Gu Bing arrived first, and the remaining three students also arrived at Princeton within two days.

After Xu Chuan helped to handle the admission, he called the four students to his office and began to familiarize himself with these students while preparing the corresponding learning content.

Four students, Gu Bing from China, majored in algebraic topology and analytic geometry, and his development discoveries during his doctoral studies were mainly based on algebraic topology.

Roger Dean, the eldest of the four students from the Politecnico di Milano, studied algebraic surfaces and commutative algebra.

Shashi Pérez, a PhD student at the University of Paris VI in France, majored in topology.

As for the last Amelia Erwyn, she studied mathematical analysis and differential geometry in mathematics, while at the same time, she followed field theory and electromagnetic physics in physics.

For these four students, Xu Chuan arranged different development directions and study plans.

Of course, it was discussed with them, after all, everyone must have their own ideas to get to the doctoral stage, and he still respects the student's own wishes.

To be honest, there are very few mentors as responsible as him, even in Princeton.

Put it in the country, then it will be even less.

Once you've decided where to go for these students, that's all that's left is the study plan.

Looking at the four students in the office, Xu Chuan spoke: "Regarding your future development, I have already determined it with you. ”

"So, the next step is the study arrangement."

"And I've got that stuff for you."

After a pause, he continued, "I guess you should have known something about me before you applied to be my student, and before that, I completed the proof of Hodge's conjecture. ”

"Of course, I'm not showing off this, but your next study schedule has something to do with it."

"Algebraic Cluster and Group Mapping Tools."

"This is the core math tool I use to prove Hodge's conjecture, and it will be your learning schedule for the next few months."

"Before this year's International Congress of Mathematics, that is, before August, I will do an assessment check on you to review your learning progress."

"If you pass my assessment, there will be a reward at that time, as for what the reward is, it will be kept secret for the time being."

Xu Chuan said with a smile.

In the office, Amelia asked curiously, "What if you don't pass the assessment?" ”

Hearing this, the other three looked over nervously, they were also concerned about this issue.

After all, when you first come to Princeton, everyone doesn't know the character of this young mentor, and if you don't pass the assessment, it will be a big trouble to be fired.

Xu Chuan said with a smile: "Then maybe your graduation will be delayed for some time." ”

"Professor, can I ask about the general content of the assessment?"

On the side, Gu Bing asked a little nervously.

When he finally came to study at Princeton, he didn't want to finish his studies.

Xu Chuan: "Of course, it's related to algebraic clusters and group mapping tools, don't worry, it won't be too difficult." ”

Hearing this, the four students all breathed a sigh of relief, when it came to graduation, they couldn't help but care, after all, they had already studied for a doctorate, and they could complete all their studies in their lives if they went one step further.

However, before they could completely relax, Xu Chuan continued: "The algebraic cluster and group mapping tool solves the Hodge conjecture, but it still has considerable value and has not yet been developed. ”

"There are a lot of algebraic clusters and differential forms, polynomial equations, and even algebraic topological orientation problems."

"For example, the 'Bloch conjecture', which belongs to the same family of conjectures as the Hodge conjecture, the problem that Hodge's theory of algebraic surfaces should determine whether the chow group of zero cycles is finite-dimensional, and the problem of homology on certain motivations of finite coefficients being homomorphically mapped to the cohomology on etale, .....etc., etc."

"Maybe I'll pick one of these questions out of the question as your assessment question."

Gu Bing: ......

Roger Dean: ???

Shahi Perez: !

！

Amelia Erwin: (っ°Д°; )っ

Did they hear it wrong? Or did they have auditory hallucinations before?

If I'm not mistaken, it doesn't seem too difficult for the instructor to say before, right?

But what he said about the "Bloch conjecture" and "whether the chow group is a finite dimensional problem" are all world-class problems.

There are even problems of the century that have not been solved for hundreds of years.

What the hell is not so difficult about this?

