Scholar’s Advanced Technological System

“Auntie!”

Zhongshan International’s villa, sitting in his study room, is holding a pen at the desk and writing something Lu Zhou, sneezing without warning.

“Who is thinking about me…”

Sucking his nose and whispering to himself, Lu Zhou continued to look at the draft paper in front of him, and the ballpoint pen on his hand was lightly lit on the table.

“It’s a bit difficult.”

[…when n is greater than 2, the two n-dimensional complexes completely intersect X^n(d), and X^n(d’) differentiates the homeomorphism if and only if their Euler number, full number of times, and Pontrjagin class are equal. 】

Strictly speaking, this is not a complex analysis problem, nor a traditional partial differential equation problem, but a very interesting classification problem for smooth manifolds.

This statement may be a bit sloppy, but in fact, in differential topology, this is a fairly popular research direction, mainly studying the invariant nature of differential manifolds under differential homeomorphic mapping.

However, it is somewhat troublesome. Although Lu Zhou has studied differential manifolds and topology, there are not many researches on the differential topology.

It can even be said that this is a completely new field for him.

However, there is nothing wrong with this situation. After all, the Chen Yang Professor studied the Hodge conjecture, and his research on GFB Riemann’s Conjecture was originally two very different problems.

Just because the hyperelliptic curve analysis method can be improved and applied to the Cauchy-Riemann equation and the Riemann surface promotion surface, it led to his Lenovo on this issue…

“I am really embarrassed, I am a fat tiger… Do you want to leave it alone?”

After thinking for a while, Lu Zhou shook his head and eventually drove this disappointing thought out of the brain.

And if you don’t talk about it, you will get the result first. Even if you don’t install it, it is not his style to give up in the face of difficulties.

Even though differential topology is not his research direction, with his understanding of differential manifolds and topological theory, there is no big problem in quickly becoming familiar with the research points in this field.

What’s more, just now GFB Riemann’s Conjecture’s research has also fallen into bottleneck. Instead of dying on a path that doesn’t work, try to look up and see if there are no other interesting clues.

If you can bridge the gap between topology problems and complex analysis problems, you can’t say that his hyperelliptic curve analysis can make a wonderful effect on the research of Riemann’s zetafunction…

“Xiao AI, help me make a cup of coffee, no sugar!”

Xiao AI : [Master, instant coffee does not need to add sugar? (°`°〃)

“…there is a skeleton skirt!

[Good, good master! (???*)]

The drone floated from the shelf and flew outside the study.

Aside from the distracting thoughts in mind, Lu Zhou focused all of his attention on this draft paper in front of him.

The thumb topped the button cover and he wrote the first line of text on the paper with a pen.

Let f1, …, fr be a homogeneous polynomial of the complex coefficients of the variables z0, …, zn+r. This set of polynomials defines a complex algebraic cluster X in the complex projective space CP^(n+r)…

[X is called a complex complete intersection. If the complex dimension of X is n, when X is a smooth manifold, it is called smooth complex complete intersection. At this time, X is a smooth closed manifold of 2n dimension… 】

First Step has been fixed.

Lu Zhou’s eyes shimmered with excited rays of light.

Although this feeling is very weak, he has a very obvious premonition, that is, he has found a correct way to the end of the maze.

“Using the smooth closed manifold of the 2n dimension as the entry point, the association is established on the complex projective space…”

Once you open a breakthrough mouth in your mind, the inspiration is like a flood, and you can’t stop it.

A line-like calculation like a note flows down like a rushing river in his pen, and soon a whole piece of draft paper has been filled with operators and numbers of densely packed.

Time passes by, and there are more and more manuscript papers piled up on the table.

Xiao AI, lying on the shelf, just sneaked aside. Since Lu Zhou banned it from randomly opening the camera, it was only available to the camera on the drone.

Although it seems a bit distressing to look at the owner’s hard work, but this kind of creative work, it really can’t help.

The sky outside the window gradually darkened.

Lu Zhou, who was at the table, had no movements other than calculations, except that he reached out to the table lamp at the corner of the table.

However, the situation does not seem to be moving towards a more optimistic direction.

As the sky outside the window gradually dim, not only the original smooth stroke gradually slowed down, one after another sweat gradually ooze out from Lu Zhou’s forehead.

The situation does not seem to be as optimistic as he imagined.

The more in-depth study of this problem, the more he discovered that the maze behind the problem was so complicated.

“Aaah… It’s so hard!”

I don’t know how many times I walked into the dead end, and finally I was unsettled. Lu Zhou was incarnation and violently elder brother. I would count the half of the draft paper that I couldn’t count on, and slammed into the paper basket next to it. in.

“Is not right! If the proposition is established, it will not be that I have thought about it for so long…”

The ballpoint pen in his hand turned faster and faster, and Lu Zhou, who was frowning, stared at the original question, and his lips opened and closed.

“But the strange thing is that it can’t prove that the proposition is wrong… no matter how many sets of parameters are taken in, you can get the result that matches the proposition.”

Put out a long breath, Lu Zhou pinched the pen that turned fast, opened the computer at the corner of the table, logged into the literature database, and entered a few lines of keywords.

Thesis retrieved in rows is quickly appearing in front of him.

After selecting a few tags and sorting by number of citations, Lu Zhou quickly picked out a few of the top ranked thesis.

“… such an interesting question cannot be studied without anyone.”

“At least you should be able to find something similar.”

The mouth was softly read, and at this time Lu Zhou’s eyes suddenly lit up, and a series of interesting titles were keenly captured from the database.

Thesis is written by Kreck Professor, a well-known big cow in the field of partial differential equations and topology, and this thesis is a thesis he published in the annual issue of “Magications” in 1999. A little high.

According to its summary section, the main content of this thesis is to improve the Surgery theory and to transform the problem of manifold classification into the computational problem of some matching groups.

There was a fascination in the eyes, and Lu Zhou quickly downloaded the thesis and looked along the body of thesis.

After about ten minutes, when he saw thesis carefully, the expression of interest in his eyes suddenly became excited.

“that’s it!”

“I said, such an interesting question must not have been studied before. At least someone must have studied a similar subject!”

“If you can convert the problem of manifold classification into the calculation of some matching group… Mom, this is the last piece of puzzle I lack!”

Excitedly stood up from the chair and walked to Lu Zhou next to the trash, and quickly pulled out the draft paper that had been smashed by him.

“Fortunately, it’s just a little wrinkled, not shredded!”

Self-talking, Lu Zhou took this draft paper and returned to the chair to sit down, flattening the draft paper in his hand on the table, and rekindling the raging fire.

“Get started!”

After all, the shua shua shua’s brushstrokes sounded again in the study.

This time, it continued until dawn until it stopped…