over the name of Li Jiangao and becomes a glorious doctoral student of Xilin University of Technology.
When everything settled and the school compiled the data and reported it, Xu Dajiang actually felt a little bit amused in his heart.
It can only be said that some people are really lucky.
Who would have thought that an unconventional mathematical genius like Qiao Ze could be discovered in a mathematics conference?
"Same joy, same joy." Li Jiangao smiled implicitly and said politely.
Once he accepted that he was destined to win in this life, he was able to be indifferent to the various emotions his colleagues had towards him.
As Zhang Chunlei joked in the group, everyone in the circle hates Li Jiangao and everyone wants to be Li Jiangao.
"By the way, I heard that Qiao Ze plans to graduate as soon as possible? Have you decided on the topic of his graduation thesis?" Looking at Qiao Ze who was still taking photos with Zhu Hongbing not far away, Xu Dajiang expressed concern again.
"Well, Qiao Ze has decided. He plans to do a mathematical proof of the mass gap hypothesis. He will graduate after writing the thesis." Li Jiangao replied.
I just completed my graduation defense, received my diploma, and applied for doctoral admission.
Next came photography.
Although Qiao Ze didn't like taking pictures, naturally he couldn't do whatever he wanted on such a memorable day.
The school also specially ordered a brand new bachelor's uniform for Qiao Ze.
"Mathematical proof of the mass gap hypothesis for your graduation thesis?" Xu Dajiang was stunned and asked: "Has he already got an idea?"
"Well, almost. I chatted with Qiao Ze yesterday. He already had a general idea. He said that he has proven a unique field in the simplest state with a standard order energy density. In this special case, more details are allowed. Studying the spectrum of m... This is probably the case, you know, I don't understand this direction either."
Li Jiangao said calmly.
Anyway, there are not many mentors in the world who can help Qiao Ze with this proposition.
The mathematical tools used to prove this high-end proposition were all invented by him, and everyone used them to do it under the same name.
Xu Dajiang subconsciously twitched his lips and said: "It is not easy to find a professor to defend this topic as a doctoral thesis. As far as I know, there are not many professors in China who study this topic... If this is really done, the defense will have to be done. Let’s make it a report meeting?”
Li Jiangao glanced at Xu Dajiang, sighed and said: "Yeah, leaving the paper to me is just a formality, and I don't know what to do then. But fortunately, Qiao Ze said that he will need about two or three months. Only then can I complete the thesis. Then it will be May or June.”
"Can it be completed in two or three months?" Xu Dajiang looked at Li Jiangao in surprise.
"Well, Qiao Ze estimated it himself." Li Jiangao nodded, and then after hesitating for a while, he said: "Qiao Ze's estimated time is generally not accurate. Every time he estimated the time before, he always left a margin. For example, when we were working on a group intelligence project, he told me that it might take half a year, but in the end, the complete results were produced in two months."
"actually……"
Xu Dajiang hesitated, and finally said: "Actually, you should talk to Qiao Ze, don't be so anxious, and enjoy life more. A high-level report meeting was held in January, and another one will be held in June. If so, will it be a little more frequent? Let’s wait for the school.”
Li Jiangao said nothing, this was not something he needed to worry about.
I just feel that people’s thoughts are indeed changing.
At the end of May last year, when he first brought Qiao Ze to school, he really hoped that Qiao Ze could slow down a little, enjoy college life first, and have a complete life. At that time, Xu Dajiang's intention was to hope that Qiao Ze could develop well...
Now that he had given up his previous idea and followed Qiao Ze, the dean hoped that Qiao Ze would slow down.
"Hey, it doesn't matter anymore. If Qiao Ze really makes it, it's really worthy of another big effort. After all, others think they haven't had the chance yet. In fact, the school basically achieved balance in the last report meeting, but there are some invisible things in the city. The cost is not included in the calculation. But if the quality gap is proven, we might as well hold a conference. The charges can also be more expensive, what do you think?" Xu Dajiang said to himself.
"Um... I don't understand these things." Li Jiangao replied, "Professor Zhu is calling us, let's go take pictures together."
"Hey, why don't you ask Qiao Ze's mother to take a photo with you? It's not good for her to be watching all the time. Take a few more pictures and hang them in my office later."
"good."
…
United States, California, San Francisco Bay Area, National Mathematical Research Center on the hill behind Berkeley.
Although it was already late at night, Robert Stephen was still sitting in front of his work with concentration, writing and drawing on the manuscript paper with a pen.
If Qiao Ze was nearby, he could tell at a glance that he was studying his superspiral space algebra.
Yes, although the boss doesn't like Qiao Ze, he is obviously very interested in this new direction proposed by Qiao Ze.
