The next day, Lu Zhou finished his retreat and went to his office at the Princeton Institute for Advanced Study.
As usual, his students were all here.
When they saw Lu Zhou at his office door, everyone had a surprised look on their faces.
The first to speak was Vera.
The little girl opened her mouth and said, "Professor, you're done with your retreat?"
"Sort of …" Lu Zhou looked at Vera, then at Hadi. He could see the shock on his students' faces. He asked, "Why are you guys looking at me like that?"
Jerick, who was sitting not far from Hadi, whispered, "Because you usually come out of your room because you've succeeded …"
Wei Wen said, "Which means, you've solved the Millennium Prize Problem of the Navier – Stokes equations?"
"No, but I have some in-progress results." Lu Zhou paused for a second and said, "But that's not why I'm here today. I'm here to talk about the Collatz conjecture."
Qin Yue, who hadn't spoken yet, asked, "Did Annual Mathematics reply?"
"Yes, your thesis was done very well. Professor Peter Sarnek, who reviewed your thesis, spoke very highly of you." Lu Zhou smiled and said, "Your thesis will be published in the latest edition of Annual Mathematics."
When Vera and the others heard that Peter Sarnek was the reviewer, they were all surprised.
In the modern mathematics world, Professor Sannek could be said to be one of the leaders in modern number theory. They had been in Princeton for a long time, so it was impossible that they hadn't heard of this big name.
Not only that, but this big name was also the editor of Annual Mathematics. He was one of the six reviewers for Lu Zhou's "Goldbach – Lu Zhou theorem" thesis. His name was on one of the reviewers.
Lu Zhou paused for a second before he spoke.
"Like I said before, the proof of the Collatz conjecture will be your graduation thesis. Although I originally only hoped that you could make some small progress based on the research of your predecessors, I didn't expect you to be able to completely prove the conjecture. I have to say, your performance really surprised me. "
Qin Yue smiled embarrassedly and said, "It's all thanks to the mathematical tools you provided. We couldn't have done it by ourselves."
Lu Zhou shook his head. "Whether the tool is good or not, it needs a smart person to use it. You guys are very talented, so don't belittle yourselves. I also wish that you guys can continue on the road of number theory in the future and achieve greater achievements in the field of additive number theory. "
After a pause, he straightened his expression and continued.
"From today onwards, all of you have graduated!"
Pa pa pa pa —
Jerick and Wei Wen clapped in the office.
Wei Wen, in particular, looked at Qin Yue with envy.
To be able to publish a thesis in a top journal like Annual Mathematics, and it was a thesis on the Collatz conjecture …
It wasn't an exaggeration to say that once the thesis was published, his name would definitely appear on the list of the Thousand People Initiative.
Whether Qin Yue wanted to continue his studies or return to China to teach or engage in academic research, the universities in China would offer him an irresistible price tag.
After pausing for a second, Lu Zhou looked at his three students and said, "I want to hear your plans for the future."
Regardless of whether his students planned to continue their studies or work at a research institute or university, he would do his best to provide them with help.
For example, write a recommendation letter or something.
In academia, a recommendation letter signed by a well-known scholar often played a crucial role in an interview. Even if the interviewer didn't have a good first impression of the interviewee, they would still seriously consider the recommendation letter …
Hadi smiled and said, "Professor, if you're still willing to take me in, of course I'm willing to continue my studies here."
Lu Zhou said, "Why wouldn't I want to? If you want to apply for a PhD, I welcome you. "
Even though Hadi's student was a bit naughty, he was still quite capable.
Anyone who applied for a master's degree in Princeton's mathematics department was basically a genius in their respective fields. The so-called strength difference was only the difference between the strong and the stronger.
Other than Hadi, Vera had already told Lu Zhou about her plans. She even handed him the application form. Needless to say, Qin Yue also planned to continue his studies at Princeton.
All three students chose to continue their studies. After the relevant procedures were completed, Lu Zhou's research team in Princeton would have one computational materials postdoc, three PhDs, and two master's students.
As for whether or not he should recruit a few more students …
That would depend on the quality of the new students and whether or not there were enough talents that he was interested in.
After the students were settled, Lu Zhou made an appointment with Professor Fefferman.
Regarding the research results of the past month, he had a lot of things that he needed to communicate with this partner of his …
…
A conference room with a blackboard at the Institute for Advanced Study.
After Professor Fefferman looked at Lu Zhou's manuscript, he rubbed his chin with his finger and spoke.
"Micromanifold manifold … Interesting."
Compared to abstract proof methods, using differential manifolds to study the Navier – Stokes equations was undoubtedly a novel idea. Introducing a topology method to partial differential equations seemed feasible.
However, Professor Fefferman had never done research in this area, so he couldn't give Lu Zhou a positive or negative answer.
Professor Fefferman read the thesis from beginning to end. He looked up at Lu Zhou and asked, "How did you think of this?"
Lu Zhou: "I was inspired when I was jogging near Lake Carnegie."
Professor Fefferman looked at Lu Zhou with surprise and said, "That's surprising … Looks like I have to go there more often in the future."
Lu Zhou didn't respond. Instead, he went straight to the point and asked, "What do you think about this method?"
"I don't know. I admit that the idea you provided is interesting, but I still prefer abstract proof methods." Professor Fefferman sighed and picked up a piece of chalk to write on the blackboard. He said, "Over the past month, I've tried to improve the bilinear operator B 'that we previously constructed. This construction is very close to the Euler linear operator B in μ (t)."
[μ (t) = e ^ (t △) · μ0 + (e ^ (t-t ') △ B (μ (t'), μ (t ')) dt']
[…]
The calculation process was similar to a month ago, and the entire calculation framework was the same.
The only difference was the construction of the B 'bilinear operator that satisfied the elimination property = 0. Professor Fefferman used a clever method to construct the B 'that was very close to the original operator B.
However …
Lu Zhou felt like something was missing.
Lu Zhou recalled the discussion from more than a month ago and compared it to the steps presented in front of him. He suddenly frowned and felt a sense of unnaturalness from the calculations …
Lu Zhou stared at the blackboard for a long time before he suddenly spoke.
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