Being approached by Peverman, Xu Chuan smiled a little embarrassedly, for more than a month, he had been obsessed with his own research and had forgotten about it.

After assuring Mr. Feverman that classes would begin this week, the head of the math department was relieved.

However, Xu Chuan's research in the past month or so has also aroused his curiosity.

The young professor, who looked a little like Peng Yuyan, asked curiously, "What have you been studying lately?" ”

Xu Chuan shook his head and said, "I didn't study anything, I was just reading some books on manifolds." ”

Peverman looked at him in surprise: "Manifolds? Which direction are you going to study? ”

Xu Chuan: "At the moment, it is a smooth manifold. ”

Hearing this, Feverman's eyes lit up: "What do you think about the problem that the cohomology on the bounded flat manifold is zero?" “

Xu Chuan thought for a while and said: "This question and Chen's conjecture, as we all know, the Euler number is a topological invariant of the manifold, and the flatness of the conjecture is a purely geometric concept, and the wonderful thing about this conjecture is that it connects these two very different mathematical concepts and reveals the deep connection between them......

"If the flat structure of the imitation flat manifold m is complete, that is, m is a quotient space of a discrete group of regular action (proper a) in the simulation space, then Chen's conjecture holds."

"From this point of view, if we want to study this aspect, we may start by defining the flat manifold as a manifold with an indefinite flat echo contact on the cut plexus (Torsio Affiffiffiion)."

Feverman thought for a moment, and said half-doubtedly: "Shoot the finite expansion of the free product of the flat structure and the music group on the amenable group?" ”

Xu Chuan thought for a while and said, "Start with the direction of the finite-dimensional Li group with a flat structure, and then turn it to ......."

In the office, Peverman, who had told Xu Chuan not to forget his position as a Princeton professor, fell into communication and thinking.

It wasn't until more than an hour had passed that the two of them couldn't get enough of it.

.......

Fefferman left satisfied, and Xu Chuan also gained a lot of ideas.

Sure enough, it is a pleasant thing to communicate with top mathematics professors, and the ideas and ideas that can be gained from one exchange are enough to think about for a long time, or even benefit for a lifetime.

Xu Chuan really wanted to sort out some thoughts and ideas now, but before that, he still had one more thing to do.

Then submit your course to Princeton.

It has been a month and a half and almost two months since the start of the Spring Festival, but his first class has not yet started.

If classes don't start again, Princeton University will probably feel like it's 600,000 meters inside Lake Carnegie.

After Xu Chuan submitted his course report to the school, Princeton immediately put it on the class schedule.

This news also caused a lot of discussion in the Princeton Department of Mathematics.

After all, many students had been expecting the young professor who had proved Hodge's conjecture to explain this.

But more than a month after the start of school, the young professor seems to have forgotten what this incident looks like.

.......

Time flies.

With the arrival of Wednesday, Xu Chuan's first class at Princeton has finally arrived.

In the first class, he hung up the curriculum on algebraic geometry.

As the hottest field of research in the history of mathematics at present, it can be said that almost everyone who studies mathematics has been exposed to this knowledge.

As the disciple of the Pope of Algebraic Geometry, although Xu Chuan is not only good at algebraic geometry, but in any case, the first lesson must be this.

When Xu Chuan walked into the school's classroom in a formal suit, he was a little taken aback.

In the lecture hall that can accommodate more than 300 people, there are no empty seats, and there are even two students squeezed into one position with each other.

The original corridor aisle was not vacant, there were no seats, and these students sat directly on the ground.

The crowded classrooms made Xu Chuan a little skeptical that there were so many math students in the Princeton math department.

In fact, he guessed correctly, it wasn't just Princeton's math department that came here, but also some of its students from New York and Philadelphia.

Some of these students came over on their own after being notified by their friends, and some were pulled over.

A mathematician's mathematician who proved Hodge's conjecture had a math class that appealed to students aspiring to go further in mathematics.

