From Almighty Scholar to Chief Scientist

Chapter 293 Scene [-], Fragmented Report

[...According to Formula 1, Formula 3, Formula 8, and Formula 12, we can get Hdg^k(X)=H^(2k)(X, Q)∩H^(k, k)(X)...]

[To sum up, we can know that when X is a projective complex manifold, each cohomology class H^(2k)(X, Z)∩H(k, k)(X) is an integral coefficient on X The sum of the torsional and cohomology classes of algebraic periods. 】

[So, after dividing by H^(2k)(X, Z)∩H(k, k)(X) by reversing the classes, each class is the image of the cohomology class of the integral algebraic period. 】

[Therefore, on non-singular complex projective algebraic varieties, any Hodge class is a rational linear combination of algebraic closed-chain classes]

[The certificate is completed. 】

After writing the last two words stroke by stroke, a slight smile appeared on Lin Xiao's face.

It's over, Hodge guesses.

The proponent of Hodge's conjecture, William Vallance Douglas Hodge, discovered this possible conjecture in his work from 1930 to 1940, but before 1950, this conjecture did not attract people's attention. attention.

It was not until Hodge mentioned this conjecture in his speech at the International Congress of Mathematicians in 1950 that people were surprised to find that this is a conjecture of great significance to mathematics, especially to algebraic geometry. and algebraic topology.

And with Grothendieck's great development of algebraic geometry, and the cohomology group that was expanded into an important mathematical tool under his single-handedly, and the Langlands program proposed later, Hodge conjectured that this could be achieved to a certain extent The conjecture that unifies the two different disciplines of algebraic geometry and topology is of great significance, and it has naturally become a major mathematical problem that people are vying to solve.

It is precisely because of this that when the Clay Institute organized many mathematicians to select the Millennium Problem, the Hodge Conjecture was also selected, and then became a problem that countless mathematicians remembered.

And until today, it finally finished in the hands of a 22-year-old math genius.

From 1930 to the present, it has spanned more than 90 years of history, experienced the worst world war, and also spanned more than 70 years of relatively peaceful periods, witnessing an increasingly prosperous mathematical community.

Its end is the end of a period of history.

Lin Xiao put down the pen, picked up the draft paper, and blew on the ink on it.

Well, although the ink has dried up a long time ago, it is still a piece of history. Let me blow it up, give the original Hodge a little dignity, and then clean up the dust for the upcoming Hodge-Lin theorem.

Suddenly realizing that something was missing, Lin Xiao frowned and said softly, "Come here!"

System: "Congratulations to the host, the proof of Hodge's conjecture has been completed, the intersection of algebra and topology, so that all qualified topologies can be expressed as polynomial solution sets, and the great unification of mathematics has moved forward again One step, your understanding of mathematics has made an important leap forward, I hope the host can make persistent efforts and grasp the ultimate truth as soon as possible! This time, you will be rewarded with 8000 mathematics experience, 150 truth points, and the halo of a mathematics master."

"Congratulations to the host, the mathematics level has been raised to level 6, and you have officially become a true mathematics master!"

"Mathematics Master Halo: When the host solves math problems, he will get a certain inspiration bonus."

The sound of the system brought surprise and surprise to Lin Xiao's face.

Actually rewarded 8000 math experience directly!

The last time he proved Lin's conjecture, he only got 4500 points of mathematical experience. He didn't expect that this time it was almost doubled.

To a certain extent, this also has the addition of the reputation of Hodge's conjecture. Of course, the most important thing is that Hodge's conjecture is more important to the great unification of mathematics. After all, it directly communicates the relationship between topology and algebraic geometry.

Because, the proof of Hodge's conjecture will enable mathematicians to know what conditions a shape needs after topological transformation before it can be described by polynomials.

Then, we can easily find out how to describe a shape and its topologically transformed homeomorphs algebraically.

This not only has important significance for mathematics research, but also has many significance for many other fields.

In any case, as one of the millennium problems, its significance to the world is self-evident.

Of course, a lot of experience is one thing. Lin Xiao quickly paid attention to another thing: "So, after I have been promoted to level 6 in mathematics, shouldn't it be time for me to develop my brain?"

The next moment, the familiar heaviness flooded his mind again.

However, due to his increasingly powerful brain development, this feeling disappeared after a while, replaced by the same familiar feeling of "I have become stronger".

Of course, his hair was still black and shiny, and since another ten days had passed and he still hadn't had it cut, it was thicker now.

"Well, compared to many mathematicians, it's obvious that my hair volume is pretty good."

Lin Xiao nodded with satisfaction.

