Great Country Academician

In the dormitory, Xu Chuan was immersed in the derivation and construction of a new tool.

In the manuscript paper left to him by Professor Mirzakhani, some ideas for the field of "irreducible decomposition of differential algebraic varieties" were indeed proposed.

But it's just an idea, and even this idea is not so perfect.

At least, in Xu Chuan's eyes, there are still many loopholes in these basic ideas. What he is doing now is to further expand on the basis of Professor Mirzakhani.

".Based on this, a mapping φ:W——G, C'→γC can be obtained."

"Let W be the set of conjugate classes of ellipses (consisting of elements in the reflected representation of W that have no eigenvalue 1). The following are some properties of φ.

(b) φ is surjective;

(c) φ| Wel: Wel — → G is internally mapped.

(d) If C ∈ Wel and w ∈ Cmin, then φ(C) is the only idempotent class γ of G such that γ∩ Gw is the conjugation of B on Gw

(e) If C ∈ W — Wel, then φ(C) has a simple description similar to φ for the Levi subgroup of the proper parabolic subgroup of g.

Following the train of thought of Professor Mirzakhani, Xu Chuan tinkered all the way and reintroduced Bruhat decomposition and Weyl group.

On this basis, go further to the field theory.

After a long time, Xu Chuan finally stopped his work, turned on the computer, and began to search for relevant information.

Mathematics is a huge subject. Now that it is the 21st century, there are not to mention hundreds, if not dozens, of fields derived from basic mathematics.

It is impossible to read all the knowledge in these fields and memorize it by heart. It is impossible for human beings to complete such a task, and it is impossible to do it in a lifetime. Unless, like in the novel, it is directly opened and hung up, the system will directly feed it into the brain.

But unfortunately, although he was reborn, he didn't have the so-called system.

Although the memory is not weak, he still needs to learn and search for all the new knowledge and things that need to be used bit by bit.

Especially when entering a frontier field that no one has ever entered, the knowledge and literature needed are even greater.

In Deligne's office at the Institute for Advanced Study in Princeton, Edward Witten opened the door and walked in.

"Huh? Is Xu Chuan not with you?"

Seeing that Deligne was the only one in the empty office, Witten asked in surprise.

At this point, his student should study in Deligne's office as usual.

Deligne raised his head, glanced at Witten, and said calmly: "He took a leave of absence and hasn't come to study for a while."

Hearing this, Wei Teng asked: "Where did you go to receive the award? When will you be back?"

It's no wonder he asked that question, after all, in his memory, the student's leave was basically to go out to receive the award.

"That's not true. He is still in Princeton. His leave seems to have something to do with Professor Mirzakhani who passed away some time ago. I heard from Xu Chuan that Professor Mirzakhani left a manuscript for him. He should be sorting out the manuscript. As for what?" When you can come back in time, you have to call him and ask him."

As he said that, Deligne looked at the calendar and added: "But it's been a long time since he asked for leave this time. If I remember correctly, he seems to have asked for leave last month. It's been more than a month. .”

"Let me call and ask. I have something to ask him."

Wei Teng shrugged, took out his cell phone from his pocket, found Xu Chuan's phone and dialed it, but after a short wait, he put down the cell phone again.

"What's wrong?" Deligne asked casually.

"Maybe something is going on, I got through, but it was hung up soon."

Wei Teng put the phone back into his pocket and did not call again. He knew that Xu Chuan would not be able to hang up his call unless there was something urgent.

"Then wait a little longer. If he sees it, he should call you. Do you want a cup of coffee?" Deligne stood up and made a cup of coffee for Witten.

For Xu Chuan, both he and Wei Teng are at ease, even if the student extended the vacation from one week to one month, he didn't bother much.

In the dormitory, Xu Chuan yawned and got up from the bed.

Get up, wash up, with a bag of yogurt in his mouth and a piece of bread in his hand, he walked towards the desk while eating.

After a few mouthfuls of breakfast in his hands, Xu Chuan quickly passed the manuscript paper on the desk, then picked up the ballpoint pen on the side and sank into it.

Not long after, a piece of white manuscript paper was half-written, and the black handwriting on it spread out, gradually covering the entire white paper.

But then, the ballpoint pen that was writing stopped, as if he was dissatisfied with it, and also seemed to have a new discovery. In short, a hand with strong bones directly took a brand new manuscript paper from the side, and began to write again. stand up.

The manuscript paper, which was filled with nearly two-thirds of the handwriting, was swept aside.

Accompanying it are other manuscript papers that are also filled with mathematical formulas and symbols, piled up messily on the long and narrow desk.

Not only that, but on the wooden floor under the desk, there were also a lot of manuscript paper scattered, some were crumpled up, while others remained flat.

I don't know how long it has passed, but the phone on the table vibrated suddenly.

The ear-piercing ringtone broke the silence, Xu Chuan impatiently touched the phone, pressed the incoming call without looking at it, turned around and devoted himself to the research again.

".Assume that Gz=GL(n, C) is a general complex linear group, and B∈Gz is an upper triangular subgroup, then GzBruhat decomposes into a double-set decomposition B\\G1/B=∏BωB. The Weyl group W is Linear isomorphism of N*N transformation matrices."

".A maximum ring T of the unitary group U(n):={diag(d, d2,...,dn):|dj|=1)(1≤j≤n), Diag represents a diagonal matrix, and d is A complex number. When U(n)∩B=T, then the double-set decomposition of the subgroup GU(n) is T\\G1/T=∏BωB.”

"."

The ballpoint pen in his hand rewrote the mathematical formulas one after another on the new manuscript paper, and it was not until the last stroke was recorded on the new manuscript paper that Xu Chuan stopped the pen in his hand and stared at his results.

The messy manuscripts on the desk and even on the wooden floor record his achievements these days, not only the problem of "irreducible decomposition of differential algebraic varieties", but also other fields extended by this work.

In fact, he has already solved the problem of "irreducible decomposition of differential algebraic varieties".

On the way to solve it, inspired by algebraic varieties and polynomial equations, he upgraded the original tool again, adapting it to algebraic topology and polynomial equations of projective algebraic varieties, non-singular complex algebraic varieties, That's why he's addicted to it.

Staring at the manuscript paper, Xu Chuan raised a smile at the corner of his mouth.

The busyness of these days has been fruitful. He has created a new mathematical tool on the problem of "irreducible decomposition of differential algebraic varieties".

And with this tool, he may be able to launch an impact on the "Hodge Conjecture", one of the seven millennium puzzles.