Chapter 296 Hodge’s conjecture is one month harder than Lin’s conjecture

The applause of the audience lasted for a long time. Even the last time Goldbach's conjecture was made, the sound was louder because there were more than 10,000 people in the audience. But now here, in the St. Petersburg National Theater, there is no applause. It was so big at first, but it lasted a long, long time.

At the end, the applause finally subsided, and Lin Xiao finally had time to speak: "Thank you for your patience in listening to all my processes. Now, it's time for questions."

He looked at the time and then smiled: "The organizing committee has given us nearly an hour of question time, so come on, I'm ready for a protracted battle."

There was laughter in the audience, and then everyone raised their hands.

Looking at so many hands, Lin Xiao smiled slightly and then chose one of them.

Soon, the selected person stood up, first smiled and nodded at Lin Xiao, and then said: "Professor Lin, please tell me, in 4.3.6, Γ`0∈H^3et(W`0, k , why does the restriction on the geometrically special fiber W`0k in Z/2(2) not disappear under the mapping to Gavarot cohomology?"

Lin Xiao smiled slightly and said, "This step is very simple."

Then he pulled a blackboard from the side and started writing.

【H^3et(W`0,k,Z/2(2))→H^3(F,Z/2(2))...where F=k(W`0,k)】

"Well, that's probably it."

Lin Xiao smiled and said: "Please note that the form of W`0 is U×S'0. Through Lemma 4.2, we can get U≌Gm, and S`0 is S`→ gauge (o` as mentioned above ) special fiber."

The questioner suddenly realized, "Thank you for your explanation, I understand."

Lin Xiao smiled and nodded, and then said: "You're welcome, it's my responsibility, then please invite the next person."

Soon, he selected another person.

"Professor Lin, why in 3.4.1, in order to improve β, we need to find a non-divergent Gavarot expansion L/Kp?"

"This step is also very simple..."

Lin Xiao quickly answered.

In this way, after asking questions one by one, the report finally came to an end, and the number of hands raised on the field became less and less, until finally, it was all cleared.

This also means that the Hodge conjecture proved by Lin Xiao has been recognized by everyone in this report. The next step is to wait for this International Congress of Mathematicians to sort out his report, and then use the conference paper as the basis The form was published.

I believe that the conference papers in this issue will be sold out by people.

In fact, the last International Congress of Mathematicians, the final conference proceedings also sold a lot of copies, after all, Lin's conjecture was proposed in it.

And this time, Hodge's conjecture has been proven. I believe everyone is willing to buy a copy as a souvenir.

Seeing that no one asked questions, Lin Xiao smiled and said: "It seems that my report ends here, thank you all."

Then he bowed to the people again.

Off the court, applause rang out again.

After the question and answer session, everyone present knew that the Hodge conjecture was completely proved.

At least, it has been recognized by people for the time being. Later, the International Congress of Mathematicians will organize many mathematicians to conduct a final analysis of the entire proof process. At the same time, even after it is announced, it will take several or even ten years of academic research. The test, of course, is actually enough after a few months of testing.

After all, the proof of this heavyweight conjecture will inevitably be observed carefully by people under a magnifying glass in the future to verify every possible error. Therefore, I believe that there are so many mathematicians in the mathematics community, and it will take a few months. enough.

Of course, people believed in Lin Xiao's proof and there would be no problems.

After all, Lin Xiao's credit is worth several top guesses.

At this moment, Jean-Pierre Ser stood up, then in the eyes of everyone, picked up a bottle of champagne, and walked to the stage.

Seeing this scene, how could people not know the old man's purpose?

So the applause got a little louder, and people all had smiles on their faces, waiting for that moment to come.

Seeing Professor Searle on stage, Lin Xiao was stunned at first, but then smiled when he saw the bottle of champagne.

"Professor Searle."

"Lin, when I see you again, you surprise me at all."

Serge smiled, and then he handed the champagne in his hand to Lin Xiao and said, "Open him, this is the moment for the winner."

After taking the champagne, Lin Xiao smiled and said, "Thank you."

Then, saying "Cleaner, I'm offended" in his heart, he shook the champagne vigorously, and then opened the champagne cap with his thumb.

"Boo~"

The wine rushed out of the bottle, spilling cheers of victory.

And the atmosphere in the audience reached another climax again.

At the same time, media photographers in the back row also captured this scene.

In the photo, Lin Xiao stood on the stage and opened the champagne of victory. In the auditorium, the audience stood up and applauded. This photo will always be engraved in the history of mathematics, and there is a line of small words below it. : "On July 10, 2022, Lin Xiao celebrated for successfully proving the Hodge conjecture at the International Congress of Mathematicians."

…

This report is over.

In fact, the news had already spread before the report was even finished.

Needless to say, the mathematics community, or the entire academic world, has long been in a frenzy over this matter.

For the general public, the Hodge conjecture, as one of the most difficult mathematical problems in the world, is also a gimmick. Therefore, this matter alone has attracted a lot of attention. Of course, as the seventh anniversary of the millennium, One of the big problems, the Hodge Conjecture, represents a prize of US$1 million, and has also become a point of great concern to people.

