Gu Bing arrived first, and the remaining three students also arrived at Princeton within two days.
After Xu Chuan helped handle the enrollment, he called the four students to his office. While getting to know these students, he began to prepare corresponding learning content.
Among the four students, Gu Bing from China majored in algebraic topology and analytic geometry. During his doctoral studies, his development discoveries were mainly algebraic topology.
Roger Dean, a doctoral student from the Politecnico di Milano in Italy, the eldest of the four students, studies algebraic surfaces and commutative algebra.
Shashi Perez, a doctoral student at the University of Paris VI in France, focuses on topology.
As for the last one, Amelia Aywin studied mathematical analysis and differential geometry in mathematics. At the same time, she studied field theory and electromagnetic physics in physics.
Xu Chuan has arranged different development directions and study plans for these four students.
Of course, we discussed it with them. After all, everyone must have their own ideas if they can 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 at Princeton.
If you put it in China, it will be even less.
After determining the development direction of these students, the only thing left 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 to make study arrangements."
"And I have already prepared this for you."
After a pause, he continued: "You must have known something about 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 subsequent study arrangements are related to it."
"Algebraic Varieties and Group Mapping Tools."
"This is the core mathematical tool I used to prove the Hodge conjecture, and it will be your study schedule for the next few months."
"Before this year's International Mathematics Congress, that is, before August, I will conduct an assessment on you to review your learning progress."
"If you pass my assessment, you will be rewarded. As for what the reward is, we will keep it secret for the time being."
Xu Chuan said with a smile.
In the office, Amelia asked curiously: "What if you fail the assessment?"
Hearing this, the other three people looked over nervously. They were also concerned about this issue.
After all, when I first came to Princeton, no one knew the character of this young instructor. If he failed the assessment and was fired, he would be in big trouble.
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 nervously.
After finally coming to Princeton to study, he didn't want to fail 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 all breathed a sigh of relief. They had no choice but to care about graduation matters. After all, they had already obtained Ph.D. degrees and could complete all their studies in life.
But before they could completely relax, Xu Chuan continued: "Algebraic varieties and group mapping tools have solved the Hodge conjecture, but it still has considerable value that has not yet been developed."
"It can be used to try many algebraic varieties, differential forms, 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 question 'The Hodge theory of algebraic surfaces should determine whether the chow group of zero cycles is finite-dimensional', and some motivations for finite coefficients
The cohomology group isomorphism maps to the etale cohomology problem, etc..."
"Perhaps I will randomly select one of these questions as your assessment question."
Gu Bing:......
Roger Dean:???
Shashi Perez:!
Amelia Elwin:(っ°Д°;)っ
Did they hear it wrong? Or did they have auditory hallucinations before?
If I remember correctly, the instructor said before that it wouldn't be too difficult, right?
But the ‘Bloch conjecture’ and ‘whether the Chow group is a finite-dimensional problem’ he mentioned are all world-class problems.
There are even century-old problems that have not been solved for hundreds of years.
How on earth is this not so difficult?
Moreover, it is already mid-to-late February, and there is only a little more than five months until the International Mathematics Congress is held.
Five months to solve a world problem.
Just kill them.
...
Xu Chuan paid no attention to the psychological activities of the four students.
In his view, this is indeed not a difficult matter.
After solving the Hodge conjecture, he learned about some problems related to it.
Based on his current mathematical ability, in his own field, he already has a certain degree of confidence in whether problems such as 'Bloch's conjecture' can be solved by 'algebraic varieties and group mapping tools'.
Of course, it is definitely difficult for these students.
But if you can skillfully master and use the "algebraic variety and group mapping tools", 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 pass 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 the arrangements for the collision experiment in the first half of this year.
See if anyone is interested.
After all, in his previous life, he was officially contacted 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 the discovery of Zai, the arrangements for the collision experiment may also be modified.
This chapter is not over yet, please click on the next page to continue reading! 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 at the beginning of the year, Witten has returned.
Seeing Xu Chuan, Wei Teng stood up with a smile, made a cup of coffee and handed it over: "I heard that the Chinese 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 shopping, lantern quizzes, dragon and lion dances, traveling 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 is a pity that the taste of the past years is getting weaker and 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 over to take a look at this year's 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 on the previous basis, 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 very 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 binary 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 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.
...
Let’s get back to the topic. In Xu Chuan’s view, arranging gravitational wave-related experiments in the collision experiments in the first half of this year is 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 the 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 by 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.
So arranging a collision experiment 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 do something big, but the current equipment and theory simply do not support it."
After a pause, he then sighed: "With the development of the physics community, 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 very 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 developing, and it's 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 at Princeton passed little by little. After confirming that there were no collision experiments that he was interested in in the first half of this year, Xu Chuan focused his attention on his target 'manifold'.
This is the first and most important learning goal, which is related to the existence and smoothness of the solution to the ns equation, and is also related to the mathematical control of turbulence simulation.
Regarding 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 problems in two different fields.
He needs more complete basic knowledge of topological manifolds and differential manifolds.
Fortunately, the Flintstone Library can fully meet this requirement. He only needs to go there to borrow books, materials, and download papers.
Time passed like this day by day, and soon it was mid-March.
Xu Chuan, who was immersed in his studies, received a call from Witten and hurried over.
On March 14, 2018, a major earthquake occurred in the physics world.
World-renowned great physicist Stephen William Hawking 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.
He had already experienced Hawking's death once in his previous life, and experiencing it again in this life still made him feel like he was suddenly separated from the rest of the world, and he also felt a sense of melancholy in his heart.
All living beings in the long river of time are as small as dust. Even the most outstanding people only exude their own brilliance for a short time, and then extinguish and submerge in the long river of time.
Sighing, Xu Chuan threw out some of the messy thoughts in his mind and cheered up again.
Everyone is a history, some stories have been written, and some stories are still being written; some people live to leave a name through the ages, and some live to live a happy life.
And he lives because he wants to make up for the regrets of his previous life and to see further places.
...
At the end of March, after attending Mr. Hawking's funeral, Xu Chuan finally remembered that he still held the position of full professor at Princeton University under the tactful reminder of Fefferman, the chairman of the mathematics department.
A month and a half has passed since the Spring Festival started, but he has not taught a single class except for four students.
The long period of inactivity made Fefferman, a good friend who had been with him for many years, unable to stand it anymore.
On the other hand, Deligne, who was also 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, and he didn't even bother.
In addition to teaching students, professors at Princeton University also have basic class tasks, although many full professors leave them to their doctoral students or assistant professors to complete.
But you have to start classes anyway.
It doesn't make sense that classes aren't even open.