Great Country Academician

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

After Xu Chuan helped to deal with the enrollment, he uniformly called the four students to his office, and began to get familiar with these students while preparing the corresponding learning content.

Four students, Gu Bing from China, majored in algebraic topology and analytic geometry. During their doctoral period, their development and discovery were mainly in algebraic topology.

Roger Dean, the oldest of the four students from Politecnico di Milano, is studying algebraic surfaces and commutative algebra.

Shahi Perez, a Ph.D. student at the University of Paris VI in France, focuses on topology.

As for the last Amelia Elwin, she studied mathematical analysis and differential geometry in mathematics. At the same time, she studied field theory and electromagnetic physics in physics.

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

Of course, it was discussed with them. After all, everyone must have their own ideas to reach the doctoral level. He still respects the wishes of the students themselves.

To be honest, there are not many mentors as responsible as him, even in Princeton.

Putting it in the country, it will be even less.

After determining the development direction of these students, the rest is the study plan.

Looking at the four students from all over the world in the office, Xu Chuan said, "I have already decided with you about your future development."

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

"As for this aspect, I have already prepared it for you."

After a pause, he continued: "You must have known me before you applied to be my student. Before that, I completed the proof of Hodge's conjecture."

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

"Tools for Algebraic Varieties and Group Mapping."

"This is the core mathematical tool I used in proving the Hodge conjecture, and it will be your study schedule for the next few months."

"Before this year's International Mathematics Conference, that is, before August, I will conduct an assessment for you to review your learning progress."

"If you pass my assessment, there will be rewards at that time. As for what the rewards are, we will keep them secret for the time being."

Xu Chuan said with a smile.

In the office, Amelia asked curiously: "Then what if you fail the examination?"

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

After all, when he first came to Princeton, everyone didn't know the character of this young mentor. If he failed the assessment and was dismissed, he would be in big trouble.

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

"Professor, may I ask the general content of the assessment?"

On the side, Gu Bing asked nervously.

After finally coming to Princeton to study, he didn't even want to graduate.

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

Hearing this, the four students were all relieved. They couldn't help but not care about the matter of graduation. After all, they have already received their Ph.

But before they completely relaxed, Xu Chuan continued: "The algebraic variety and group mapping tool solved the Hodge conjecture, but it still has considerable value that has not been developed."

"Many algebraic varieties and differential forms, polynomial equations, and even algebraic topological problems can be used to try."

"For example, the 'Bloch conjecture' which belongs to the same conjecture family as the Hodge conjecture, 'the Hodge theory of algebraic surfaces should determine whether the zero-cycle Chow group is finite-dimensional', and some motivations for finite coefficients The cohomology group isomorphism maps to the etale cohomology problem and so on."

"Perhaps I will randomly select one of these questions as your assessment topic."

Gu Bing: .

Roger Dean: ? ? ?

Shahi Perez: ! ! !

Amelia Allwin: (っ°Д°;)っ

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

If I remember correctly, what the instructor said before doesn't seem to be too difficult, right?

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

Among them, there are even century-old problems that have not been solved for hundreds of years.

Where the hell is it not difficult?

And it's already mid-to-late February, and there are only a little more than five months before the International Mathematical Conference is held.

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

kill them.

Xu Chuan ignored the psychological activities of the four students.

In his opinion, this is really not a difficult task.

After solving Hodge's conjecture, he understood some problems related to it.

As far as his current mathematical ability is concerned, in his own field, he already has a certain degree of certainty in his heart whether the problems of the "Bloch Conjecture" can be solved by the "Algebraic Variety and Group Mapping Tool".

Of course, for these students, there must be some difficulties.

However, if one can master and use the "algebraic variety and group mapping tool" proficiently, it is still possible to solve these problems.

Since he brought students, he had to be responsible to the students. Anyway, for him, it was impossible for the students to go through the doctorate too easily under his hands.

That is irresponsible to them, a waste of their time, and a waste of their own energy.

After arranging the tasks, the four students left, and Xu Chuan came to Weiteng's office. He was going to inquire about the arrangements for the collision experiment at CERN in the first half of this year.

See if anyone is interested.

After all, in his previous life, he formally contacted CERN in the second half of 2018. 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 his discovery at CERN, the arrangement of the collision experiment may also be modified.

After all, the method of mathematically calculating the search channel of physical particles is very important, and it can change many things.

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

Just at the beginning of the year, Weiteng has returned from CERN.

Seeing Xu Chuan, Wei Teng got up with a smile and made a cup of coffee and handed it over: "I heard that the New Year in Huaguo will be very lively."

Xu Chuan smiled and said, "Of course, if you go there, you can see many different scenery there."

"Such as collecting New Year's goods, guessing riddles with lanterns, dragon and lion dances, wandering gods and boats and other activities, these are quite interesting."

