"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 of Qiao Ze's graduation, and it is also the day when Qiao Ze officially worships under the name of Li Jiangao and becomes a glorious doctoral student of Xilin University of Technology.

When everything settled and the school counted the information and reported it, Xu Dajiang also had some taste in his heart.

It can only be said that some people's luck is really good.

Who would have thought that a math conference would unearth an unconventional math genius like Joze?

"Rejoice, rejoice." Li Jiangao smiled implicitly and said politely.

Once he accepts the setting that he is destined to lie down and win in his life, he can already be pampered and not shocked by the various emotions that his colleagues have towards him.

In Zhang Chunlei's joking words 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 a photo with Zhu Hongbing not far away, Xu Dajiang was concerned again.

"Well, José has determined, and he intends to do a mathematical proof of the mass gap hypothesis. Graduation is done after the thesis is written. Li Jiangao replied.

I have just completed my graduation defense, obtained my graduation certificate, and completed my doctoral admission.

This was followed by photography.

Although Qiao Ze doesn't like to take pictures very much, such a commemorative day naturally can't all follow Qiao Ze's meaning.

The school also ordered a brand new bachelor's uniform for Qiao Ze.

"Mathematical proof of the mass gap hypothesis to do a dissertation?" Xu Dajiang was stunned and asked, "He already has eyebrows?" ”

"Well, almost. Yesterday I talked to Jozer, and he already had a general idea, saying that it has been proved that there is a single field with a standard order energy density in the simplest state, and in this special case, it is allowed to study the spectrum of m in more detail...... That's probably the case, you know, I don't know about this direction. ”

Li Jiangao said very calmly.

Anyway, there are not many people in the world who can help Qiao Ze with any mentor in this proposition.

The mathematical tools used to prove this high-end proposition were all invented by himself, and everyone is famous.

Xu Dajiang subconsciously pulled the corners of his mouth and said: "If this proposition is a doctoral dissertation, it is not easy to find the professor in charge of defense, as far as I know, there are not many professors who study this proposition in China...... If this is really done, it will have to be made into a report meeting, right? ”

Li Jiangao glanced at Xu Dajiang, sighed and said, "Yes, anyway, handing over the paper to me is going through the motions, and I don't know what to do when the time comes." But fortunately, Qiao Ze said that he would probably need two or three months to complete his thesis. Then it's May or June. ”

"Can it be done in two or three months?" Xu Dajiang looked at Li Jiangao in some surprise.

"Well, Jozer estimated it himself." Li Jiangao nodded, and then after hesitating, he said, "Qiao Ze's estimated time is generally not accurate. Before, he had always estimated the time with leeway. For example, when I was doing the group intelligence project, he told me that it might take half a year, but the complete results were made in two months. ”

"Actually......"

Xu Dajiang hesitated, and finally spoke: "Actually, you should talk to Qiao Ze, don't be in such a hurry, enjoy life more." A high-level report meeting was held in January, and if it is held again in June, will it be more frequent? Wait for school. ”

Li Jiangao didn't say anything, this is not something he needs to worry about.

I just think that people's minds are really 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, enjoy his college life first, and have a complete life. At that time, Xu Dajiang meant that he hoped that Qiao Ze could develop well......

Now that he had given up his previous idea and went with Qiao Ze, the dean hoped that Qiao Ze would slow down.

"Well, but it doesn't matter. If Qiao Ze really does it, it is indeed worth doing it again. After all, others don't think they have a chance. In fact, the school basically broke even at the last report meeting, but some hidden costs in the city were not calculated. But if the quality gap proves to be a problem, let's just hold a conference. What do you think about the fees, which can be a little more expensive? Xu Dajiang muttered to himself.

"Uh...... I don't understand this. Li Jiangao replied and said, "Professor Zhu is calling us, let's go take pictures together." ”

"Hey, you call Qiao Ze's mother to take a group photo together, it's not good that she has been watching from the side, take a few more photos, and hang them in my office when you turn around."

"Okay."

……

National Center for Mathematical Research on the hill behind the University of Berkeley, San Francisco Bay Area, California, USA.

Although it was late at night, Robert Stephen was still engrossed in sitting in front of his work, holding a pen and writing and drawing on the manuscript paper.

