Rebirth of science and technology academic master

Chapter 328: Proof of the narrow Hodge conjecture

During the Dragon Boat Festival, Qin Yuanqing made rice dumplings with his children and told them stories about Qu Yuan. As a history buff, Qin Yuanqing was familiar with these stories.

In ancient times, people have always been obsessed with immortality. They practiced Taoism and took elixirs, but they did not know that real immortality is actually like this. Although the body is dead, his spirit has always been remembered and missed by people. This is It's a kind of immortality.

It is said that parents are their children's first and most important teachers. This is absolutely true. Although both children are naughty, they love Qin Yuanqing telling them stories the most. This is human beings' innate love for knowledge. Yearning and longing.

"Daughter, my mother will be back in a few days. How about we go back to our hometown together?" Qin Yuanqing personally fed his daughter rice dumplings and asked.

"Dad, what is hometown?" The daughter tilted her head and asked curiously.

"My hometown is where my father lived when he was a child. It's so fun there. Didn't you and your brother play there before? Take a look. Do you remember it?" 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 that she can't even remember this. I remember wherever there are strawberries." The son said angrily.

"You are the brother and I am the sister!" The daughter immediately retorted: "Who says I don't remember? I remember it clearly."

Qin Yuanqing couldn't help but have a headache. The two children never stopped fighting over who was the brother and who was the sister.

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

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

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

What Qin Yuanqing dislikes the most is owing favors to others.

So he spent some time on the Hodge conjecture and proved it to repay Grothendieck's favor.

This old guy passed away in his last life in 2014, but for some unknown reason, he is still alive and well, and there is no news of hospitalization.

Qin Yuanqing kept writing down calculations one after another on the draft paper. Qin Yuanqing's attention was constantly focused. 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 error tolerance!

This is an important difficulty in proving world-class mathematical problems. The logical thinking must be rigorous and the steps must not be wrong. Otherwise, even if the paper is published, it will be denied and overturned during the verification process.

Time passed like this little by little, one draft paper after another, but the progress of the entire derivation process was very slow.

There are twenty or thirty sheets of scratch paper piled up, and the pen is out of ink. Qin Yuanqing stood up and shook his sore wrist, stretched, and turned his head slightly, making a crackling sound.

I looked at the clock on the wall and saw that it was already half past three in the morning.

When a person is completely immersed in something, he is completely selfless and cannot feel the passage of time at all.

"Hodge's conjecture is indeed a hard bone. No wonder it has troubled the mathematics community for nearly a hundred years. Even Grothendieck couldn't solve it." Qin Yuanqing shook his head, "But no matter how hard the bone is, it is just a bone. Sooner or later you will chew it!"

When he first solved Goldbach's conjecture and the Yang-Mills equation, Qin Yuanqing would feel as if he had encountered a huge mountain that was difficult to overcome, and would feel irritated and distressed from time to time. Now, with a mathematics level of 15, standing at the pinnacle of mathematics, Qin Yuanqing is now solving the Hodge conjecture. Although the speed is not fast, he does not feel irritable.

After refilling the pen with ink, Qin Yuanqing found that he was in good spirits now and probably couldn't sleep, so he simply picked up Grothendieck's manuscript. The manuscript had many sheets of paper, about three to four hundred sheets.

Qin Yuanqing scanned it slightly and took out more than twenty pieces of paper. These were Grothendieck's original attempts and thoughts on Hodge's conjecture.

Qin Yuanqing didn't understand why Grothendieck chose to give his manuscripts to him. After all, these manuscripts were very precious and of immeasurable value. For algebraic geometry scholars, they were no different from the Bible.

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

Qin Yuanqing read it carefully. Perhaps for many people, the characters on this manuscript were like ghost drawings and could not be understood at all, but for Qin Yuanqing, there was no obstacle at all.

"So that's it. Grothendieck has indeed gone very far on the road of Hodge's conjecture. If he continues to study like this, it is really possible to solve the Hodge's conjecture." Qin Yuanqing thought to himself.

Qin Yuanqing made a cup of tea, drank it, and then continued to immerse himself in calculations.

Bits of sunlight shined on Qin Yuanqing through the glass of the study room.

One after another, formula symbols, as if receiving some kind of summons, took shape on the paper in front of Qin Yuanqing.

Qin Yuanqing didn't even feel that it was already dawn.

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

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

It can be considered a big gain.

"Okay, let's go have breakfast." Qin Yuanqing held his daughter's hand. Her daughter was jumping up and down. It must be said that the child was indeed full of vitality, as if she had inexhaustible energy.

Breakfast has been prepared on the dining table. Jing's mother is feeding the brat breakfast, while Qin Yuanqing gets a bowl of hot milk for his daughter and lets her eat it by herself.

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

During the entire Dragon Boat Festival and the two-day college entrance examination holiday, there were four days in total. Qin Yuanqing played with his two children during the day and visited a class once. In the evening, he sorted out papers. On the last day of the holiday, he wrote "Non-Singular Projective Algebra Varieties Based on Harmonic Differentials". The paper "Proof of the formal narrow Hodge conjecture" is finally out.

The title of the paper is very long, and in summary it is the proof of the narrow Hodge conjecture!

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

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

Reaching this point is actually nothing more than taking the Hodge conjecture from one step to ninety-nine steps, and the remaining step is crucial.

Just like the original Goldbach's conjecture, Chen Jingrun's '1+2' has reached the last 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 popular.

In the field of mathematics, it has always been results-oriented. We will not look at the contribution of a certain scholar in the process, but only the proposer and the final prover. As for the contributions of the intermediate scholars in the proof process, they will only exist. in a certain chapter in the history of mathematics.

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

Therefore, although he has completed the proof of the narrow Hodge conjecture and has written all the papers, Qin Yuanqing has not published the paper. When the general Hodge conjecture is also proved, then the two papers will be published one after another, and the sensation will be even greater. .

Just like the previous Yang-Mills theory, several key nodes were solved successively, but the paper was also not published. Instead, it was published at once and directly shocked the entire mathematics and physics circles, having a real sensational impact.

After the vacation, Qin Yuanqing went to school every day again. However, now that undergraduate students have begun to enter the exam week, the atmosphere is different than before. Students are obviously working harder than before. There are no seats in the library, and the lights in the classroom are often dimmed. It was still light at twelve o'clock.

As Shuimu University continues to deepen its reform, there is no rule to turn off lights in libraries and classrooms. You can read until dawn without any problem. The cafeteria also operates in three shifts and can provide students with meals at any time. If you go to the cafeteria at night, whether you want to Whether it’s a meal or noodles, etc.

After the new Shahe campus is built in the future, almost scientific research institutions will move there, and even most doctoral students will also go to the Shahe campus. Tsinghua Campus is for undergraduates, graduate students and individual majors.

"Boss, is the school asking if you will recruit graduate 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. Physics Application has not recruited graduate students for many years, and even fewer doctoral students have been recruited. But there are always students majoring in mathematics, sometimes five or six, 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 moment before saying.

Next, the chemical laboratory and biological laboratory will also be expanded on a large scale. His main energy is there, so Qin Yuanqing does not have the energy to recruit more graduate students and doctoral students.

According to the plan, all 400 researchers recruited last year will arrive in August this year, and each project team will officially be on track.