I Just Want to Be a Quiet Top Student

Algebraic geometry is the most popular research field in today's mathematics field. More than half of mathematicians are devoted to this field. Shen Qi is not the only one who aspires to complete the Langlands program or the Hodge conjecture.

The Wu Baozhu team of the University of Chicago and the Laforge team of the Paris Ecole Normale Supérieure are at the forefront of the Langlands program. It is generally believed in the mathematics community that whoever can first prove and perfect the Langlands program will realize the dream of mathematicians. Great unity.

The Langlands program is quite difficult to deal with. Wu Baozhu and Lafoge have each studied it for more than ten or twenty years, and so far they have only proved one lemma and one inference in the Langlands program.

It is with this lemma and this inference that Wu Baozhu and Lafoge won the Fields Medal respectively.

The Langlands program builds a system, and the Hodge conjecture is the most complicated case.

Since the Hodge conjecture was proposed in 1950, mathematicians have been trying to prove it.

The fruitful research results come from the University of Bonn, Germany. Peter Schulz's team proved a corollary to partially characterizable algebraic cohomology classes on non-singular projective complex algebraic varieties two years ago.

Schultz, who missed out on the Philippine Prize two years ago, had a hard time learning from it. In the past two years, he has attacked Hodge's conjecture with full firepower. His latest paper published on "Mathematical Invention" made Shen Qi slightly nervous.

"Schultz has proved the similarity of elements in the cohomology class in his latest research results. It has to be said that this is a very beautiful proof." Shen Qi repeatedly studied Schultz's new paper, and he felt that Schultz Ertz is doing the right thing on the right path: "I must never let Schultz or anyone else prove Hodge's conjecture before me. Completing the proof of Hodge's conjecture is one of my must-choice tasks."

However, mathematics is not a confrontational fighting sport, and the rules of ebb and flow do not apply to mathematics.

If you want to beat your opponent in the field of mathematics, the only effective way is to do it faster and better than your opponent.

Mathematics is more like sprinting, one person has one track, one doesn't have to care too much about whether the opponent runs fast or slow, what Shen Qi has to do is to run the fastest in the field on his own track.

After the Christmas vacation, Yu Lei and Ralph returned to campus. This is their second semester of doctoral students.

"Boys, Schulz from the University of Bonn is about to catch up with us. Yes, he and his team are also solving the Hodge conjecture! We must be clear that the Hodge conjecture is not our patent, and anyone has the right to it Have ideas and take practical actions! Obviously, the number and quality of the teams competing with us on the Hodge conjecture far exceeds the Riemann conjecture. After all, there are only a few internationally renowned number theory teams, and the algebraic geometry team... Countless!" The battlefield between Shen Qi and his two doctoral students was transferred from the outdoors to his office.

In this special period, it must be kept secret, and it is best not to let others see even one formula in the semi-finished product.

Although the vast majority of people in the world cannot understand Hodge's conjecture, and it is impossible to understand Shen Qi's team's idea of ​​proof, they have mobile phones with camera functions.

"Peter Schulz, who obtained a corollary for partially characterizable algebraic cohomology classes on nonsingular projective complex algebraic varieties two years ago, has just proved the similarity of elements in cohomology classes. These two results Add it all together, he has... oh no, he is about to catch up with us in the proof of Hodge's conjecture." Ralph's brows were furrowed, and any mathematician has a heart of "first proof".

"Ralph, are you timid? Are you afraid?" Shen Qi asked.

"No, we will never back down, and there is no way back."

"Very good." Shen Qi expressed his satisfaction, he was very concerned about Ralph's state of mind and state.

Ralph is the only American in the entire team. His undergraduate, master, and doctoral students all studied in Princeton.

"This Schultz is a two-hander. It is said that he is Sister Mary's ex-husband?" Yu Lei's thinking is relatively divergent. He is good at analyzing and solving problems comprehensively and objectively from multiple angles.

Shen Qi nodded: "Yes, this German lunatic loves mathematics more than his wife."

"Study mathematics to the point where you don't even want your wife. You are not afraid of dying, but you are afraid of losing your wife...Schultz, he is our strongest opponent." Yu Lei felt a chill, and he said: "Shen Professor, I think you are more human, so you won the Fields Medal, but Schultz did not."

"Remember, we don't make friends with men who don't love their wives. Well, let's get down to business, I hope your two papers can be published within this semester, or at least pre-recorded on arVix. We need to show our strength." Shen Qi put forward specific requirements for the two doctoral students, followed by technical guidance.

Shen Qi's thinking has something in common with Schultz, but also has unique highlights.

It is inevitable that Shen Qi will have an intersection with Schultz in the part of the cohomology. It is all such a routine, so you can use it or not.

Schultz is a master at playing routines, and he is more exciting than Schultz. Shen Qi needs to play some anti-routines. The most important thing is how to reversely deduce that non-singular projective complex algebraic varieties are a special type of complex flow shape.

The reverse deduction lasted for more than half a year. Lei and Ralph were responsible for the details, and Shen Qi grasped the direction.

In the proof of Hodge's conjecture, to put it bluntly, Schulz adopted forward and forced methods. His core logic was based on pure algebraic geometry methods, and achieved good results.

Shen Qi adopted a combination of forward, reverse, and sideways. His core logic is based on algebraic geometry, mathematical analysis, and topology. The system framework is more complete, but the verification process is more brain-intensive and complicated, requiring a huge The basic theory team and he completed this arduous task.

Yu Lei and Ralph were working under Shen Qi's nose. Shen Qi was very clear about the progress of the two doctoral students' projects. He thought that he was a qualified doctoral supervisor because he was a good supervisor.

Shen Qi is also very concerned about the progress of the project that Lu Guozhen and Director Wu are responsible for in China. They keep in touch and exchange information.

"Director Lu, how is the progress of your mathematical analysis section?" Shen Qi asked in the video call.

"It's going well, so don't worry! My 973 project is an annual major project in the hospital. The dean has sent me two more elites. The morale of our team is high, and the situation is very good!" Lu Guozhen in the video screen His face was full of red, and the old man chatted like a teenager.

Shen Qi was greatly encouraged: "That's great, Director Lu is really awesome! We don't need to communicate with each other in the video call on specific technical details, and we can't communicate clearly. Director Lu, please tell me the truth. When can we have the first cooperation?" draft?"

Lu Guozhen: "It's expected to be in July."

Shen Qi: "Okay, it's about the same time as I imagined, and I look forward to your research results!"