The only pity is that this is still a subject that has just started.
There is too little information to draw from.
Apart from the video of Qiao Ze’s lecture, there is only Qiao Ze’s paper on solving the general solution of the Yang-Mills equation.
This also makes research more difficult.
Just when he was thinking about another difficult point, the phone suddenly rang.
Seeing Daniel's name displayed on the screen, Robert Stephen finally answered the phone with dignity.
"Hey Robert, did you read the question I sent you in the email?"
"Huh? I haven't checked my email today."
"Oh, if you are still studying superspiral space algebra, I suggest you take a look now. I have sent you a set of questions on superspiral space algebra specially designed by the institute. You can try it. "
"Thank you, Daniel."
"You're welcome, just remember to treat me to a drink next time you come to Princeton. By the way, if you can't do it, you can contact Edward and ask him for the answer... Sixty percent of the questions in this set of questions are He came up with it, but he doesn’t plan to publish the answer for the time being.”
"I know, thank you again."
…
After hanging up the phone, Robert immediately opened the mailbox.
If you want to quickly enter a new field of mathematics, brushing up on questions is undoubtedly one of the fastest ways.
Unfortunately, for the brand-new direction of superspiral space algebra, if you want to write questions, you must first have an in-depth understanding of the relevant theories.
So as far as the current situation is concerned, it is difficult to clear the questions.
Soon, the relevant files were downloaded.
Opening the file, Robert Stephen briefly browsed through all the questions.
There are six questions in total, but it can be seen that the gold content is still very high.
Then Robert Stephen focused his energy on the first question:
"Consider a one-dimensional superspiral space algebra model, whose Hamiltonian is h=t∑(upper n lower j)=1(cfjcj+1↑+cfjcj+1↓+.)+u∑j=1nnj↑nj ↓μ∑j=1n(nj↑+nj↓)
where cjσ and cjσ are the electron annihilation and creation operators at position j respectively. σ=↑, ↓ represents spin, njσ=cjσcjσ is the electron number operator. t is the electronic transition strength, u is the hubbard interaction strength, and μ is the chemical potential.
a. Prove the commutation relationship of this Hamiltonian [h, cjσ] = t (cj1σ + cj + 1σ) + u (nj, σnjσ) cjσ.
b. Consider the mean field approximation of the system, assuming cjσclσ′=δj, lδσ, σ′cjσcjσ, where cjσcjσ is the average number of electrons at spin σ and position j. Write the Hamiltonian hmf under the mean field approximation. "
I have to say that this question was answered very well.
Robert Stephen has been studying superspiral space algebra for two months. It is natural to see that this question tests the basic understanding of the superspiral space algebra model. It has to be said that Princeton has once again reached the forefront of its peers in researching new algebra.
Soon Robert was addicted.
I have to say that when studying such a new mathematical direction, it is also a blessing to have problems to solve.
After three hours of scribbling and correcting, Robert finally completed the problem-solving process and found the answer to the second question nj↑nj↓≈nj(nj1).
Full sense of accomplishment.
In excitement, Robert took a video of the problem-solving process and sent it directly to Edward Witten. By the way, he asked, did I solve it correctly?
After sending the email, Robert looked at the time. It was already one o'clock in the morning.
He didn't expect Edward Witten to reply to his email at this time.
With a hint of sleepiness coming over him, Robert was about to pack up and go to bed. Unexpectedly, just as he had packed up all the manuscripts on his desk, an email notification suddenly came from the speaker. Subconsciously, he opened the mailbox and took a look. Haha... Edward wasn't even asleep yet.
"Congratulations, Professor Stephen. Although the proof process of the first question is slightly flawed, it is generally correct. In addition, I would like to ask, how do you feel about these questions? In addition to the six example questions in the first part, there are also For the other six questions in Part 2, I am considering making these question banks available directly to the public.”
After thinking for a moment, Robert began editing the email.
"A very meaningful topic, Professor Witten, has been very helpful to me. It can help me sort out some basic concepts in this new algebraic direction. Since symmetry in this special space is often missing, only in extremely special circumstances, In order to consider the exchange problem, the entire mathematical system is extremely abstract.
The questions you asked can make some abstract theories concrete and are very meaningful for everyone to understand superspiral space algebra. If I have that honor, I would very much like to join your team! "
After clicking the reply button, Robert Stephen suddenly felt no longer sleepy.
It can only be said that the persistence of mathematicians is difficult for ordinary people to imagine.
Fortunately, Edward Witten replied to him soon.