He even had the luxury of cutting his head.

"It's time to take care of it. In five days, I have to make a report."

Letting down his hair, he asked how much the system had increased his brain development. This time it had increased by 0.7%, and his brain development had also reached 8.85%.

From 10%, there is only 1.15% gap left.

With a sigh of emotion, Lin Xiao stopped thinking about it and went out to get a haircut.

……

The proof of Hodge's conjecture, Lin Xiao will naturally have to wait until the International Conference of Mathematicians to officially reveal the answer. Let's hope he gets the Fields Medal.

Otherwise, if you want to witness the proof of Hodge's conjecture, you can only go to Beijing University to listen to his report.

I don't know if the dean of their School of Mathematical Sciences hopes for a non-named permanent professor who won the Fields Medal, or is the academic report proving Hodge's conjecture conducted here?

In this way, the time came to June 6.

On this day, Lin Xiao will give a report on the proof of Lin's conjecture in the auditorium.

Because the time of this report is very close to that of the International Congress of Mathematicians, and it is more convenient to fly from Beijing to St. Petersburg, so many mathematicians came to listen to this report.

In addition, this is also Lin Xiao's first report on Lin's conjecture, so many mathematicians want to communicate with Lin Xiao about the problems.

Although before, they could communicate with Lin Xiao by email, but obviously, face-to-face communication is more convenient.

Until nine o'clock in the morning, the report was held as scheduled.

Lin Xiao, who had undergone some grooming and had a hairstyle specially done, appeared in front of many mathematicians present with great energy.

Now at the age of 22, he has become more mature than before, no matter in terms of appearance or other aspects.

Facing these mathematicians, he said with a smile on his face: "Mathematicians who have come from afar, welcome to Shangjing University. I hope that you can leave a good impression on you during your few days here."

"Lin, if you can complete the last part of your report at the International Congress of Mathematicians, I will definitely be impressed."

At this time, a mathematician sitting in the first row said.

Lin Xiao saw that this mathematician was Pierre Deligne who flew from the United States.

And Deligne's words quickly resonated with other mathematicians.

"Yeah! Lin, you either don't write that part, or write more! You're making us feel bad!"

"Lin, you are so maddening!"

……

Seeing that there were at least six or seven mathematicians who were familiar with him expressing their opinions, Lin Xiao couldn't laugh or cry, and then said with a smile: "At that time, you will get a satisfactory answer."

"This is what you said, we all remember it!"

"of course."

Lin Xiao gave an OK gesture.

So these mathematicians spared him for the time being and listened to his report.

Regarding the proof of Lin's conjecture, since it has passed the approval of "Annual of Mathematics", of course there is basically no problem. Lin Xiao's academic report can also be regarded as a process.

Mainly for future communication.

So Lin Xiao spoke very quickly, in about 20 minutes, he finished the thesis.

This is followed by a question and answer session.

Lin Xiao left enough time to communicate with the mathematicians present about the process of proving Lin's theorem and some methods of application.

The questioning session lasted for more than 40 minutes. Those students who came to join in the fun, or some teachers with weaker ability, had already fallen into confusion. They were extremely impressed by the questions of these big guys and Lin Xiao's answers. At a loss.

They could only groan in their hearts: It's too high-end!

Of course, after four or ten minutes, seeing that no one asked any more questions, Lin Xiao finally began his conclusion.

He smiled and said: "Actually, there is a great connection between Lin's theorem and Hodge's theorem... conjecture, I believe everyone is very clear, and I also found a The magical method can bring us great help in proving the Hodge conjecture."

"Of course, if you want to know what's going on, let's listen to the breakdown of my next report. This is the end of today's report. Thank you everyone. I look forward to seeing you at the International Congress of Mathematicians."

Then he bowed deeply, and then, as if fleeing, he left the podium.

The mathematicians present were stunned for a while, and suddenly recalled it.

Lin Xiaolian said "Hodge's Theorem" twice, is it a coincidence or intentional?
But according to common sense, when they mention the Hodge conjecture, they must all say "Hodge-conjecture", so how can they say "Hodge-theorem"?
Could it be?

Deligne reacted first, then quickly got up and ran to the top, shouting at the same time: "Lin! Don't run! Stop!"

Other mathematicians also reacted one after another, this hateful Lin Xiao, unexpectedly broke the context again?

Suddenly, such a strange scene appeared for the first time in the Great Hall of Peking University since its completion: a group of world-renowned mathematicians ran up to the rostrum to chase after a young mathematical genius.

And the audience who didn't know what happened in the back showed a look of bewilderment.

What happened?

(End of this chapter)