Omnipotent Data

Chapter 414

"That's all I want to say. The derivation process is here. You can understand after reading it a few times at your level. I don't bother to explain it a few more times." Cheng Nuo stretched himself and stood up from his seat, " Charlie, I'll withdraw first, and if you encounter this kind of thing in the future, just send the topic directly, you are still quite far from the experimental building."

He raised his wrist to check the time, pointed out the door, "It's getting late, if there's nothing else, I'll be leaving."

"Wait...wait!" When Cheng Nuo took a few steps towards the door, Mi Luo, whose expression was changing, called Cheng Nuo loudly.

"I'm sorry! I shouldn't have questioned your strength just now." Milo bowed down to Cheng Nuo to apologize.

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

"Believe it or not, I really didn't take this matter to heart." Cheng Nuo turned around and waved to everyone, "Let's go!"

Cheng Nuo couldn't afford to waste the leisure time of the day like this.

…………

the next day.

Cheng Nuo came to a cafe on the MIT campus with his bag on his back, ordered a cup of coffee, and drank it leisurely while starting today's work.

According to the schedule of the project, today is the first formal meeting of the group on geometric coherence.

Although the research team this time was of a high level, consisting of a full professor, two associate professors, and a graduate student, the main content of the discussion was nothing more than the overall framework of the research, plus the specific division of labor for research tasks and the like.

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

Cheng Nuo: "Hey, hey, can you hear me clearly?"

Miller: "Hahaha, Tom, you sound very young!"

Cheng Nuo didn't answer, but asked, "Is the team leader there?"

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

Tens of seconds later...

Bourne: "Tom, sorry for the long wait. Now that everyone is here,

Then let's stop chatting and go straight to the topic! "

Miller: "OK!"

Hatch: "OK!"

Cheng Nuo: "OK."

After a few seconds of silence, there were a few light coughs, and then Professor Byrne's voice sounded, "We all know that Cheng Nuo's theorem directly connects the algebraic varieties and complex algebraic varieties in geometry. At the same time, the homology method, which only exists in topological spaces, has the possibility of being applicable to clusters and schemes."

"I have to say that the proposal of Cheng Nuo's theorem has had a great impact on our geometric world. And that young man named Cheng Nuo, even I admire him a lot. If it is possible, I really want to Go and ask him a lesson."

Cheng Nuo couldn't help but blush when he heard Bourne's praise of Cheng Nuo through the earphones.

Am I... am I that powerful now?

Fortunately, Professor Byrne quickly ended this meaningless flattery, and continued to say solemnly, "The purpose of our project is to derive a homology theorem applicable to algebraic varieties on the basis of combining Cheng Nuo's theorem. And then by the homology theorem..."

Professor Byrne's way of speaking seems to be very similar to Huaguo's leadership. It is obviously a few words and concise things, which were added by Professor Byrne for nearly half an hour.

Fortunately, this was an audio conference, and Cheng Nuo was still distracted. As for Miller and Hatch, who are now in front of Professor Byrne, I am afraid it will be very uncomfortable.

"Let me talk about this first. Next, let's express our opinions. Let's put together the overall framework of this subject." Professor Byrne finally ended his rambling.

The atmosphere fell into silence again.

Professor Miller broke the awkward atmosphere, "Tom, why don't you say a few words?"

"Ah, me?" Cheng Nuo was taken aback for a moment. Did he just think it was Miller who wanted to speak first? For a long time I wanted him to talk.

He rationalized his thoughts in his mind, "Then let me tell you my point of view."

"As we all know, homology is a positive variable functor on the category of topological spaces, that is to say, it does not change the direction of the arrow. It also satisfies a series of axioms including. It has descending operations on a chain complex, such as Say the boundary operation: dn:Cn→Cn-1. After performing two boundary operations, you will get 0: dn-1*dn:Cn→Cn-2=0.”

"... Suppose X is a d-dimensional smooth projective variety on Fq, convention=X-Fq, on the projective variety X, we can define Fx, F^2x, F^3x,...Fq^n points on the projective variety X The set X(Fq^n) is exactly the set of fixed points of the automorphism F^nx:X→χ!"

"Then how do you calculate the number of fixed point sets on the projective cluster?" Professor Miller couldn't help asking before Cheng Nuo could finish speaking.

Cheng Nuo smiled and said slowly, "Lefshetz fixed point theorem!"

Miller: "Lefshetz fixed point theorem?"

Cheng Nuo emphasized his tone, "Yes, it's the Lefshetz fixed point theorem!"

"Let X be a compact differential real manifold, f:X→X is a differential map, a fixed point of f is 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. A fixed point x is said to be non-degenerate if 1-df(x) is reversible. This condition is to say that the fixed point has 'multiplicity 1'!"

Cheng Nuo said this almost without thinking.

"That's right, I really didn't realize it for a moment just now!" Miller's voice suddenly came from over there.

Professor Byrne then said, "My starting point is similar to Mr. Tom's. Using the basic properties of homology groups in topology, we construct a smooth algebraic projective group and use fixed point sets to cut in."

Then, Professor Byrne shared his thoughts with Cheng Nuo and the others.

Much the same.

Except for the difference between good and bad in some specific details, the general content is the same.

Professor Miller focuses on topology. Although his understanding of geometry is not as good as the other three, as a well-known young mathematician in the field of topology, he naturally has a deep understanding of homology groups in topology.

But even he, after Cheng Nuo's explanation, couldn't raise any flaws with this plan.

Professor Hatch has no objection either.

Bourne immediately made a decision, "In this case, let's follow the ones of me and Tom. As for the different details, it depends on whose plan is easier to calculate, and we can use whose plan."

Once the entry point is finalized, the rest is easy.

Although it is impossible to propose specific processing measures for some things without actually calculating the results, building a framework that only contains bones does not require such precise things.

It took a whole morning, and after Cheng Nuolian drank three cups of coffee, the framework was finally set up, and the tasks were assigned at the same time.

In the eyes of Miller and Byrne, Cheng Nuo was naturally regarded as a mathematician at the same level as them, so he didn't take advantage of the assignment.

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