So under the media's publicity, ordinary people expressed envy of Lin Xiao.

That's a million dollars!

Who wouldn’t want to get their hands on it?

Here we have to talk about the cleverness of the Clay Research Institute. The Clay Research Institute was established in 1998. It was originally quite unknown. However, in 2000, it came up with a million-dollar bonus gimmick and let it The reputation is also known in academia.

However, for Lin Xiao, although 1 million US dollars is very coveted, it is not that he cannot make money now. In addition, if he wants to receive 1 million US dollars, he will probably have to go to Colorado, where the Clay Research Institute is headquartered. He will definitely not go unless they are held in China.

So he didn't care about the awards.

In the following time, he naturally continued to stay in St. Petersburg and participated in the next conference report. He originally wanted to communicate with Perelman, but it was a pity that Perelman finished his speech. After the report, he disappeared, so he had no choice but to give up.

In this way, time passed quickly.

This International Congress of Mathematicians has finally come to an end.

Undoubtedly, this conference will be one of the most historically significant among all international conferences of mathematicians in the past and in the future.

Every participant felt that the trip was worthwhile.

However, when it is finally time to leave, you still have to leave.

July 15, St. Petersburg Airport.

On this day, many mathematicians who participated in the meeting left together, and Lin Xiao also followed the Huaguo team and arrived at the airport.

Of course, before boarding the plane, Lin Xiao was surrounded by many mathematicians, who all said goodbye to him.

Professor Serge said to him with a smile, "Lin, I hope that the next time we see you, you will bring us another surprise."

Lin Xiao smiled: "Of course, I will try my best."

"Then I'm looking forward to it." Serge nodded and said with a smile: "If possible, try to hear a few more important conjectures completed by you before I pass away."

Lin Xiao nodded solemnly.

Professor Searle is over ninety years old. Although he seems to be in good health, who knows if an accident will happen.

Lin Xiao could only hope that his former mentor would live longer.

Next to him, Carlos Kenig, the president of the International Mathematical Union, was also here. Although he had to wrap up the conference and couldn't leave for the time being, he still took the initiative to see Lin Xiao off.

He patted Lin Xiao on the shoulder and said with a smile: "Professor Lin, I have seen the miracle you mentioned at the beginning, but I also hope you can let me see it more times."

"I also hope that I can let you see it more times." Lin Xiao responded with a smile.

Everyone else nodded.

They all believed that Lin Xiao would continue to create more miracles.

Then, other mathematicians including Deligne, Terence Tao, Pompieri and other mathematicians also said goodbye to Lin Xiao one by one.

After a while, Lin Xiao looked at the time and was about to get ready to board the plane, so he smiled and said: "Okay everyone, it's time for me to leave. If you are free, you must come to China!"

These mathematicians all laughed and said: "Definitely next time."

Then, Lin Xiao also left the lobby and headed to the boarding gate.

Under the protection of Shi Hao and four other bodyguards, they boarded the plane, and then the plane took off smoothly and began a nine-hour flight.

After today, the average IQ in St. Petersburg has returned to its original point.

…

On July 16, Lin Xiao’s plane arrived at Shangjing Airport.

When he arrived at the airport, he was naturally picked up by a large number of people, which made Lin Xiao feel the grand treatment he received as a Fields Medal winner and the prover of the Hodge conjecture. The Chinese Mathematical Society and Ma Gaoliang all came to pick him up. As I said, many important figures from the government also came to pick me up.

In addition, CCTV reporters also recorded the incident and interviewed him.

However, because he had been on a plane for so long, he could say as little as possible during the interview.

Reporter: "Professor Lin, how does it feel to prove Hodge's conjecture? Do you feel a sense of accomplishment in your heart?"

Lin Xiao: "If it proves Hodge's conjecture, it's okay, not bad."

Reporter: "...You are really 'humble'."

"We have also learned about the Hodge conjecture. It is a very difficult problem. It is said that many mathematicians in the world have devoted their lives to proving the Hodge conjecture. You must have spent a lot of time to prove this conjecture. Less?"

Lin Xiaoshen agreed: "Of course! It took me nearly four months to solve this problem. It really cost a lot."

I don’t think anyone could recognize him after he went out.

reporter:"……"

Four months?

talent?

What about Versailles?

The reporter took a deep breath and then continued to ask: "So how does it compare with your Lin's conjecture? Which one do you think is more difficult?"

"Well... then the Hodge conjecture is probably more difficult. After all, the Hodge conjecture has to take n-dimensional conditions into consideration."

Finally, there was a normal answer. The reporter breathed a sigh of relief, and then asked curiously: "How difficult do you think it is?"

"It's... it'll be difficult for a month."

Reporter: "?? What does it take to be difficult for a month?"

Lin Xiao said with a smile: "It took me about three months to prove Lin's conjecture, and four months for Hodge's conjecture. Isn't this just one month difficult?"

Reporters and everyone around them: "..."

Since when has the difficulty of a top-level mathematical conjecture been calculated in terms of months?

Probably Lin Xiao is the only one who has this ability!