And it's mid-to-late February, just over five months before the International Congress of Mathematics.

In five months, a world puzzle has to be solved.

Kill them.

......

Xu Chuan ignored the mental activities of the four students.

In his opinion, this is indeed not a difficult thing to do.

After solving the Hodge conjecture, he learned about some of the problems associated with it.

In terms of his current mathematical ability, he is already certain in his mind whether the 'Bloch conjecture' can solve these problems by the 'algebraic cluster and group mapping tool' in his own field.

Of course, for these students, there is definitely difficulty.

However, if you are proficient in the 'algebraic cluster and group mapping tools', then it is still possible to solve these problems.

Since he brought the students, he had to be responsible for the students, anyway, for him, it was impossible for the students to get through the doctor too easily under his hands.

That's irresponsibility to them, a waste of their time, and a waste of their own energy.

After arranging the task, the four students left, and Xu Chuan came to Witten's office, where he wanted to inquire about the arrangements for the collision experiment in the first half of this year.

See if there's anything interested.

After all, in his last life, he was officially contacted in the second half of 18 years, and he was very clear about the arrangements for the second half of the year, but he didn't know much about the first half of the year.

Of course, with his rebirth and discovery, the arrangement of the collision experiment may also be modified.

After all, it is important to mathematically calculate the search channels of physical particles, and it can change a lot of things.

The flapping of a butterfly's wings is often inadvertent.

At the beginning of the year, Witten had already returned.

Seeing Xu Chuan, Witten got up with a smile and made a cup of coffee and handed it over: "I heard that Huaguo's New Year's party is very lively." ”

Xu Chuan smiled and said, "Of course, if you go over, you can see a lot of different scenery there." ”

"For example, various activities such as New Year's goods sweeping, lantern quizzes, dragon and lion dances, and traveling gods and boats, these are quite interesting."

Compared with the New Year's Day in foreign countries, the traditional customs of the Spring Festival in China are undoubtedly more and more lively.

It's a pity that the flavor of the past is getting thinner and thinner year by year, but Xu Chuan is quite happy to recommend these things to others.

After all, it is to promote the traditional culture of China.

"Looks like I'm going to find a chance to go over and see it." Witten said with a smile.

"Welcome."

The two chatted for a while, and Witten turned the topic to the other side: "Are you interested in going over and seeing this year's experiment?" ”

Without waiting for Xu Chuan to ask about this, the old man took the initiative to speak.

Xu Chuan asked, "What were you studying over there in the first half of the year?" ”

Witten shrugged his shoulders and said, "It's better to deepen on the previous basis, such as studying the Higgs boson, looking for pentaquark particles, etc., and some complementary experiments to the Standard Model." ”

"Oh, by the way, there's a small number of collision experiments looking for gravitational waves, maybe you'll be interested in that?"

Xu Chuan shook his head with a smile and said, "If it's just these things, I'm probably not very interested." ”

The Higgs boson study and the discovery of the pentaquark particle, he didn't bother to get past them, these two things were all too clear in his mind.

】

As for gravitational waves.

In fact, this is not the first time that humans have discovered gravitational wave signals.

Back in 2016, Ligo detected the first gravitational wave signal from the merger of two black holes.

In 2017, gravitational waves from the merger of binary neutron stars were observed.

The successful discovery of gravitational waves fills in the last missing piece of the puzzle in the experimental verification of Einstein's general theory of relativity.

If Einstein were still alive, he would 100% win the Nobel Prize in Physics again with his theory of general relativity.

Unfortunately, until his death, the physics community was still in the initial stage of research on general relativity, and no significant results were found.

The Nobel Prize, on the other hand, is not awarded to deceased ancestors.

Of course, even if he has only won the Nobel Prize once, no one can deny Einstein's great position in physics.

This old man won the Nobel Prize, which is an honor for the Nobel Prize.

......

Back to the topic, arranging experiments related to gravitational waves in the collision experiment in the first half of this year is, in Xu Chuan's view, a complete waste of money.