"Thank you for your evaluation, and you are very welcome to join. Unfortunately, we have missed something. This has led to our slow progress in the basic theoretical understanding and research of superspiral space algebra. Tonight I will share everything The questions are placed in the shared question bank of the Institute for Advanced Study in Princeton, which is updated regularly.
Of course, if you have good questions, you can send them to me, or Professor William, and they will be put into the corresponding question bank after cross-checking. It must be admitted that this is indeed a very interesting research direction. Joe's research is shocking. "
After reading this reply, Robert Stephen felt uninterested.
It's that Qiao Ze again.
Please visit the latest address
Robert didn't like this Chinese boy before, but he doesn't like him even more now.
In his opinion, Qiao Ze is not a pure mathematician, he is too utilitarian.
Any mathematician who creates a new school will probably drop everything to perfect the entire theory in order to promote this new algebraic form. But Qiao Ze actually chose to ignore it.
But it also happened to arouse Robert Stephen's competitive spirit.
Many times the founder may not be able to perfectly interpret the entire theory.
Since Qiao Ze voluntarily gave up this part of the work, they could just make up for it.
So after holding back his breath and thinking for a moment, Robert began to reply again.
"Professor Witten, I think in addition to sharing the topic, we can also share some thoughts on superspiral space algebra. The following are two theorems that I have recently summarized.
Theorem 1: The conditions for the formation of spin density waves. Within the appropriate parameter range of the one-dimensional superhelical space algebra model, the system may undergo a spin density wave phase transition, that is, the electrons with spin up and down show periodic changes. Arrange in order. "
Theorem 2: The existence of topological haldane phase. For the one-dimensional chain of the superhelical space algebra model, within the appropriate parameter range, the system may support the topological haldane phase, which has non-trivial topological properties. "
The wait was shorter this time, and Edward Witten received a reply within two minutes.
"Thank you very much, Professor Stephen. We also have related research on the first theorem you summarized, but the description of the second theorem is very interesting and we will verify it. If you are willing, you can attach the complete theorem proof process. Publish it. We will include it in the shared space related to superspiral space algebra.
We hope together that we can resolve a series of related issues as soon as possible. I believe you have the same feeling after conducting research during this period. This may indeed be a key to unlocking the mystery of great unification. I suspect that this special mathematical structure includes the structure of space-time and gravity at the microscopic level. Unfortunately, we are not yet able to fully grasp it.
We are organizing a research team. The main members that have been identified are me, Daniel, Professor William and Professor Schultz. If you are willing to join, we very much welcome you to join. "
After reading this email, Robert had a smile on his face.
He immediately created a new email, his hands dancing on the keyboard.
"Of course, I very much hope to join this team! Thank you, Professor Witten, we will definitely be able to solve this series of problems."
…
China, Xilin University of Technology.
After spending a whole morning, Qiao Ze finally breathed a sigh of relief.
Compared with doing research in his office, completing graduation defense and taking photos, he felt even more tired.
Especially the teacher appreciation banquet at noon, the atmosphere made him feel quite weird.
Whose teacher-appreciation banquet, the teacher always thanks the students...
This made Qiao Ze very uncomfortable.
Not because Lu Xiuxiu and Su Mucheng were happy today, Qiao Ze planned to go back to the third floor directly after answering his question.
After dinner, Su Mucheng and Lu Xiuxiu went to select the photos they took today. They might need to polish them a bit more, and they didn't know when they would be finished.
Qiao Ze was not interested in any of this, so he returned to the research institute on his own.
Sitting at his desk, Qiao Ze glanced at Doudou on the computer as usual.
Being an Internet celebrity on Weibo and other software is just Doudou's side job. Its most important job is still to help Qiao Ze find papers, manage mailboxes and other auxiliary tasks through intelligent search and crawler technology under the crowd intelligence framework. .
Especially managing Qiao Ze's mailbox.
It can really help Qiao Ze review a lot of things.
Since he solved the general solution of the Yang-Mills equation and turned a blind eye to the development of superspiral space algebra, there have been more and more "spam emails".
Too many people email him with weird questions.
Some people have even started sending him papers on superspiral space algebra.
It would be fine if the writing was good, but at least judging from the few papers he had received so far, he couldn't even understand what the other party wanted to express.
This made Qiao Ze begin to understand why after receiving the paper, the editor of the top journal would directly delete some papers after just taking a look at the author's affiliation.
The ignorant are truly fearless.
He even received a paper claiming to use superspiral space algebra to solve the unified problem of mathematics. I wrote eight pages eloquently, but the first theorem I gave was full of loopholes.
Well, this is a paper written by a professor at a university in Morocco.
That is to say, starting from the paper sent to the mailbox, Qiao Ze directly entrusted the mailbox to Doudou.
