Princeton usually throws graduate and doctoral students into the "river" and lets them swim on their own, and they can graduate by swimming to the other side.

Before writing a doctoral dissertation, the most important thing is to find a professor with both qualifications and strength to support your project.

Professors in the Department of Mathematics know PhD students well and will not hesitate to ask students to change their topics if they think they are not capable of completing their chosen project.

With the support of professors, PhD students at the University can usually get a PhD in two or three years, while at Harvard it takes four or five years or more.

Ouye completed her doctoral dissertation in the usual way, and she received her PhD in two years, proving Jesmanovich's conjecture for the first time in the world.

Zhou Yu'an became a doctoral student in the Department of Mathematics at Princeton on the same day as Ou Ye, and he received strong support from his supervisor Fei Jiali when he opened the project, but he collapsed in the middle and late stages, and is currently overvising his doctoral thesis.

Yu Lei and Ralph became doctoral students a year later than Zhou Yu'an, and their doctoral dissertation progress has caught up with or even surpassed Zhou Yu'an.

"If a soldier is strong, he will be strong. Zhou Yu'an admitted that it was the right choice for Yu Lei to follow Shen Qi.

"Brother Xiaoyu, my Ph.D. year has been very fulfilling and painful, and you can't experience this feeling. In the past month, Yu Lei worked day and night, and finally completed the academic task assigned to him by Shen Qi.

"So your Hodge conjecture is done?" Zhou Yu'an asked.

"Under the guidance of Brother Qi, Ralph and I have completely completed the part we are responsible for, and now we have to wait for news from Yan University and the Morningside Math Center. Yu Lei took a long breath, he could learn a lot from Shen Qi, but it was also very hard, but fortunately, the hard work paid off, and the sweat was not in vain.

"So, you and Ralph will be able to participate in the doctoral defense right away?" Zhou Yu'an asked.

Yu Lei nodded: "Yes, Brother Xiao Qi helped us register for the department, and after we came back from California, we participated in the doctoral defense." ”

"You two are too fast, you can defend your PhD in one year! The tutor is awesome, you can really do whatever you want. Zhou Yu'an wiped his sweat, his mentor was obviously not as good as Shen Qi: "By the way, what are you doing in California?"

Yu Lei said: "There is an academic conference in the field of algebraic geometry at the California Institute of Technology, and Brother Qi takes me and Ralph to study, and the opportunity is rare for the world's top masters in algebraic geometry to go there." ”

"Yu Lei, take the wrench, you can go. Zhou Yu'an handed Yu Lei a wrench, both of them lived in the dormitory building for doctoral students, and Yu Lei came to him to borrow a wrench.

The next day, Shen Qi, Yu Lei, and Ralph arrived in Pasadena, California, where the California Institute of Technology, a famous research university in the United States, is located.

Caltech on the West Coast and Princeton on the East Coast have similar tenets, believing in small but fine, not big and complete.

Princeton has a small student population, and Caltech has even fewer students, with just over 6,000 students enrolled.

Before the 60s of the last century, some of the most accomplished scholars in China basically came from Caltech, such as Qian Xuesen, Zhou Peiyuan, Guo Yonghuai, Tan Jiazhen, Yuan Jialiu, Qian Weichang, etc.

Mr. Qian Xuesen wrote in his memoirs: "In the autumn of 1935, I went to MIT from Shanghai Jiaotong University to become a professor, and found that the curriculum of Shanghai Jiaotong University was all copied from MIT, and even the experiments were the same. Therefore, the undergraduate teaching of Shanghai Jiaotong University at that time reached the world's advanced level. A few years later, I went to Caltech to become a professor, only to discover that some of MIT's best courses were adapted from Caltech. ”

There are many stories about Qian Lao, Shen Qi is familiar with them, he wandered around the campus of Caltech, imagining the demeanor of those meritorious scientists in my country back then.

Except for geneticist Tan Jiazhen, these meritorious scientists from the California Institute of Technology are all physicists, and they are doing big projects such as "two bombs and one satellite".

Caltech's strongest majors are physics, chemistry, and astronomy, and have been so for hundreds of years.

Mathematics is not Caltech's strength, or even its shortcoming.

How can a research university with science and engineering as the main subject be without mathematics?

Although the mathematics of our school is weak, but our school also has an ambition to boost the strength of mathematics, the "International Algebraic Geometry Academic Exchange" is arranged to be held at Caltech, which is the initiative of Caltech.

Shen Qi's conference paper submitted to the organizing committee of the "International Algebraic Geometry Academic Exchange" is a summary version, that is, a short condensed version of "Hodge's Algebraic Geometry Methods of Conjecture", and he believes that it is necessary to publish his team's latest research results in public, and Schultz cannot be robbed of the limelight.

Schultz has been very popular lately, and he has made presentations all over the world, claiming that his team has proved the Hodge conjecture in exceptional circumstances.

Regrettably, and remaining mysterious, no one has seen Schultz's full paper on "Proof of the Hodge Conjecture in Special Cases", and it is the abstract version that has been published to the world.

Schultz also came to Caltech this time to continue his global presentation.

In the academic lecture hall of the California Institute of Technology, the International Algebraic Geometry Academic Exchange Conference was held as scheduled.

According to the meeting, Schultz was the first to give a presentation, and the title of the report was "Proof of the Hodge Conjecture in a Special Case".

Shen Qi, Yu Lei, and Ralph sat side by side, listening attentively to Scholz's report, knowing themselves and their opponents, and the latest information was very important.

“...... Thus, we prove that every harmonic differential form on a β class of nonsingular projective algebraic clusters is a rational combination of the upper cohomology class of algebraic closure. The next thing we need to do is to prove the Hodge conjecture in the general case, which has already begun and has made breakthroughs. Thank you, my report is complete. Scholz's debriefing was not long, ten minutes, and the report document was also a summary version.

The audience applauded thunderously, and some people asked, "Hey, Professor Schultz, when will we see all of your research results?"

Schultz replied: "I believe that day will come soon, and for now, we have to keep it a secret." ”

Everyone applauded again, understood, all understood, confidential.

Schultz is making a lot of noise around the world but at the same time he is cautious, because he knows that more than one team in the world is tackling the Hodge conjecture, and the paper that has not yet been completely completed is published publicly, and who is it to reason with if it is stolen by others?

Don't worry about academic plagiarism that doesn't change a word, no mathematician with a slight reputation would do such a thing that will be infamous for thousands of years.

But a smart mathematician knows how to borrow from someone else's academic ideas and adapt them, and this situation cannot be blamed, so he can only do his own work of secrecy.

Scholz's report is nothing new compared to his last report in Munich. Yu Lei whispered.

"He defines β class of nonsingular projective algebraic clusters in the summary version, but he doesn't see the detailed proof process, whether he doesn't have a proof at all, it's just a guess, or he doesn't want to make it public," Ralph said.

"As a competitor, we should think that Schultz has proved the Hodge conjecture in exceptional circumstances, not questioned him. Shen Qi said.

At this time, the host of the conference said: "I would like to invite Professor Shen Qi to give a report on "Hodge Conjecture Algebraic Geometry Method"!"

Shen Qi tidied up the collar of his suit and shirt, and then came to the stage, and the audience erupted in more enthusiastic applause.

"Yes, as you can see, I changed my major again, this time in algebraic geometry. Shen Qi's opening remarks sparked a burst of laughter, and he often changed majors, from number theory to functionals, to condensed matter physics and solid state physics, and turned around back to mathematics, this time aiming for the most difficult millennial puzzle, the Hodge conjecture. ()

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