Reborn Tech Scholar

Chapter 327 Proof of Hodge's Conjecture in the Narrow Sense

Chapter 328 Proof of the Hodge Conjecture in the Narrow Sense
On the Dragon Boat Festival, Qin Yuanqing took his children to make zongzi and told them the stories of Qu Yuan. As a history lover, Qin Yuanqing was familiar with these stories.

In ancient times, people have always been obsessed with immortality. They practiced the truth and took the medicine of immortality, but they didn’t know that the real eternal life is like this. Although the body died, his spirit has always been remembered and cherished by people. It is a kind of immortality.

It is said that parents are the first and most important teachers of children. This is true. Although the two children are skinny, they love Qin Yuanqing to tell them stories. longing and longing.

"Daughter, mother will come back in a few days, shall we go back to our hometown together?" Qin Yuanqing asked while feeding his daughter rice dumplings.

"Father~~ what is hometown?" The daughter asked curiously, tilting her head.

"My hometown is the place where my father lived when I was a child. It's fun there. Didn't you and your brother go to play before? Take a look, remember?" Qin Yuanqing pointed to the photo hanging on the wall. It was when he returned to his hometown last year , photos taken together.

"I'm not a younger brother~~I'm an older brother~~My sister is so stupid, I can't even remember this. I remember where there are strawberries." The son said in a low voice.

"You are the younger brother, and I am the older sister!" The daughter immediately retorted, "Who says I don't remember, I remember clearly."

Qin Yuanqing couldn't help feeling a little headache, these two children never stopped thinking about who was the elder brother and who was the elder sister.

After the children made a fuss, they went to bed one by one. Qin Yuanqing calmed down rarely. When he came to the study, he took out the draft paper, showing a contemplative expression.

During this period of time, he didn't focus on mathematics and physics, but that didn't mean he gave up completely. Sometimes when he was alone at home in the dead of night, Qin Yuanqing would still study the subject.

After all, Grothendieck presented his manuscript to him at the academic report meeting on the proof of Goldbach's conjecture, which was a favor.

What Qin Yuanqing dislikes the most is being in debt to others.

So he spent a little time on Hodge's conjecture, proving Hodge's conjecture in order to repay Grothendieck's favor.

This old guy passed away in 2014 in his last life, but now he doesn't know what happened, he is still alive and well, and there is no news of being hospitalized.

Qin Yuanqing kept writing down calculations one by one on the draft paper. Qin Yuanqing's attention was constantly concentrated. The whole process required a very clear derivation. If any step was slightly wrong, the results would be very different.

This is a reasoning with almost zero tolerance for error!
This is an important difficulty in proving a world-class mathematical problem. Logical thinking is rigorous, and the steps cannot be wrong. Otherwise, even if the paper is published, it will be denied and overturned during the verification process.

Time passed by like this bit by bit, the draft papers followed one by one, but the progress of the whole derivation process can be said to be slow.

There are twenty or thirty sheets of draft paper piled up, and the ink in the pen is out of water.Qin Yuanqing got up and shook his sore wrist, stretched his waist, turned his head slightly, and made a crackling sound.

Looking at the clock on the wall, it was already 03:30 in the morning.

When a person is completely immersed in one thing, he completely forgets himself and cannot feel the passage of time at all.

"Hodge's conjecture is really a hard bone. No wonder it has troubled the mathematics world for nearly a hundred years, and even Grothendieck couldn't solve it." Qin Yuanqing shook his head, "But no matter how hard a bone is, it's just a bone, and sooner or later it will be gnawed!"

When solving Goldbach's conjecture and the Yang-Mills equation, Qin Yuanqing would feel as if he had encountered a mountain that was difficult to overcome, and he would feel irritable and distressed from time to time.But now, the mathematics level has reached level 15, standing on the peak of mathematics, Qin Yuanqing is now solving Hodge's conjecture, although the speed is not fast, but he will not feel irritable.

After refilling the pen with ink, Qin Yuanqing realized that he was in good spirits and probably couldn't fall asleep, so he simply picked up Grothendieck's manuscript, which contained many sheets, about three to four hundred sheets.

Qin Yuanqing scanned slightly and took out more than 20 sheets of paper. These were Grothendieck's attempts and thoughts on Hodge's conjecture.

Qin Yuanqing didn't understand why Grothendieck would choose to present his manuscripts to himself. After all, these manuscripts are very precious and of immeasurable value. To algebraic geometers, they are no different from the Bible.

But there is no doubt that this manuscript is extremely valuable.

Qin Yuanqing looked at it carefully, perhaps for many people, the characters on the manuscript were like ghostly drawn symbols, and they couldn't understand at all, but for Qin Yuanqing, there was no obstacle at all.

"So it turns out that Grothendieck did go a long way on Hodge's conjecture at the beginning. If he continues to study like this, it is really possible to solve Hodge's conjecture." Qin Yuanqing secretly thought.

Qin Yuanqing made a cup of tea, drank it, and then continued to count.