Not only the students, but also some Princeton professors, walked into the lecture hall and sat quietly in the corner waiting for the class to begin.

......

Although he was a little surprised by the number of people in the classroom, and he didn't think too much about his popularity in the mathematics world, Xu Chuan still walked onto the podium with a smile on his face.

】

There is no such thing as stage fright in him today, let alone a ladder classroom with three or four hundred people, or a math report meeting with thousands of people, he is at ease.

Walking up to the podium, Xu Chuan looked at the students in the audience, and his expectant eyes made him feel as if he had returned to the past.

Coming back from his thoughts, Xu Chuan adjusted the headset and spoke gently.

"Let me introduce myself, my name is Xu Chuan, I am from Huaguo, you can call me Professor or Professor Xu."

"Today is my first class at Princeton, and to be honest, I owe a debt of gratitude to Professor Feverman, who would have almost forgotten who I was if he hadn't reminded me."

Hearing this, the classroom erupted in laughter.

"Is it because you are too nervous to start a class as a professor for the first time?" A student asked jokingly in the audience.

Xu Chuan shrugged his shoulders and said, "That's not it, it's no more difficult to give you a lecture than to stand in the auditorium and explain the Hodge conjecture to those masters in the math world." ”

In the classroom in the United States, the relationship between students and teachers is more relaxed than in China, and it is not uncommon for students to ridicule and question teachers.

Regarding this student's ridicule, Xu Chuan didn't know whether he was intentional or unintentional, but he had to suppress this ridicule, otherwise it might not be easy to bring it to class in the future.

After all, he is so young, so young that the students here are basically older than him.

In this case, even if he is a professor, he will give students some unreliable or different thoughts.

And his answer is exactly that.

It means that you people are all scum, and it is easy to teach you lessons.

Hearing him say this, the student who asked the question seemed to notice that there was something wrong with his question, and some were embarrassed to touch their heads and stop talking.

"Professor, can you tell us how you proved Hodge's hypothesis?" In the classroom, a student asked curiously.

Xu Chuan smiled and said, "Of course you can." ”

"For this, I would like to thank a great mathematician who gave me the initial inspiration."

In English, he and she are two completely different pronunciations, and when they heard Xu Chuan say this, the students in the classroom suddenly became interested and raised their heads to look at the podium.

Xu Chuan continued: "In July last year, Professor Mirzahani, the first female Fields Medal winner in mathematics, left us forever. ”

"And the professor left me a manuscript paper before his death, and on that manuscript paper I saw some of her thoughts on the fields of the 'Weyl-Berry conjecture' and the 'unreducible decomposition of differential algebraic clusters' that I had previously demonstrated."

"On this basis, I refined her idea and solved the problem of 'unreducible decomposition of differential algebraic clusters'."

"Based on this, I extended it again, and finally created the 'Algebraic Cluster and Group Mapping' tool, which finally solved the Hodge conjecture."

"So I'm grateful to Professor Mirzahani, and if it weren't for her, maybe I would never have gone down the path of studying the Hodge conjecture."

After the words fell, some students sensitively noticed some of the details.

"Professor, you said you only received Professor Mirzahani's posthumous manuscript in July last year, and then you started to turn to the study of the Hodge conjecture, right?"

Xu Chuan nodded: "That's true, is there any problem?" ”

Hearing this, everyone in the lecture hall couldn't help but swallow their saliva.

Is there anything wrong with what it means?

That's a big problem, okay!

From July to November, when the Hodge conjecture was published, there was only a five-month gap.

Five months, proving Hodge's conjecture, what the hell is this?

For a moment, there was a rooster silence in the huge lecture hall, and then there was a cacophony of exclamations and noises.

"How is this possible!"

"Five months to prove the Hodge conjecture, it's definitely a joke."

"God can't do it when he comes."

“........”

More than 400 people would rather believe that Xu Chuan was joking with them than believe that it was true.

