Chapter 200 How Is This Not Difficult?

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 get familiar with them while preparing the corresponding learning content.

Among the four students, Gu Bing from China mainly studied algebraic topology and analytic geometry, and his development during his doctoral studies was mainly based on algebraic topology.

Roger Dean, the oldest doctoral student from the Polytechnic University of Milan in Italy, studied algebraic surfaces and commutative algebra.

And Shashi Perez, a doctoral student at the University of Paris VI, mainly studied topology.

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

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

Of course, he discussed with them. After all, everyone must have their own ideas to reach the doctoral stage, and he still respects the students' own wishes.

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

In China, there are even fewer.

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

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

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

"And I have prepared things for you in this regard."

After a pause, he continued: "I believe that before you apply to become my students, you should have known about me. Before that, I completed the proof of the Hodge conjecture."

"Of course, I am not showing off this, but your next study arrangement is related to it."

"Algebraic clusters and group mapping tools."

"This is the core mathematical tool I used when proving the Hodge conjecture. It will be your study arrangement for the next few months."

"Before this year's International Mathematical Congress, that is, before August, I will conduct an assessment and inspection on you to review your learning progress."

"If you pass my assessment, there will be rewards at that time. As for what the rewards are, keep it confidential 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, they had just arrived at Princeton, and no one knew the character of this young tutor. If he failed the assessment and was dismissed, it would be a big trouble.

Xu Chuan smiled and said, "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 nervously.

It was not easy to come to Princeton to study, and he didn't want to fail to graduate.

Xu Chuan: "Of course it is 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 comes to graduation, they can't help but care about it. After all, they have already obtained a doctorate, and if they go further, they can complete all their studies in their lives.

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

"It can be used to try many algebraic clusters and differential forms and polynomial equations, and even difficult problems in the direction of algebraic topology."

"For example, the 'Bloch conjecture', which belongs to the same family of conjectures as the Hodge conjecture, the 'Hodge theory of algebraic surfaces should determine whether the Chow group of zero cycles is finite-dimensional' problem, and the problem of isomorphism mapping of certain motivated cohomology groups of finite coefficients to etale cohomology problems, etc."

"Maybe I will randomly pick one of these problems as your test questions."

Gu Bing:.

Roger Dean: ? ? ?

Shashi Perez: ! ! !

Amelia Irwin: (っ°Д°;)っ

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

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

But the 'Bloch conjecture' and 'Is the Chow group a finite-dimensional problem' he mentioned are all world-class problems.

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

What is so difficult about this?

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

Five months to solve a world problem.

Kill them.

Xu Chuan ignored the psychological activities of the four students.

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

After solving the Hodge conjecture, he learned about some related problems.

With his current mathematical ability, in his own field, he has a certain degree of confidence in whether these problems such as the 'Bloch conjecture' can be solved by the 'algebraic cluster and group mapping tool'.

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

But if they can master and use the 'algebraic cluster and group mapping tool' proficiently, then it is still possible to solve these problems.

Since he has brought students, he must be responsible for them. Anyway, for him, it is impossible for students to get through the doctorate easily under his hands.

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

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

See if anyone is interested.

After all, in his previous life, he officially came into contact with CERN in the second half of 2018. He knew the arrangements for the second half of the year very well, but he didn't know much about the first half of the year.

Of course, with his rebirth and discovery at CERN, the arrangements for the collision experiment may also be modified.

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

Butterflies flap their wings often inadvertently.

Just in time for the beginning of the year, Witten has returned from CERN.

Seeing Xu Chuan, Witten stood up with a smile, made a cup of coffee and handed it over: "I heard that China's New Year will be very lively."

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

"For example, various activities such as New Year's goods sweeps, lantern quizzes, dragon and lion dances, wandering gods and boat racing, etc. are all quite interesting."

Compared with New Year's Day abroad, China's Spring Festival undoubtedly has more and more lively traditional customs.

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

After all, it is to promote traditional Chinese culture.

"It seems 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 changed the topic to the other side: "Are you interested in going and taking a look at this year's CERN experiment?"

Before Xu Chuan asked about it, the old man took the initiative to speak.

Xu Chuan asked along the way: "What are you studying there in the first half of the year?"

Witten shrugged and said: "We will continue to deepen our research on the basis of the past, such as studying the Higgs boson, searching for pentaquark particles, and some supplementary experiments on the standard model."

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

Xu Chuan smiled and shook his head, saying, "If it's just these things, I might not be too interested."

He was too lazy to study the Higgs boson and the discovery of the pentaquark particle. These two things were very clear 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 dual black holes for the first time.

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

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

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

But unfortunately, until his death, the physics community was still in the initial stage of research on general relativity and failed to discover any significant 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 complete waste of money.

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

Even if such a black hole could produce gravitational waves, current detection equipment would not be able to detect them at all.

In Xu Chuan's opinion, the gravitational waves produced by the black holes knocked out of the Large Strong Particle Collider are no higher than those of two cars colliding.

To detect such weak gravitational waves, the current detection equipment may not be able to do so unless it evolves to a dozen or so levels.

Therefore, CERN's arrangement of collision experiments is a complete waste of time and money.

Xu Chuan had no interest in this at all.

On the side, Witten spread his hands and said: "But there is nothing we can do. We always hope to create a big one, but the current equipment and theory simply do not support it."

After a pause, he then sighed: "With the development of physics, to be honest, nothing new has appeared for a long time. We are still tinkering with the previous standard model."

"It will be impossible to verify my M theory 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 had a different view. He smiled and comforted: "That won't happen."

“Technology is always evolving, and faster than you and I can imagine.”

"Perhaps in the near future we will find something beyond the Standard Model?"

Witten smiled and said, "I hope so."

Xu Chuan smiled and said, "Definitely."

The days in Princeton passed by little by little. After confirming that there was no collision experiment that he was interested in at CERN in the first half of this year, Xu Chuan focused his attention on his goal, ‘manifold’.

This is the first and most important learning goal, which is related to the existence and smoothness of the solution of the NS equation, and also to the simulation and control of turbulence from a mathematical perspective.

As for 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 these two aspects, but that is not enough. The Hodge conjecture and the Navier-Stokes equations are problems in two different fields.

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

Fortunately, the Flint Library can fully meet this requirement. He only needs to borrow books, materials and download papers.

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

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

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

Stephen William Hawking, the world-renowned great physicist, passed away at the age of 76.

This news made Xu Chuan stunned for a long time.

Compared with Professor Mirzakhani before, he was undoubtedly more familiar with Hawking.

He had experienced Hawking's death once in his previous life. When he experienced it again in this life, he still felt as if he was in another world, and there was more melancholy in his heart.

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

With a sigh, Xu Chuan threw out some messy thoughts in his mind and cheered up again.

Everyone is a history book. Some stories have been written, and some stories are still being written; some people live to leave their names for eternity, and some live to live a happy life.

And he lives to make up for the regrets of his previous life and to go to a farther place 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 under the subtle reminder of Fefferman, the head of the Department of Mathematics.

It has been one and a half months since the start of the Spring Festival, but he has not taught a single class except for four students.

The long-term passive slacking made Fefferman, a close friend of his, a little bit frustrated.

Deligne, a professor in the Department of Mathematics, didn't care about this at all. Xu Chuan went to him almost every two or three days, but he didn't ask.

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

But you have to teach classes.

It's unreasonable not to even teach classes.