If José was around, it would have been obvious at a glance that he was working on his supercoiled space algebra.

Yes, although the big guy did not like Jozer, he was clearly interested in this new direction that José proposed.

The only pity is that this is still a beginner subject.

There is too little information to draw on.

In addition to the video of Josser's presentation, only Josser's paper on solving the general solution of the Yang-Mills equation remains.

This also makes the research more difficult.

Just as 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 a lot of face.

"Hey, Robert, did you read the question I sent you in my email?"

"Huh? I haven't read the email today. ”

"Oh, and if you're still working on supercoiled space algebra, I suggest you check it out now. I have sent you a set of topics on supercoiled space algebra specially designed by the Institute, and you can try to do it. ”

"Thank you, Daniel."

"You're welcome, just invite me for 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 answers...... Sixty percent of the questions in this set of questions were written by him, but he does not plan to publish the answers for the time being. ”

"Got it, thank you again."

……

Hanging up the phone, Robert opened the mailbox for the first time.

If you want to quickly enter a new field of mathematics, brushing questions is undoubtedly one of the quickest ways.

Unfortunately, for the new direction of supercoiled space algebra, you must first have a deep understanding of the relevant theories.

So in the current situation, it's really difficult to brush up on the questions.

Soon, the relevant files were downloaded.

Clicking on the document, Robert Stephen first skimmed 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 on the first question:

"Consider a one-dimensional algebraic model of supercoiled space, where the 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 generation operators at position j, respectively. σ=↑, ↓ represents spin, and njσ=cjσcjσ is an electronic number operator. t is the electron transition intensity, u is the hubbard interaction strength, and μ is the chemical potential.

a. Prove the reciprocal relation of this Hamiltonian [h,cjσ]=t(cj1σ+cj+1σ)+u(nj,σnjσ)cjσ.

b. Considering the mean field approximation of the system, it is assumed that 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 topic is very level.

Robert Stephen has been studying supercoiled space algebra for two months, and it is natural to see that this question tests the basic understanding of the supercoiled space algebra model. It has to be said that in the field of new algebra research, Princeton has once again come to the forefront of its peers.

Soon Robert was indulging in.

I have to say that when researching such a new direction of mathematics, it is also a kind of happiness to have problems to solve.

After three hours of scribbling and correction, Robert finally finished the problem-solving process and followed the answer to the second question nj↑nj↓≈nj(nj1).

Full of a sense of accomplishment.

In his excitement, Robert filmed the process of solving the problem, and then sent it directly to Edward Witten, and asked by the way, 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 email him back at this time.

Coupled with a hint of sleepiness, Robert was about to pack up and go to bed, but he didn't expect that he had just packed up all the manuscripts on the desktop, and suddenly there was an email prompt sound from the speaker. Subconsciously clicked on the mailbox and looked at it, heh...... Edward hadn't even slept yet.

"Congratulations, Professor Stephen, although the proof process for the first question is slightly flawed, it is generally correct. I would also like to ask, how do you feel about these topics? In addition to the six sample questions in the first part, there are six other questions in the second part, which I am considering directly disclosing to the public. ”

After a moment of thought, Robert began to edit the email.

"A very meaningful topic, Professor Witten, has helped me a lot and helped me sort out some basic concepts in this new algebraic direction. The symmetry between this particular space is often missing, and the commutative problem can only be considered in very special cases, resulting in an extremely abstract system of mathematics.

Your topic can concretize some abstract theories, which is very meaningful for everyone to understand supercoiled space algebra. If that's an honor, I'd love to be part of your team! ”

After clicking the reply button, Robert Stephen suddenly stopped sleepy.

It can only be said that the persistence of mathematicians is difficult for ordinary people to imagine.

Fortunately, Edward Witten soon wrote back to him.

"Thank you for your evaluation and you are very welcome to join. It's a shame we missed something. As a result, our basic theoretical understanding and research of supercoiled space algebra has been slow. Tonight, I'll put all the questions into the shared question bank of the Institute for Advanced Study in Princeton, and I will update them from time to time.