With the current LHC collision energy level, even if it is opened to the maximum, it can at most create an extremely small black hole, with a diameter of more than minus 20 power.

Even if such a black hole could generate gravitational waves, current detection equipment would not be able to observe it at all.

The gravitational waves produced by the black hole in the large strong particle collider are, in Xu Chuan's view, no higher than the collision of two cars.

And to explore such a faint gravitational wave, the current detection equipment may not be able to do it at all without evolving a dozen grades.

So arranging a collision experiment is a complete waste of time and money.

For this, Xu Chuan was not interested in it at all.

On the side, Witten spread his hands and said: "But there is no way, we always hope to make a big one, but the current equipment and theory do not support it at all." ”

After a pause, he then sighed: "The physics world has developed so far, and to be honest, nothing new has appeared for a long time. We're also tinkering with the previous standard model, knocking it out. ”

"It's simply impossible for my M theory to be verified for at least a century, and the rest ....."

"To be honest, I'm pessimistic."

As he spoke, the old man sighed again and shook his head slightly.

Xu Chuan had a different opinion on this, he smiled and comforted: "That's not going to happen." ”

"Technology is always evolving, and it's faster than you and I think."

"Maybe in the near future, we'll be able to find something beyond the standard model?"

Witten smiled and said, "Hopefully." ”

Xu Chuan smiled: "Definitely." ”

.......

As his days at Princeton passed, after determining that there were no collision experiments that interested him in the first half of this year, Xu Chuan focused on his target 'manifold'.

This is the first and most important learning objective, which is related to the existence and smoothness of the solution of the ns equation, as well as to the mathematical simulation control of turbulence.

When it comes to manifolds, the two most important directions are topological manifolds and differential manifolds.

Thanks to his previous research on the Hodge conjecture, he has a certain foundation in both aspects, but that is not enough, the Hodge conjecture and the Navier-Stokes equation are two different fields.

He needed a more complete basic knowledge of topological manifolds and differential manifolds.

Fortunately, the Flintstone Library can fully meet this point, and he only needs to borrow books and materials to download papers.

Time passed day by day, and soon it was the middle of March.

Xu Chuan, who was immersed in his own study, received a call from Witten and hurried over.

On March 14, 2018, a major earthquake struck the physics community.

The world-famous great physicist Stephen William Hawking, died at the age of 76.

This news made Xu Chuan stunned for a long time.

He is undoubtedly more familiar with Hawking than his previous professor, Mirzahani.

Hawking's death, he had already experienced it once in his previous life, and after experiencing it again in this life, it still made him feel like he was suddenly separated from the world, and he also felt more melancholy in his heart.

All living beings in the long river of time are as small as dust, and even the most outstanding ones only exude their own brilliance for a short time, and then disappear and drown in the long river of time.

With a sigh, Xu Chuan threw out some of the messy thoughts in his mind and regained his spirits.

Everyone is a history, some stories are finished, and some stories are still being written; Some people live to leave a name for eternity, and some people live for a happy life.

And he lives because he wants to make up for the regrets of his previous life, and he wants to go farther away to see.

......

At the end of March, after attending Mr. Hawking's funeral, Xu Chuan finally remembered that he still had a full professor position at Princeton University hanging on his body, under the euphemistic prompting of Feverman, the head of the mathematics department.

And from the beginning of the Spring Festival to now, a month and a half has passed, but until now, except for four students, he has not started a single class.

The long-term negative slacking off made Peverman, a friend who forgot about the year, a little unbearable.

But Deligne, who is also a professor in the Department of Mathematics, doesn't care about this at all, Xu Chuan runs to him almost every two or three days, and he doesn't even ask.

Professors at Princeton University, in addition to taking students, also have basic class tasks, although many full professors will leave them to their doctoral students or assistant professors to complete.

But you have to start the class.

If you don't even have classes, you can't talk about it.

.......