universal data

Chapter 411 Voice Conference
414 chapter

"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 standard, consisting of one full professor, two associate professors and one graduate student, the main content discussed was nothing more than the overall framework of the research, plus the specific division of labor in the research tasks.

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 and asked, "Is the team leader here?"

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

Tens of seconds later...

Bourne: "Tom, I'm sorry for waiting. Now that everyone is here, let's stop chatting and get straight to the point!"

Miller: "OK!"

Hatch: "OK!"

Cheng Nuo: "OK."

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

"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 seemed to be very similar to that of Chinese leadership. It was obviously just a few words, concise and concise, but Professor Byrne continued to talk for nearly half an hour with added additions.

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 stunned for a moment. Did he think Miller was going to say it 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."

"We all know that homology is a positive variable functor on the category of topological space, that is to say, it does not change the direction of the arrow. It also satisfies a series of axioms including excision lemma. It has descending operations on a chain complex , for example, 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 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, "Lefschetz fixed point theorem!"

Miller: "Lefschetz's fixed point theorem?"

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

"Let X be a compact differential real manifold, f:X→ X be a differential map, a fixed point of f is a point x\in X such that f(x)=x . For a fixed point of X 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 means 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 specializes in topology. Although his understanding of geometric content 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 the homology groups of topology.

But even he, after Nuo's explanation, could not find any flaws in this plan.

Professor Hatch has no objection either.

Bourne immediately made the decision, "In that case, let's follow what Tom and I have said. As for the different details, it will depend on whose plan the calculation process is simpler, and whose plan will be used."

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.

In the eyes of Miller and Byrne, Cheng Nuo was 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.

(End of this chapter)