A little bit of sunlight shines on Qin Yuanqing through the glass of the study.

One after another, the formula symbols took shape on the paper in front of Qin Yuanqing, as if they were summoned by some kind.

It was already dawn, but Qin Yuanqing didn't feel it.

"Father~~grandma asked you to have breakfast~" The daughter broke into the study and woke up Qin Yuanqing who was immersed in Hodge's conjecture world.

Looking at the seventy or eighty pages of paper on the table, Qin Yuanqing smiled slightly. Although the Hodge Conjecture was not solved, the Hodge Conjecture in the narrow sense was proved.

It is also a big gain.

"Okay, let's go, let's go have breakfast." Qin Yuanqing held his daughter's hand, and the daughter was bouncing around. I have to say that the child is indeed full of vitality, as if he has inexhaustible energy.

On the dining table, breakfast was already prepared. Mama Jing was feeding the brat breakfast, while Qin Yuanqing fetched a bowl of hot milk for her daughter to eat by herself.

Qin Yuanqing is used to sweet potato porridge with some pickles in the morning, while children are already used to a bottle of milk, eggs and some steamed buns in the morning.

During the entire Dragon Boat Festival and the two-day holiday of the college entrance examination, Qin Yuanqing spent a total of four days in total. During the day, Qin Yuanqing played with his two children and visited the class once. In the evening, he sorted out his thesis. The Proof of the Formal Hodge Conjecture in the Narrow Sense" is finally freshly released.

The title of the paper is very long, and it can be summed up as a proof of Hodge's conjecture in a narrow sense!

"The Hodge conjecture in the narrow sense has been solved, and the next step is to attack the Hodge conjecture in the general and narrow sense!" Qin Yuanqing is in a good mood. Although the mathematics level has reached level 15, Qin Yuanqing still has a sense of accomplishment in solving the conjecture of the century such as the Hodge conjecture in the narrow sense. of.

However, the narrow Hodge conjecture is only the first step, and the generalized Hodge conjecture is the real goal. After all, compared with the narrow Hodge conjecture, the generalized Hodge conjecture is a more difficult existence, and it is the complete body of the Hodge conjecture.

Getting to this step is actually nothing more than taking the Hodge conjecture from one step to 99 steps, and the remaining step is crucial.

Just like Goldbach's conjecture at the beginning, Chen Jingrun's '1+2' has reached the final step of Goldbach's conjecture, but it is just short of the last step to cap the building of Goldbach's conjecture, and its reputation is much less.

In the world of mathematics, it has always been a result-only theory. It does not look at the contribution made by a certain scholar in the process, but only looks at the proposer and the final prover. As for the contributions made by the scholars in the middle of the proof process, they will only exist. in a chapter of the history of mathematics.

So Qin Yuanqing didn't think about it, but wanted to cap Hodge's conjecture building, so that his name would be engraved on Hodge's conjecture building.

Therefore, although the proof of the Hodge Conjecture in the narrow sense has been completed and the papers have been written, Qin Yuanqing has not published the paper. When the Hodge Conjecture in the general sense is also proved, the sensation will be stronger when two papers are published one after the other. .

Just like the Yang-Mills theory before, several key nodes were solved successively, but the paper was also not published, but a one-time publication directly shocked the entire mathematics and physics circles, and had a real sensational impact.

After the holiday, Qin Yuanqing also went to school to go to work normally again, but now that the undergraduate students have started to enter the exam week, the atmosphere is different than before, the students are obviously working harder than before, there are no seats in the library, and the classroom lights are often on. It was still lighted at twelve o'clock.

With the deepening reform of Shuimu University, there is no regulation to turn off the lights in the library and classrooms. You can see the dawn even if you read a book. The cafeteria also works in three shifts. Meals can be provided for students at any time. If you go to the cafeteria at night, no matter you want to Whether it's eating or eating noodles.

After the new Shahe campus is completed, almost all scientific research institutions will move there, even most doctoral students will go to the Shahe campus.Tsinghua Park is for undergraduates, graduate students and individual majors.

"Boss, the school is asking, are you still recruiting graduate students and doctoral students this year?" Xu Jiayi came to Qin Yuanqing's office and asked.

In the past, Qin Yuanqing recruited graduate students and doctoral students every year, but in the field of physics applications, he has not recruited graduate students for many years, even doctoral students are less recruited.But there are always mathematics majors, usually five or six, and sometimes three or four.

"Let's recruit one graduate student and one doctoral student in mathematics this year. The other two graduate students this year will see if they want to continue their Ph.D. studies with me, graduate or go overseas for further study!" Qin Yuanqing pondered for a while before saying.

Next, the chemical laboratory and the biological laboratory will also be launched on a large scale. His main energy is there, so Qin Yuanqing has no energy to recruit more graduate students and doctoral students.

According to the plan, the [-] researchers recruited last year will all arrive in August this year, and each project team will officially enter the orbit.

(End of this chapter)