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

It's a pity that the taste of the past years has become weaker every year, but Xu Chuan is quite happy to recommend these things to others.

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

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

"welcome."

The two chatted for a while, and Wei Teng turned the topic to the other side: "This year's CERN experiment, are you interested in going to see it?"

Before Xu Chuan could ask about it, the old man took the initiative to speak up.

Xu Chuan asked along the way: "What did you study in the first half of the year?"

Witten shrugged and said: "Still deepening on the previous basis, such as studying the Higgs boson, searching for pentaquark particles, and some supplementary experiments to the Standard Model."

"Oh, by the way, there are still a small number of collision experiments looking for gravitational waves, maybe you will be interested in this?"

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

He didn't bother to study the Higgs boson and the discovery of the pentaquark, these two things were clearly in his mind.

As for gravitational waves.

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

As early as 2016, LIGO detected the gravitational wave signal from the merger of binary black holes for the first time.

In 2017, humans observed gravitational waves from the merger of two neutron stars.

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

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

But unfortunately, until his death, the physics community was still in the initial research stage of general relativity, and failed to discover any major results.

The Nobel Prize is not awarded to deceased ancestors.

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

It is an honor for this old man to win the Nobel Prize.

Back to the topic, CERN arranged gravitational wave-related experiments in the collision experiment in the first half of this year. In Xu Chuan's view, it was a waste of money.

With the current collision energy level of the LHC, 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 twenty powers.

Even if such a black hole can produce gravitational waves, current detection equipment cannot detect them at all.

In Xu Chuan's view, the gravitational waves produced by the black holes collided by the Large Intense Particle Collider are no higher than the collision of two cars.

And to detect such weak gravitational waves, the current detection equipment may not be able to do it at all unless it has been improved by a dozen or so levels.

So CERN's arrangement for a collision experiment is a complete waste of time and money.

Xu Chuan had no interest in this at all.

On the side, Wei Teng 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: "To be honest, nothing new has appeared for a long time since the development of physics. We are still tinkering with the previous standard model."

"My M-theory is simply impossible to test for at least a century, and other things"

"To be honest, I'm pessimistic."

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

Regarding this, Xu Chuan held a different view. He smiled and comforted: "That's not the case."

"Technology is always evolving, and faster than you or I can imagine."

"Maybe in the near future, we'll find something beyond the Standard Model?"

Wei Teng smiled and said, "I hope."

Xu Chuan smiled and said, "For sure."

The days in Princeton passed by bit by bit. After confirming that CERN did not have any collision experiments of his interest in the first half of this year, Xu Chuan devoted his attention to his goal 'manifold'.

This is the first and most important learning goal. It is related to the existence and smoothness of the solution of the NS equation, and it is also related to the simulation control of turbulent flow from the mathematical aspect.

As for manifolds, the two most important directions are topological manifolds and differential manifolds.

Thanks to the 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 problems in two different fields.

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

Fortunately, the Flint Library can fully satisfy this point. He only needs to borrow books and materials to download papers in the past.

The time passed day by day, and soon it was mid-March.

Xu Chuan, who was immersed in his own study, received a call from Weiteng and rushed over in a hurry.

On March 14, 2018, a major earthquake occurred in the world of physics.

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

This news stunned Xu Chuan for a long time.

Compared with the previous Professor Mirzakhani, he is undoubtedly more familiar with Hawking.

Hawking's death, he had already experienced it once in his previous life, and he experienced it again in this life, it still made him feel like a world away, and there was more melancholy in his heart.

All living beings in the long river of time are as insignificant as dust, and even the most outstanding people only radiate their own brilliance for a short time, and then extinguish and drown in the long river of time.

Sighing, Xu Chuan threw out some messy thoughts in his mind and regained his energy.

Everyone is a book of history, some stories have been written, and some stories are still being written;

And he is alive because he wants to make up for the regrets of his previous life, and because he wants to take a look further afield.

At the end of March, after attending the funeral of Mr. Hawking, under the tactful reminder of Fefferman, the dean of the Department of Mathematics, Xu Chuan finally remembered that he still had a full professorship at Princeton University.

It has been a month and a half since the beginning of the Spring Festival, but he has not opened a single class except for accepting four students.

The long-term passive sabotage has made Fefferman, who has never made friends for a long time, a little bit unbearable.

On the other hand, Deligne, who is also a professor in the Department of Mathematics, didn't care about it at all. Xu Chuan went to him almost every two or three days, and he didn't bother to ask.

In addition to teaching students, professors at Princeton University also have basic class tasks, although many full professors will leave it to their own doctoral students or assistant professors to complete.

But you gotta start class.

Not even classes are held, which is unreasonable.