Omnipotent Data

Chapter 414

"That's all I want to say. The derivation process is here. You can understand it after reading it a few times at your level. I'm too lazy to say it a few times." Cheng Nuo stretched out and stood up from his seat. Chali, I will withdraw first, and when you encounter this kind of thing in the future, you can just post the question directly. You are still quite far away from the experimental building."

He raised his wrist to check the time, and pointed out the door, "It's too early. If there is nothing else, I will leave."

"That... wait!" When Cheng Nuo walked a few steps towards the door, Milo, whose face changed, called Cheng Nuo aloud.

"I'm sorry! I shouldn't question your strength just now." Milo bent over to apologize to Cheng Nuo.

Cheng Nuo waved his hand indifferently, "Ann, An, I'm used to it, and I don't mean to hate you!"

"Believe it or not, but I really didn't take this matter to heart." Cheng Nuo turned around and waved his back to everyone, "Go!"

A day of leisure time, Cheng Nuo can not be so wanton waste.

…………

The next day.

Carrying a bag, Cheng Nuo came to a coffee shop on the Massachusetts Institute of Technology, ordered a cup of coffee, and drank leisurely while starting today's work.

According to the schedule of the subject, today is the first formal meeting of the subject group on geometric homology.

Although the level of the research group is very high this time, it is composed of a full professor, two associate professors and a graduate student, but the main content of the discussion is nothing more than the overall framework of the research, plus the specific division of research tasks.

Putting on the headset, Cheng Nuo and the three Princeton professors started talking.

Cheng Nuo: "Hello, can you hear me clearly?"

Miller: "Hahaha, Tom, your voice sounds very young!"

Cheng Nuo did not answer, and asked, "Is the team leader here?"

Hatch: "Wait a minute, the boss is answering the phone, I'll be fine soon."

After dozens of seconds...

Byrne: "Tom, sorry for the long wait. Now that everyone is here, we won't chat, let's go straight to the topic!"

Miller: "OK!"

Hatch: "OK!"

Cheng Nuo: "OK."

After the atmosphere was silent for a few seconds, there was a few soft coughs, and then Professor Byrne's voice sounded, "We all know that the proposal of Cheng Nuo's theorem directly connects the algebraic clusters and complex algebraic clusters in geometry deeply. At the same time, the homology method that only exists in topological space can also be applied to clusters and general shapes."

"I have to say that the proposal of Cheng Nuo's theorem has had a great impact on our geometric world. There is also the young man named Cheng Nuo, even I am impressed. If it is possible, I really want to Go and ask him for advice."

Cheng Nuo could not help blushing when he heard Berne's praise of Cheng Nuo in the earphones.

Am I... so good?

Fortunately, Professor Byrne quickly ended this meaningless flattery, and continued to solemnly said, "The purpose of this project is to derive the homology theorem that is applicable to algebraic families based on the combination of Cheng Nuo theorem. Then through the homology theorem..."

Professor Byrne’s speech seems to resemble a Chinese-style leader. It is clearly a few words, concise and concise, and Professor Byrne added it for nearly half an hour.

Fortunately, this is a voice conference, and Cheng Nuo can be distracted. As for Miller and Hatch, who are now in front of Professor Byrne, I'm afraid they are uncomfortable.

"I'll talk about this first. Next, let's express our own views, let's put together the overall framework of this topic." Professor Byrne finally ended his chatter.

The atmosphere fell silent again.

Professor Miller broke the awkward atmosphere, "Tom, would you like to say something?"

"Ah, me?" Cheng Nuo was taken aback. He thought it was Miller who was going to talk first? For a long time I wanted him to say.

He rationalized his thoughts in his mind, "Then I will talk about my views."

"We all know that homology is a positive variable functor in the category of topological space, which means that it does not change the direction of the arrow. At the same time, it satisfies a series of axioms included. It has descending operations on a chain complex, such as Say boundary operation: dn:Cn→Cn-1. After performing two boundary operations, you will get 0: dn-1*dn:Cn→Cn-2=0."

"... Let X be a d-dimensional smooth projective cluster on Fq, and the convention = X-Fq. On projective cluster X, we can define Fx, F^2x, F^3x,... Fq^n point on projective cluster X The set X (Fq^n) happens to be the set of fixed points of automorphism F^nx: X→χ!"

"Then how to calculate the number of fixed point sets on the projective cluster?" Professor Miller couldn't help asking before Cheng Nuo finished.

Cheng Nuo smiled and slowly said: "Lefshetz's fixed point theorem!"

Miller: "Lefshetz fixed point theorem?"

Cheng Nuo emphasized, "Yes, it is Lefshetz's fixed point theorem!"

"Suppose X is a compact differential real manifold, f:X→X is a differential mapping, a fixed point of f refers to a point xinX such that f(x)=x. For a fixed point x of X, the differential df_{x} is a linear transformation of the tangent space T_{x}X. It is said that a fixed point x is non-degenerate, if 1-df(x) is reversible. This condition is that the fixed point has a multiplicity 1'!"

Cheng Nuo said these words almost without thinking.

"That's right, I really didn't react for a while just now!" Miller's sudden voice came from over there.

Professor Byrne also went on to say, "My point of entry is similar to Mr. Tom's view. Using the basic properties of homology groups in topology, by constructing a smooth algebraic projective cluster, using fixed point sets for entry."

Then, Professor Byrne gave his thoughts to the three of Cheng Nuo.

Same but little difference.

Except for some specific details that are unclear between the good and the bad, the general content is the same.

Professor Miller is mainly engaged in topology. Although his understanding of geometric content is not as good as the other three, he is a well-known young mathematician in the field of topology and naturally has a deep understanding of the homology group of topology~www. readwn.com~ But even he, after Nuo's explanation, has no flaws in this plan.

Professor Hatch has no objection.

Byrne immediately made the decision, "In that case, follow Tom and I. As for the different details, it will be easier to see whose scheme is simpler, and whoever chooses it will do."

The entry point is finalized, and the rest is simple.

Although it is impossible to propose specific measures for some things before the results are actually calculated, building a frame that only contains bones does not require such precise things.

In the morning, after Cheng Nuo drank three cups of coffee, the framework was finally built and the tasks were assigned.

In the eyes of Miller and Byrne, Cheng Nuo is naturally regarded as a mathematician of the same level as them, so he did not take any advantage when assigning tasks.

Looking at the items in his task list, Cheng Nuo moved his fingers.