I Just Want to Be a Quiet Top Student

Princeton usually throws graduate students and doctoral students into the "river" and lets them swim by themselves, and they can graduate when they swim to the other side.

Swimming in the river aimlessly is of course not good. Before writing a doctoral thesis, the most important thing for a doctoral student is to find a professor with both qualifications and strength to support his project.

The professors of the Department of Mathematics are very familiar with doctoral candidates. If they think that a certain student is not capable of completing the selected topic, they will not hesitate to ask the student to change to a new topic.

As long as the doctoral students of Puda get the support of professors, they can usually get a PhD within two or three years, while it takes four or five years or even longer at Harvard.

Ouye completed her doctoral dissertation according to the usual routine. She obtained the PhD within two years and proved the Jesmanovich conjecture for the first time in the world.

Zhou Yu'an became a doctoral candidate in the Department of Mathematics of Princeton on the same day as Ouye. He received strong support from his tutor Figalli when he proposed the topic, but his writing collapsed in the middle and later stages, and he is currently overhauling his doctoral thesis.

Yu Lei and Ralph became doctoral students one year after Zhou Yu'an, and their doctoral thesis progress has caught up with or even surpassed Zhou Yu'an.

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

"Brother Xiao Yu, I have had a fulfilling and painful year in my Ph.D. You can't experience this feeling." In the past month, Yu Lei has been working day and night, and finally completed the task that Shen Qi entrusted to him. academic tasks.

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

"Under Xiao Qi's guidance, the part that Ralph and I are in charge of has been completely settled, and now we have to wait for news from Yanda and Morningside Mathematics Center." Yu Lei took a long breath, and learned a lot from following Shen Qi, but It was very hard work, 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 soon?" Zhou Yu'an asked.

Yu Lei nodded: "Yes, Brother Xiao Qi has registered for us in the department. After we return from California, we will participate in the doctoral defense."

"The two of you are too fast, and you can answer after one year of Ph.D.! Your tutor is awesome, and you can really do whatever you want." Zhou Yuan wiped off his sweat, and his tutor was obviously not as awesome as Shen Qi: "By the way, why are you going to California? "

Yu Lei said: "There is an academic conference in the field of algebraic geometry at Caltech. Xiao Qi took me and Ralph to study. It is a rare opportunity. The world's top algebraic geometry masters will go there."

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

The next day, Shen Qi, Yu Lei, and Ralph arrived in Pasadena, California, where the famous American research university Caltech is located.

Caltech on the west coast and Princeton on the east coast are similar in terms of school mission, believing in small but refined, not seeking big but comprehensive.

Princeton has a small number of students, and Caltech has even fewer students, with just over 6,000 students.

Caltech has a very high status in the eyes of the older generation of Chinese scholars. Before the 1960s, some of the most accomplished scholars in my country were basically 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 from Shanghai Jiaotong University to MIT as a professor, and found that the curriculum of Shanghai Jiaotong University was all copied from MIT, even the experiments were the same. The undergraduate teaching has reached the world's advanced level. A few years later, I went to Caltech as a professor, but found that some of the best courses at MIT were adapted from Caltech."

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

Except for the geneticist Tan Jiazhen, these meritorious scientists from Caltech are all physicists, and they are working on such big projects as "two bombs and one satellite".

Caltech's strongest majors are physics, chemistry, and astronomy, which has been the case for hundreds of years.

Mathematics is not Caltech's strong project, and it can even be said to be their shortcoming.

How can a research university that focuses on science and engineering lack mathematics?

Although our school's mathematics is weak, our school also has an ambition to boost its mathematical strength. This "International Algebraic Geometry Symposium" is arranged to be held at Caltech, which was requested by Caltech.

The conference paper submitted by Shen Qi to the Organizing Committee of the "International Symposium on Algebraic Geometry" is an abstract version, that is, a short and condensed version of "Hodge's Conjecture Algebraic Geometry Method". He believes that it is necessary to publish the latest research results of his team in public , the limelight cannot be robbed by Schultz.

Schultz has been very popular recently. He made reports all over the world, claiming that his team has proved the Hodge conjecture under special circumstances.

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

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

In the academic report hall of Caltech, the International Symposium on Algebraic Geometry was held as scheduled.

According to the arrangement of the meeting, Schultz was the first to make a report. 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 intently to Schultz's report, knowing themselves and the enemy, and the latest information is very important.

"...So, we prove that every harmonic-differential form on non-singular projective algebraic varieties of type β is a rational combination of the cohomology class of algebraically closed chains. The next thing we have to do is to prove that in the general case Hodge guessed that this work has already started and has made a breakthrough. Thank you, my report is over." Schultz's report was not long, ten minutes, and the report document was also a summary version.

There was thunderous applause from the audience, and someone asked, "Hey, Professor Schultz, when can we see all your research results?"

Schultz replied: "I believe that day will come soon, and right now, we must keep it secret."

Everyone applauded again, understanding, everyone understands, keep it secret.

Schultz is cautious while building momentum all over the world, because he knows that more than one team in the world is trying to overcome Hodge's conjecture, and the papers that have not been fully completed are published publicly.

There is no need to worry about academic plagiarism without any changes. Any mathematician with a little reputation will not do such a notorious thing.

But smart mathematicians know how to learn from other people's academic ideas and adapt them. This situation cannot be blamed, and they can only keep it secret.

"Schultz's report this time is nothing new compared to his last report in Munich." Yu Lei whispered.

"He defined β-type non-singular projective algebraic varieties in the abstract version, but he couldn't see the detailed proof process. I don't know if he didn't prove it at all, but he just guessed, or he didn't want to make it public?" Ralph said.

"As a competitor, we should think that Schultz has proved the Hodge conjecture under special circumstances, instead of questioning him." Shen Qi said.

At this time, the host of the conference said: "Professor Shen Qi will be invited to give a report on "Hodge's Conjecture Algebraic Geometry Method"!"

Shen Qi straightened the collar of his suit and shirt before going on stage, and the audience burst into even more enthusiastic applause.

"Yes, as you can see, I changed my major again, this time to algebraic geometry." Shen Qi's opening remarks caused a burst of laughter. He often changes majors, from number theory to functionals, to condensed matter physics and earth sciences. Solid state physics, turned back to mathematics, this time his goal is the hardest millennium problem Hodge conjecture.