The two years that everyone speculated about to solve the Hodge conjecture was already terrifying, after all, it took Wiles eight years to prove Fermat's theorem, and Pelleman to prove the Poincarai conjecture seven years.

Two years is too short a time in comparison.

And now, this has been shortened to five months, and no one can believe that it is true.

They prefer to believe that this is just a joke made by Xu Chuan, and it actually took two years to prove Hodge's conjecture.

On the podium, Xu Chuan didn't care about his words, and five months proved that Hodge's conjecture was too outrageous, and no one believed him when he said it, and everyone would just take it as a class fun.

But he followed this path and turned the conversation to today's class.

"Although the time to prove Hodge's conjecture is short, but before that, I laid the foundation for more than ten years, and high-rise buildings are not built in a day, only by laying a good foundation, can we pave the way step by step."

"And today's lesson is the part of knocking the foundation......."

The professor who had been a professor for more than ten years in his previous life was not in vain, and his abundant energy allowed him to smoothly turn the topic into a formal class and start lecturing.

During the ninety minutes of class time, not a single person left early.

Only a few people couldn't make a few trips to the toilet while listening to the lecture, but they came back quickly.

The lecture on the first day was very smooth, and Xu Chuan's speed of flipping through the book and turning the ppt was also very fast, and he directly turned over nearly half of a 100-page algebraic geometry textbook.

Of course, this also has something to do with the students for whom today's class is facing.

This kind of big course is very miscellaneous for students, undergraduates and graduate students can listen to it, and in order to make most people understand, the knowledge explained must not be very advanced.

Truly top-notch knowledge can only be learned in small lessons and with a mentor.

However, this kind of big class is not without merit, in the big class, some of the ideas and ideas taught in the lecture are more critical and important things than those advanced knowledge.

Knowledge can be learned, but ideas and ideas can only come from creation.

In mathematics, listening to a top expert's understanding of a basic area can be of great help to students.

Sometimes, a word from these big bulls can bring great gains and give them a deeper level of understanding.

As for the basic knowledge in the textbook, it may be useful for undergraduates, but for graduate and doctoral students, those have already been learned.

However, sometimes, different professors will bring different insights when they explain the same knowledge point.

This depends on the professor's own knowledge reserve, teaching ability, and teaching experience.

Most of the students who came to the class today didn't really have much hope in this regard.

Even if the lecturer is a top expert who proves Hodge's conjecture, he is the first time to start the course, and the teaching experience is almost zero.

But what is surprising and no one expected is that this extremely young professor seems to have more than ten years of experience in teaching.

In simple terms, he can make you understand complex questions and ideas in simple language, which is especially valuable for a professor.

How to let students understand and absorb knowledge and understand problems in the fastest way, good tutors and professors and poor tutors are often different here.

And this young professor, even for the first time, did just that.

To the amazement of the students in the classroom and some of the math professors.

......

Ninety minutes passed, Xu Chuan did not delay the class, ended the class on time, and then left three questions as homework.

Princeton's big classes can be homeworked, and of course, they can be left unattended.

This depends on the will of the lecturer professor.

As for whether to do it or not, it also depends on the student's own wishes, and the professor will not check it anyway.

"A wonderful lecture, I was worried about whether you would be nervous or something, but now it seems that I have thought too much, and in terms of teaching, you are far better than I imagined."

As class ended, Peverman, the head of Princeton's mathematics department, walked out of the corner of the lecture hall and stood in front of Xu Chuan and congratulated him with a smile.

He listened to the ninety-minute lecture in its entirety, and although the basics didn't do much to him, he saw the young professor and friend's ability to teach.

Princeton's annual salary of 600,000 meters of gold is undoubtedly worth it.

Xu Chuan smiled and said, "Thank you." ”

After complimenting him, the head of the mathematics department did not leave, but continued: "After communicating with you last time, I have some new ideas for the smooth pop part, I don't know if you have time recently, I want to communicate with you again." ”

Xu Chuan quickly said: "I am very happy." ”

......