Although Doudou's current logical thinking ability cannot find excellent papers, it can still be used to filter out a series of unreliable arguments.
However, today’s first tip is not about how many more “spams” have been filtered out by Doudou, but about the new progress in Princeton’s research on superspiral space algebra.
Although Qiao Ze is too lazy to spend time doing popular science on superspiral space algebra, he is still quite concerned about research in this direction.
No one is omniscient.
Although he was the first to invent this system, maybe others can come up with some content that he didn't expect after studying it to assist?
Just like what Su Mucheng said.
The world’s understanding of this proposition is too superficial, and it is nothing more than a matter of time.
Now that he has pointed out the direction and has enough research time, he may be able to gain something unexpected.
"Princeton Research Institute has just announced the four basic theorems and twelve examples of superspiral space algebra?"
"Yes, Master. All information is disclosed under the new algebra research direction section of the official website. Do you need me to help you retrieve the data now? Cute..."
If netizens were to see Doudou in Qiao Ze's computer like this, they would probably have mixed feelings.
After all, this thing has an arrogant character that criticizes everything on Weibo and other software. Even if it occasionally uses a friendly tone, it is most likely sarcastic.
However, when Qiao Ze used it, he became like a licking dog.
It really vividly explains what oranges are when they grow in Huainan, and when they grow in Huaibei they become oranges.
"Yeah." Qiao Ze responded.
Soon the research contents published on the official website of the Institute for Advanced Study in Princeton were displayed in front of Qiao Ze in the form of pictures.
In addition to the two theorems that Robert sent to Edward, two other theorems are given in the picture.
They are very interesting descriptions of the topological properties of superhelical space algebra, quantum phase transitions, and the mott insulating phase of strongly correlated systems.
Except for the second one, each summarized theorem is followed by two or three names.
Then there are twelve related example questions.
From Qiao Ze's perspective, these twelve questions are very simple.
Basically it revolves around the three theorems that have been published.
But for beginners, it is really useful.
This also inspired Qiao Ze.
Although he does not intend to waste too much time on the popularization of superspiral space algebra, he can give some small help to mathematicians and physicists who are devoted to studying this subject.
After all, setting questions is a very simple thing for him and it takes almost no time.
By the way, it can also extend the transcendental geometry corresponding to the superspiral space algebra.
Do whatever comes to your mind.
Soon, Qiao Ze directly designed two questions.
The first question is an advanced question about superspiral space algebra: set a high-dimensional superspiral space algebra model, and its Hamiltonian is [ h =-t\sum_{j=1}^{n}(c_ {j\uparrow}^{\dagger}c_{j+1\uparrow}+ c_{j\downarrow}^{\dagger}c_{j+1\downarrow}+ext{.})
Please prove that: under certain conditions, the ground state of the system may undergo a spin-density wave (sdw) phase transition, that is, an ordered periodic arrangement of spins is formed in the system. Please analyze the spin density wave phase transition conditions of this model at zero temperature and give the corresponding physical explanation.
The second question is about the transcendental geometry he studied.
Qiao Ze named the problem Door Through Dimensions. The topic was not difficult, but very special.
The problem is described as follows:
If there is a mysterious dimensional door in the universe, which connects the four-dimensional space and the six-dimensional space, its mathematical description is: [ v =\int d^4x \sqrt{g}\left(\frac{ 1}{2}\mathbf{r}+\frac{1}{2}abla\phi \cdot abla\phi - v(\phi)ight)]
Among them, (v) represents the action of the gate of this dimension, (\sqrt{g}) is the square root of the metric of four-dimensional space-time, (\mathbf{r}) is the scalar curvature of four-dimensional space-time, (abla\phi) is the six-dimensional The gradient of the scalar field in the dimensional space, and (v(\phi)) is the potential energy term interacting with the scalar field.
In this six-dimensional space, a curve (c) is defined as a path connecting both sides of the dimensional gate and satisfying the following conditions. The length of path (c) is (l) and its action is minimal. Considering that the metric in the four-dimensional space is (\sqrt{g}= 1), the scalar field is (\phi =\phi_0).
Request solution: The curve (c) with the smallest amount of action in six-dimensional space.
Tip: The correlation theory of superspiral space can be used to solve the problem. The minimum action should correspond to the equation of motion that the path (\mathbf{x}(t)) satisfies.
After designing the question, Qiao Ze directly asked Doudou to send it out.
In order to ensure that everyone can understand it, the question stems are specially written in Chinese and English.
Especially for some special terms in new mathematics, Qiao Ze also specially explained them, which was very considerate and did not require the other party to express gratitude.
It can only be said that everyone is making contributions to academic progress.
Please visit the latest address
