National Top Stream

Chapter 286 Manifold

The students began to discuss in a low voice, "Isn't it, Differential Manifold?"

"Oh my god, is Professor Zhuang crazy?"

"Help, topology is already difficult, why tell us this kind of content."

"Ah, it's dead, it's dead, I don't understand the Riemannian manifold at all!"

"Completeness is also difficult!"

"I don't want to live..."

Pierce was arranging things when he heard the voices of the students and said with a straight face, "Quiet."

As Zhuang Weiran's assistant, he is still very dignified.Usually he likes to laugh and laugh, but when the students ask questions, Pierce especially likes to reprimand the students.When everyone heard Pierce speak, they hurriedly lowered their heads, not daring to continue speaking.

"Okay." Zhuang Weiran said thoughtfully, "I know you don't have a special understanding of differential manifolds. Today I'm not going to talk about Riemannian manifolds, nor Lorentz manifolds and symplectic manifolds."

Turning around, he whispered, "When I was studying differential manifolds a few days ago, I discovered an interesting thing."

"Today, I guess many of you don't understand it. But it doesn't matter whether you understand it or not. It's not complete enough."

Director Zhou looked at Li Fei who was beside Wei Yaoyang and said, "What does this guy want? Isn't this an excellent class?"

"Who knows, he won't be a problem of wanting to make a manifold?"

"He wants to introduce a measure of rows to form a new manifold." Professor Langlands sat aside and said in a low voice, "I thought he was playing around these days, but I didn't expect that he would actually want to do something in this area effort."

"New manifold?" Director Zhou was dumbfounded, and Academician Zeng beside him pondered, "He has already solved Hodge's conjecture, and he is basically at the top level in topology, especially differential geometry. At this time It is not impossible to refine new metrics to form new manifolds."

"But he never talked about this before." Academician Zeng shook his head, "His mind is jumping."

"But isn't the subject he gave me non-linear partial differential equations? If he can really make new manifolds, then in the field of differential geometry, new classifications will inevitably be derived."

"Let's take a look." Academician Zeng changed into a comfortable position, "Anyway, I'm already used to him beating the hearts of us old people."

Professor Lin chuckled beside him and said, "Academician Zeng dare not compete with Academician Zhuang?"

"If Professor Lin is interested, how about comparing with Academician Zhuang in the field of mathematics or theoretical physics? How about topological quantum field theory?" Academician Zeng said with a smile, "I think Professor Lin is very good at this."

"I'll forget it." Professor Lin shook his head and said, "Anyway, after Director Zhou retires, this position must belong to Academician Zhuang. I'd better sing some folk songs on some hill."

"Professor Lin seems to be very resentful." Li Fei said abruptly from the side, "I remember that Professor Lin hasn't contributed to a journal in the first district for a long time, right?"

"Of course I can't compare to Academician Zhuang's brother. The name of Academician Zhuang is on the corresponding author, and I can submit to any journal I want to submit to."

"Enough." Director Zhou said in a low voice, "Professor Lin, is it interesting to be eccentric every day?"

"It's not interesting." Professor Lin said with a smile, "Academician Zhuang is the treasure of our Dragon City University. I can't make it with a lemon? Isn't it?"

"Jumping up and down every day." Academician Zeng said with a cold snort, "Doing academics well is much better than being a monkey here and being played by others."

"No way, I can't reach the height of our pope of mathematics." Professor Lin seemed to be breaking a can, "Differential manifolds!"

"Forget it, Professor Lin, let's not say a few words. You also know that he is the Pope of Mathematics, and he is respected not only at home, but also abroad. He came all the way to my grandfather's school, and even Princeton The chair professor has also resigned. Don’t worry, it’s nothing for us to be suppressed. Anyway, there are many people who are suppressed, and we are not bad.”

"Several, it's almost enough." Someone next to him said with a sneer, "Why don't you go and get a Fields Medal too? Oh, I forgot, you are all over the age."

"Hmph." Professor Lin snorted softly, "I want to see what our academician Zhuang will do to make it popular."

Wei Hongzhi frowned slightly listening to these professors who were either helping to speak, or having yin and yang voices. It seems that this daughter-in-law is really an important person in Longcheng University.Just standing on the stage, before he even started to speak, he has already aroused so many people's discussions.Then he shook his head again, and it is mediocrity that is not envied by others. It seems that this daughter-in-law must be very powerful, otherwise it would be impossible for so many people to envy him.

Zhuang Weiran didn't know that the professors below were talking about him, so he took a pen and began to write on the blackboard, "I'll start now, whether you can understand it depends on your luck."

【…

Suppose it is an n-dimensional topological manifold, assuming that a={(uα, φα):α∈i} is a set of coordinate cards and satisfies the following conditions:

(1) {uα:α∈i} constitutes an open cover of the manifold

(2) Any two coordinate cards belonging to a are related to cr

(3) a is maximal in cr, that is: if (u, φ) is a coordinate card of , and (u, φ) is related to each member of a in cr, then (u, φ) must belongs to a.

At this time, we call the coordinate card set a a cr differential structure on the manifold, (, a) is a differential manifold When r=∞, a is called a smooth structure on the manifold, (, a) is a smooth manifold When r=w, a is called an analytic structure above, and (, a) is an analytic manifold.