Of course, if you have a good question, you can also send it to me, or Professor William, and it will be cross-checked and put into the corresponding question bank. Admittedly, this is an interesting area of study. Joe's research is astounding. ”

After reading this reply, Robert Stephen only felt a sense of excitement.

It's that José again.

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Robert didn't like this Chinese boy before, but now he doesn't like it even more.

In his opinion, José was not a pure mathematician, too utilitarian.

Any mathematician who has started a new school of thought will probably drop everything to perfect the whole theory in order to promote this new form of algebra in the first place. But Jozer chose to ignore it.

But it also happened to pique Robert Stephen's competitive spirit.

In many cases, the founder may not be able to perfectly interpret the entire theory.

Since Qiao Ze took the initiative to give up this piece of work, then they can just add it.

So, after thinking for a while, Robert began to reply again.

"Professor Witten, I think that in addition to sharing the topic, we can also share some thoughts on supercoiled space algebra. Here are two theorems that I have recently come up with.

Theorem 1, the formation conditions of spin density waves, within the appropriate parameters of the one-dimensional supercoil space algebra model, the system may undergo spin density wave phase transition, that is, the electrons on and off spin show a periodic orderly arrangement. ”

Theorem 2, the existence of topological haldane phases, for the one-dimensional chain of the supercoiled space algebraic model, within the appropriate parameter range, the system may support the topological haldane phase, which has nontrivial topological properties. ”

This time the wait was shorter, and two minutes later, Edward Witten replied.

"Thank you very much, Professor Stephen. We have also studied the first theorem you have summarized, but the second theorem is very interesting, and we will verify it. If you wish, you can attach the complete theorem proof process and publish it. We will include it in the shared space related to the algebra of the supercoiled space.

We hope that we can solve a series of related problems as soon as possible. I'm sure you feel the same way from this period of research, and this may indeed be a key to solving the mystery of unification. I suspect that this particular mathematical structure contains the framework of space-time and gravity at the microscopic level, but unfortunately we have not yet fully grasped it.

We are in the process of organizing a research team, and the main members have been confirmed: me, Daniel, Professor Wilhelm, and Professor Schultz, if you would like to join, we would love to have you join. ”

After reading the email, Robert had a smile on his face.

Immediately create a new email, and dance your hands on the keyboard.

"Of course, I really want to be part of the team! Thank you, Professor Witten, that we can certainly solve this set of problems. ”

……

Huaxia, Xilin University of Technology.

After spending the morning, Qiao Ze finally breathed a sigh of relief.

Compared with doing research in his own office, he felt more tired about things like graduation defense and taking pictures.

Especially the thank-you banquet at noon, the atmosphere made him feel quite weird.

Whose family is thanking the teacher, the teacher has been thanking the students......

This made José very uncomfortable.

It's not for the sake of Lu Xiuxiu and Su Mucheng that they are very happy today, Qiao Ze plans to go back to the third floor directly after he defends.

After eating, Su Mucheng and Lu Xiuxiu went to choose the photos taken today, maybe they will have to refine it, I don't know what time it will be finished.

Qiao Ze was not interested in any of this, and returned to the institute on his own.

Sitting at the 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 hustle, and its most important job is still to help Qiao Ze find papers and manage mailboxes and other auxiliary work through intelligent search and crawler technology under the framework of crowd intelligence.

Especially managing Joze's mailbox.

can really help Qiao Ze review a lot of things.

Since he solved the general solution of the Yang-Mills equation and ignored the development of supercoiled space algebra, there has been more and more "spam".

Too many people have emailed him to discuss outlandish questions.

Someone has even started sending him papers on supercoiled space algebra.

If it was well written, it would be fine, but at least judging from the few papers he had received so far, he couldn't even understand what the other party was trying to say.

This made Qiao Ze begin to understand why the editors of top journals would delete some of the papers directly after receiving them with just a glance at the author's office.

The ignorant are truly fearless.

He even received a paper claiming to use supercoiled space algebra to solve the problem of mathematical unification. Eight pages were written, but the first theorem given was all loopholes.

Well, this is a paper written by a professor at a university in Morocco.

It was from this paper sent to the mailbox that Qiao Ze directly hosted the mailbox to Doudou.

