The top student must be diligent

Today's class is number theory.

When they came to the classroom, there were already many people sitting inside.

And Xiao Yi's appearance once again attracted the attention of the students.

After greeting each other with these classmates, Xiao Yi also found a place to sit down with his roommates.

"Brother Xiao, I feel like you are like a star every time you come to class."

Ye Cheng paid attention to the looks from around him and whispered to Xiao Yi.

Xiao Yi rolled his eyes: "You think I want it."

That's why he doesn't go to class much.

Ye Cheng chuckled, and then without saying much, he took out his laptop from his schoolbag and said to Xiao Yi: "Brother Xiao, come and help me analyze the problems I am encountering now."

They turned on the computer, entered the document, and started reading.

Song Ziyang and Luo Qiao, who were standing next to him, also came over to take a look. Good guy, this guy's paper has already been written for more than ten pages.

It’s so hidden.

The two of them looked at each other in silence for a while, then finally took out the book and started studying.

They also have to write papers!

…

After Ye Cheng took out his computer, he began to talk about his problem. After going through it, Xiao Yi quickly figured it out.

His thesis was on a problem in the field of algebraic geometry, which somewhat surprised Xiao Yi. He didn't expect that this kid would actually start studying algebraic geometry.

Perhaps it has something to do with the Schulz edition of "Principles of Algebraic Geometry" he brought back from Germany.

As for the topic selection of the paper, it mainly involves layers and layer varieties on algebraic varieties, and discusses their applications in algebraic geometry.

"To put it more generally, your problem is how to calculate the homology group of the layer cluster above an algebraic variety in the projective space." Xiao Yi concluded.

Ye Cheng nodded: "Yes, I always feel that I have a little trouble in this aspect."

Xiao Yi smiled and said: "After all, you are a beginner, so it is normal to find trouble."

"As for the problem you encountered, I won't give you a detailed explanation. You can solve it yourself later."

"I'll give you an example."

"Suppose we study the layer-cluster homology group H^i(X, OX(d)) of a straight beam OX(d) on an algebraic variety X on the projective plane P^2, where OX(d) represents a Twist the wire harness, d is the degree of twist.”

"In order to calculate the layer cluster homology group H^i(X, OX(d)), we can use the layer cluster homology theory on the projective space."

"Bott's norm theorem, and Searle's theorem."

"Do you know these two theorems?"

Hearing Xiao Yi's question, Ye Cheng nodded: "Yes! There is Searle's theorem in EGA, and I learned Bott's norm theorem from another book."

"That's good." Xiao Yi raised his eyebrows and said, "Then we will go directly to the specific calculations."

"First on the projective plane P^2, we consider X=P^2 and calculate the homology group of O(d). According to Bott's norm theorem, for d greater than 2, we have..."

[H^i(P^2, O(d))=0, i\u003e0]

"This result tells us that for sufficiently large d, only H0 may be non-zero."

"After that, we continue to introduce..."

As Xiao Yi told it, Ye Cheng kept nodding his head to show that he understood.

Until the end, he said happily: "That's it! I understand!"

Xiao Yi smiled and nodded: "That's good. The main thing is to expand your knowledge as much as possible."

"In addition, after using Bott's norm theorem, you can also use the Riemann-Roch theorem to deal with the straight line bundle above P^2."

"Riemann-Roch theorem?" After Ye Cheng thought for a while, his eyes suddenly lit up again: "I understand!"

"Hmm." Xiao Yi asked again at this time: "How many times have you read that EGA?"

Ye Cheng said with a little embarrassment: "I've finished reading it. I've started to read it for the third time now, but there are still many things in it that I don't understand at all."

"Just take your time and watch, don't be in a hurry." Xiao Yi said, "After all, it is EGA."

Looking at Ye Cheng, Xiao Yi couldn't help but recall the first time he met him. At that time, Ye Cheng said that his goal was the Fields Medal.

Obviously, he is constantly working hard in that direction.

However, Song Ziyang and Luo Qiao next to them couldn't sit still at this time: "What the hell? You guys have already started watching it for the third time?"

Xiao Yi also gave them both a copy at the beginning, but they didn't even finish reading it for the first time. This kid...

Just when they were about to get ready to punish the child who secretly took exams, they saw the substitute professor of this class walk in.

"I'll take care of you when I get back."

Two people: Husky pointing at people.jpg

…

The substitute professor of their number theory class was named Wang Bolin. After entering the classroom, he glanced at it and then saw Xiao Yi.

He then laughed: "Yo! I didn't expect that my class actually attracted a big shot."

Of course everyone knew who Professor Wang was talking about, and they all laughed.

"If we talk about the scholars with the most outstanding achievements in number theory in today's mathematics world, the big guy who came to our class today can definitely be included among them."

"I wouldn't dare to let a little professor like me lecture in front of him."

Professor Wang said: "Well... so I have a suggestion. Why don't we let him give a lecture to everyone? What do you think?"

The many students below were immediately happy: "Great!"

Let Xiao Shen give them a lecture?

There is such a good thing?

Everyone looked at Xiao Yi: "Xiao Shen, go!"

Ye Cheng and others beside him were even more gloating.

Song Ziyang: "Brother Xiao, you just gave Cheng'er such a good lecture, why don't you give it to the brothers too!"

Looking at this scene, Xiao Yi's mouth twitched.

Fuck.

This is the legendary flipped classroom, right?

But other people's flipped classrooms are for all students in the class, but his flipped classroom is only for him, right?

Professor Wang, who was standing on the podium, looked at Xiao Yi with a smile and said, "Go! You see everyone is so enthusiastic, it's hard to refuse such a kind invitation! Today I just happen to be a student, listening to Teacher Xiao's teachings, you can say whatever you want."

Xiao Yi sighed helplessly. He came here to experience life, but how did he become the one being experienced?

Okay, just talk!

He stood up, left his seat, and walked up to the podium.

Professor Wang sat directly on his seat.

Ye Cheng and the others beside him immediately sweated profusely, and sat up straight, not daring to move.

Xiao Yi, who walked to the podium, was happy to see this scene, but then it was his turn to be entangled.

What should I talk about?

He had never come to class before, so he didn't know where their course progress was.

However, Professor Wang also said that he could talk about whatever he wanted.

Hmm...

His eyes lit up and he had an idea.

Since it was a number theory class, why not talk about the Goldbach conjecture directly?

It just so happened that he was only a few steps away from solving the Goldbach conjecture, and the rest was to organize the paper, so he could use this class to sort out some of the previous parts.

Hmm.

It was just right for his classmates to get in touch with these cutting-edge mathematical knowledge.

Of course, in order to avoid the students not understanding at the beginning and scaring them, it would be better to start with the most basic.

The corners of his mouth curled up.

As his roommates, Ye Cheng and the other two suddenly felt that their lives were in danger.

Xiao Yi said, "Then, I will start with a very basic method in number theory."

He wrote the words [Sieve Method] on the blackboard.

The students below suddenly brightened up.

They knew how great Xiao Yi's achievements in the sieve method were. After all, it was an achievement that could change the world's cryptography system.

Even Professor Wang became very interested and began to focus his attention.