Caltech Seminar
Princeton typically throws its graduate and doctoral students into a "river" and lets them swim to the other side to graduate.
Just as swimming aimlessly in a river is not an option, the most important thing for a doctoral student before writing their Doctoral Thesis is to find a qualified and capable professor to support their research.
Mathematics Department professors know their doctoral students quite well, and if they believe a student is not capable of completing their chosen topic, they will not hesitate to have the student switch to a new one.
At Princeton University, doctoral students can usually obtain their PhDs within two or three years if they have the support of their professors, while at Harvard it takes four or five years or even longer.
Ou Ye completed her Doctoral Thesis following the conventional path, and obtained her PhD within two years, becoming the first person in the world to prove the Yesmanovich Conjecture.
Zhou Yu'an and Ou Ye became doctoral students in the Princeton Mathematics Department on the same day. He received strong support from his advisor, Faltings., during the initial proposal stage, but his Doctoral Thesis fell apart in the later stages, and he is currently revising it extensively.
Yu Lei and Ralph became doctoral students a year after Zhou Yu'an, and their Doctoral Thesis progress has caught up with or even surpassed Zhou Yu'an's.
"A strong soldier makes one strong, a strong general makes an entire army strong." Zhou Yu'an admitted that Yu Lei following Shen Qi was correct.
"Little Brother Yu, my year of doctoral studies has been very fulfilling, but also very painful. You can't understand this feeling." In the past month, Yu Lei worked day and night, finally completing the academic task assigned to him by Shen Qi.
"So you've solved Hodge conjecture?" Zhou Yu'an asked.
"Under Little Brother Qi's guidance, Ralph and I have completely finished our part. Now we just have to wait for news from Yanda University and Morning Star Mathematics Center." Yu Lei breathed a sigh of relief. He could learn a lot from Shen Qi, but it was also very hard work. Fortunately, hard work pays off and his sweat was not in vain.
"So, you and Ralph will be able to participate in your doctoral defense soon?" Zhou Yu'an asked.
Yu Lei nodded. "Yes, Little Brother Qi helped us register with the department. After we returned from California, we will participate in our doctoral defense."
"You two are moving way too fast! You defended your dissertations after only one year of doctoral studies! Your advisor is amazing; he can really do whatever he wants." Zhou Yu'an wiped his sweat; his advisor was clearly not as impressive as Shen Qi's. "By the way, what are you two doing in California?"
Yu Lei said, "There's an academic conference on Algebraic Geometry at Caltech. Little Brother Qi took me and Ralph there to learn. It's a rare opportunity; the world's top Algebraic Geometry masters will be there."
"Yu Lei, here's a wrench, you can go now." Zhou Yu'an handed Yu Lei a wrench. They both lived in the doctoral student dormitory building, Yu Lei had come to borrow a wrench from him.
The following day, Shen Qi, Yu Lei, Ralph arrived in Pasadena, California, where the renowned American research university Caltech, is located.
Caltech on the West Coast and Princeton on the East Coast share similar educational philosophies, believing in small, high-quality education rather than large, all-encompassing institutions.
Princeton has a small student body, Caltech has even fewer, with just over six thousand students.
Caltech holds a very high position in the hearts of older generations of Chinese scholars. Before the 1960s, National First Prize were graduates of Caltech, such as Qian Xuesen, Zhou Peiyuan, Guo Yonghuai, Tan Jiazhen, Yuan Jialiu, and Qian Weichang.
In his memoirs, Qian Xuesen wrote, "In the autumn of 1935, I went from Shanghai Jiao Tong University to MIT as a professor and found that Shanghai Jiao Tong University's curriculum was completely copied from MIT's, even the experiments were the same. Therefore, Shanghai Jiao Tong University's undergraduate teaching at that time reached the world's advanced level. A few years later, I went to Caltech as a professor, but I found that some of MIT's best courses were adapted from Caltech."
There are many stories about Qian Xuesen, which Shen Qi is very familiar with. As he strolled around the Caltech campus, he imagined the demeanor of those meritorious scientists in China back then.
Apart from geneticist Tan Jiazhen, all these distinguished scientists from Caltech were physicists who worked on major projects like the "Two Bombs, One Satellite" program.
Caltech's strongest programs are physics, chemistry, and astronomy, and this has been the case for over a century.
Mathematics is not Caltech's strong suit; in fact, it could be considered their weakness.
How can a research university, primarily focused on science and engineering, be without mathematics?
Although our school's mathematics program is weak, we have the ambition to improve it. The fact that this "International Conference on Algebraic Geometry" was held at Caltech was at Caltech's own request.
Shen Qi submitted an abstract version of his conference paper to the organizing committee of the "International Conference on Algebraic Geometry," which was a short and condensed version of "The Algebraic Geometry Method of the Hodge conjecture." He felt it was necessary to publish his team's latest research results in public, so that Schultz wouldn't steal the spotlight.
Schultz is currently very popular, giving reports all over the world claiming that his team has proven the Hodge conjecture under special circumstances.
Regrettably and shrouded in mystery, no one has ever seen the full text of Schultz's paper on "the proof of the Hodge conjecture in special cases"; only an abstract version has been made public.
Schultz also visited Caltech to continue his global reporting.
The International Conference on Algebraic Geometry was held as scheduled in the Caltech Academic Hall.
According to the meeting schedule, the first speaker was Schultz, whose report was titled "A 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 your enemy and yourself is crucial; the latest intelligence is very important.
"... Therefore, we have proven that every harmonic differential form on a nonsingular Projective algebraic variety of class β is a rational combination of the cohomology classes of algebraic chains. Our next task is to prove the Hodge conjecture in the general case; this work has begun and has made groundbreaking progress. Thank you, that concludes my report." Schultz's presentation was short, only a dozen minutes, and the report document was also an abstract.
The audience erupted in applause, and someone asked, "Hey, Professor Schultz, when can we see all your research findings?"
Schultz replied, "I believe that day will come soon, and for now, we must keep it a secret."
Everyone applauded again. They understood, they all understood, it was a secret.
While Schultz was campaigning globally, he remained cautious because he knew that more than one team was working on the Hodge conjecture. If his incomplete paper was published and stolen, who could he complain to?
There's no need to worry about academic plagiarism that's completely copied word for word; no mathematician with even a modicum of fame would do something that would bring them eternal infamy.
However, clever mathematicians know how to borrow and adapt the academic ideas of others, and this cannot be criticized; they can only keep it confidential themselves.
"Schultz's report this time is nothing new compared to his last report in Munich," Yu Lei said softly.
"He defined a beta-class nonsingular Projective algebraic variety in the abstract, but there is no detailed proof. I wonder if he didn't prove it at all and was just guessing, or if he didn't want to make it public?" Ralph said.
"As competitors, we should consider that Schultz has proven the Hodge conjecture in a special case, rather than questioning him," Shen Qi said.
At this point, the conference host announced, "Next, please welcome Professor Shen Qi to give a report on 'Algebraic Geometry Methods for the Hodge conjecture'!"
Shen Qi straightened the collar of his suit and shirt before going on stage, whereupon the audience erupted in even more enthusiastic applause.
"Yes, as you can see, I've changed my major again, this time it's Algebraic Geometry." Shen Qi's opening remarks elicited a burst of laughter. He often changes his major, from number theory to functional theory, then to Condensed Matter Physics and Solid State Physics, and finally back to mathematics. This time, his goal is the most difficult Millennium Prize Problem, the Hodge conjecture.