Although Doudou's current logical thinking ability can't find excellent papers, it can still be used to screen out a series of unreliable arguments.

However, today's first tip is not about filtering out the "spam" that Doudou has judged, but about Princeton's new progress in supercoiled space algebra research.

Although Qiao Ze is too lazy to spend time on the popularization of supercoiled space algebra, he is still more concerned about the research in this direction.

No one is omniscient.

Although he was the first to invent this system, maybe someone else could come up with something he didn't expect to help after researching?

Just like 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's pointing the way, and with plenty of time to study, he might be able to find something unexpected.

"The Princeton Institute has given four fundamental theorems and twelve example problems for supercoiled space algebra that has just been published?"

"Yes, master. All the information is published on the official website under the new algebra research direction section, do you need to help you call up the data now? Cute ......"

If netizens see Doudou in Qiao Ze's computer, they will probably have mixed feelings.

After all, this thing is an arrogant character in Weibo and other software, even if it occasionally uses a cordial tone, it is probably ironic.

However, when Qiao Ze used it, it became like a licking dog.

It is really vividly explained what it means to be born in Huainan and orange in Huaibei.

"Hmm." Qiao Ze answered.

Soon, the research published on the website of the Institute for Advanced Study in Princeton was presented in the form of pictures in front of Josser's eyes.

In addition to the two theorems that Robert sent to Edward, two other theorems are given in the picture.

It is interesting to describe the topological properties of supercoiled space algebra and the MOTT insulating phase of quantum phase transitions and strongly correlated systems.

With the exception of the second one, each of the concluded theorems has two or three names attached to it.

Then there are the 12 sample questions.

From Qiao Ze's point of view, these twelve questions are all very simple.

Basically, it revolves around the three theorems that have been published.

But for beginners, it's really useful.

This also inspired José.

Although he does not intend to waste too much time on the science of supercoiled space algebra, he can give some small help to these mathematicians and physicists who have devoted themselves to the study of this science.

After all, it is a very simple matter for him to come up with a question, and it hardly takes much time.

By the way, it is also possible to derive the transcendental geometry corresponding to the algebra of supercoiled space.

Just do it when you think about it.

Soon, Qiao Ze directly devised two problems.

The first question is an advanced problem about supercoiled space algebra: set up a high-dimensional algebraic model of supercoiled space with a Hamiltonian of [ 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 the spin-density wave (SDW) phase transition may occur in the ground state of the system under certain conditions, that is, a spin-ordered periodic arrangement is formed in the system. Please analyze the spin density wave phase transition conditions of the model at zero temperature, and give the corresponding physical explanation.

The second question is about the transcendental geometry that he studied.

Qiao Ze named the problem Crossing the Dimensional Gate, and the title was not difficult, but it was very special.

The problem is described as follows:

Suppose there is a mysterious dimensional gate in the universe that connects the four-dimensional space with the six-dimensional space, which is mathematically described as: [ v =\int d^4x \sqrt{g}\left(\frac{1}{2}\mathbf{r}+\frac{1}{2}abla\phi \cdot abla\phi - v(\phi)ight)]

where ( v ) is the action of the gate of this dimension, (\sqrt{g}) is the square root of the gauge of the four-dimensional space-time, (\mathbf{r}) is the scalar curvature of the four-dimensional space-time, (abla\phi ) is the scalar field gradient of the six-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 that connects the two sides of the gate of dimensions and satisfies the following conditions. The path (c) is of length (l) and it has the least amount of action. Considering that in a four-dimensional space the gauge is (\sqrt{g} = 1 ) and the scalar field is (\phi = \phi_0).

Request Solution: The curve with the smallest amount of action in the six-dimensional space (c).

Hint: It can be solved using the correlation theory of supercoiled spaces, where the minimum action should be for the equation of motion satisfied by the path (\mathbf{x}(t)).

After designing the problem, Qiao Ze directly asked Doudou to send it out.

In order to ensure that everyone can understand it, the question part is specially used in Chinese and English.

Especially for some new mathematical terms, Qiao Ze also specially explained, which is very intimate and does not need to be thanked by the other party.

It can only be said that everyone is contributing to academic progress.

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