……

Consider a system composed of two particles 1 and 2, the distance between particle 1 and fixed point o is r1, and the distance between particle 1 and 2 is r2.This is a free pendulum composed of two thin rods connecting a fixed point and two mass points. The mass of the rods is ignored.

……1】

After Zhuang Weiran finished writing, the bell rang for the end of get out of class.

Professor Langlands stood up, "Zhuang, I still don't quite understand. Can you elaborate on the completeness issue?"

The students were so confused, their heads were about to explode.

"Of course." Zhuang Weiran nodded slightly, turned around and continued writing.

【…

xλ can also take other functions of u1,...,u3n, as long as the jabi determinant is not zero.

The above two equations establish a one-to-one correspondence between c-space and x-space over the region in question.

……2】

"Does Professor Langlands understand now?"

"It's very clear." Professor Langlands said with a smile, "But there is still a certain amount of time before a manifold is formed. I hope you can complete the last part as soon as possible."

"No problem, maybe Professor Langlands will be able to see it on arxiv next week."

"If everyone has no questions, then let's dismiss the get out of class." After Zhuang Weiran finished speaking, he hadn't left yet, and the students didn't dare to leave.

It was not until Zhuang Weiran and the professors left that the group of students dared to leave the classroom.

"Dad." Wei Yaoyang walked on the campus road, "How about we go and see Professor Zhuang?"

"Will it bother him?"

"Probably not." Wei Yaoyang smiled, he didn't see Professor Zhuang for a while, and he began to miss Professor Zhuang again.

"I said Yaoyang, you are a great daughter-in-law. So many professors are talking about him."

Wei Yaoyang said with a smile, "Dad, Professor Zhuang...that's what he is."

"Very good, why did I fall in love with you, a fool." Wei Hongzhi is not blind, Wei Yaoyang would only smile foolishly when he saw Zhuang Weiran, such a good person, and Wei Yaoyang.It was also Wei Yaoyang who saved the Milky Way in his previous life.

When they came to Zhuang Weiran's office, Professor Langlands was discussing things with Zhuang Weiran in English, and Pierce was serving tea by the side.

When Liang Ming saw Wei Yaoyang, he hurried forward and said softly, "Officer Wei, sit down first. The professor and Professor Langlands are talking about something."

"En." Wei Yaoyang nodded slightly, sitting on the sofa with Wei Hongzhi without disturbing Zhuang Weiran, Pierce raised his head to see Wei Yaoyang, and nodded slightly at him.

Wei Yaoyang introduced, "This is Professor Zhuang's graduate student Liang Ming, and this is Professor Zhuang's doctoral student Pierce, who is from England."

"This is Professor Zhuang's younger brother, Qian Mingzhang who came here from UCAS for an academic exchange."

"Professor Langlands." Liang Ming said with a smile, "Professor Zhuang hired him from the Princeton Institute for Advanced Study."

"The Zhuang-Langlands program was formed by Professor Zhuang's extension of the topological reciprocal conjecture from the Langlands program." Liang Ming said while pouring water, "Uncle Wei, Officer Wei, please drink tea first."

Qian Mingzhang turned his head and saw Liang Ming was busy.Hastily got up and said in a low voice, "Uncle Wei, do you want to eat something?"

"No, no, I'm just walking around, come in and sit for a while." Looking at the enthusiasm of these students towards him, Wei Hongzhi was still not used to it.

"Do things by yourselves, I'll just sit with Yaoyang for a while."

Liang Ming and Qian Mingzhang did not speak, and sat down to continue talking about the subject.

It wasn't until almost five o'clock in the afternoon that Professor Langlands left with a lot of satisfaction.

Zhuang Weiran sent Professor Langlands out, turned to Pierce and said, "Dr. Pierce, how is your project going?"

Pierce looked at Wei Yaoyang for help, "Professor, I still have a problem that I haven't understood... But, I think I can understand it."

"Really?" Zhuang Weiran outlined a smile, "Dr. Pierce, I don't want you to delay your graduation either."

"It will definitely not be delayed." Pierce blinked at Wei Yaoyang, and Wei Yaoyang was really helpless.

"Professor, should I do the subject first?"

"Dr. Pierce, if your eyes are uncomfortable, you can go to the hospital for examination."

"No, no, no!" Pierce hurriedly sat down, wanting to do the question.

"Okay, you guys go back today first."

Zhuang Weiran said with a smile, "It's almost time, you should go back and have a rest and eat. In the evening, you can go to the library to look at the documents and materials, or if there is something you don't understand later, contact me by phone or email send to me."

Liang Ming started to pack his things. Pierce did not dare to be too slow, so he did it slowly.

When Qian Mingzhang left, he said to Zhuang Weiran, "Brother, I'm leaving first."

"Professor, I'm leaving too." Liang Ming nodded slightly.

Zhuang Weiran folded his arms in front of his chest, leaned against the door and looked at Pierce who kept talking, but didn't speak.

Just smiling like that, Wei Yaoyang couldn't help coughing slightly.

"Cough cough!"