The next day, Lu Zhou, who had finished his retreat, came to the office of the Institute for Advanced Study in Princeton.

As usual, his students are here.

When Lu Zhou appeared at the door of the office, everyone's faces showed a surprised expression.

The first to speak was Vera.

The little girl opened her mouth slightly and said in a surprised tone, "Professor, is your retreat over?" ”

"Sort of...... Glancing at Vera, and then at Hardy next to him, reading the shock from the students' faces, Lu Zhou couldn't help but ask suspiciously, "Why are you looking at me like this?" ”

Jericho, who was sitting not far from Hardy, whispered, "Because usually you are willing to come out of the house, most of the time you succeeded......"

Wei Wen looked solemn: "In other words, the millennial problem of the NS equation...... You've already figured it out? ”

"No, but there have been some phased results," after a pause, Lu Zhou continued, "But what I'm here today is not about this, but about the subject of our Kakutani conjecture. ”

Qin Yue, who had not spoken, opened his mouth and asked, "The Annals of Mathematics has already replied?" ”

"Yes, your paper is excellent, Professor Peter Sanek, who reviewed your paper, and he has a very high opinion of you," Lu Zhou nodded with a smile, "Your paper will soon be published in the latest edition of the Annals of Mathematics." ”

When they heard that the reviewer was Peter Sanek, Vera and the others had surprised expressions on their faces.

In the field of contemporary mathematics, Professor Sanek can be said to be one of the leading figures of modern number theory. After being in Princeton for so long, it was obviously impossible for them not to have heard the name of the big bull.

Not only that, but he is also the editor of the Annals of Mathematics, and his name was included in Lu Zhou's paper on "Goldbach-Lu theorem".

After a pause, Lu Zhou continued.

"As I said before, the proof of Kakutani's conjecture is your graduation thesis. Although I had hoped that you would make a small improvement on the research of your predecessors, I did not expect that you would be able to prove the whole conjecture in its entirety. I have to say, you guys really surprised me. ”

Qin Yue smiled embarrassedly: "Mainly thanks to the mathematical tools you provided, it is impossible to do it with our strength alone. ”

Lu Zhou shook his head: "No matter how good the tool is, it needs a smart person to use it." You are very talented, there is no need to be presumptuous, and I also wish you that you can continue on the road of number theory in the future and make greater achievements in the promising field of additive number theory. ”

After a pause, he looked slightly furnished and continued.

"Starting today, you've graduated!"

Bang Bang Bang -

There was applause in the office, and it was Jericho and Wei Wen who applauded.

Wei Wen, in particular, looked at Qin Yue with envious eyes.

Able to publish a paper in a top journal such as the Annals of Mathematics, and it is also a paper on the proof of major mathematical propositions such as the "Kadotani Conjecture......

It is no exaggeration to say that as soon as the paper is published, his name will definitely appear on the list of the Thousand Talents Project.

Whether Qin Yue plans to continue his studies or return to China to teach and engage in academic research, domestic universities will offer prices that most people cannot refuse.

After a pause, looking at his three students, Lu Zhou continued, "Regarding your future, I would like to hear your plans. ”

Whether his students are planning to continue their studies, graduate school or university, he is there to help them within his means.

For example, write a letter of recommendation or something.

In academia, a letter of recommendation signed by a well-known scholar can often play a crucial role in an interview. Even if the interviewer's first impression of the interviewee is not good, the referee's opinion will be carefully considered......

Hardy smiled embarrassedly, "Professor, if you are still willing to take me in, of course I am willing to continue my studies with you." ”

Lu Zhou said with a pleasant face: "Why don't you want to? If you want to apply for my Ph.D., of course I welcome you. ”

Although Hardy's student is a little skinny, his ability is still okay.

Those who can apply for a master's degree in Princeton's mathematics department are basically strong people who are extremely talented in their respective research fields, and the so-called strength gap is just the difference between strong and stronger.

In addition to Hardy, Vera's plan had already been told to Lu Zhou a year ago, and even the application form had been handed over to him. Needless to say, Qin Yue also intends to continue his studies at Princeton.

After completing the relevant procedures, Lu Zhou's research team at Princeton will become a postdoctoral fellow in the direction of computational materials, as well as three PhDs and two masters.

As for whether to recruit a few more students......

It depends on the quality of this batch of freshmen, and whether there are enough talents to arouse his interest.

After the students' affairs were arranged, Lu Zhou made an appointment with Professor Feverman.

He had a lot to share with his partner about the results of the past month or so......

……

A meeting room with a blackboard at the Institute for Advanced Study.

After reading Lu Zhou's manuscript paper, Professor Feverman's index finger rubbed the stubble on his chin and said thoughtfully.

Differential Manifold...... It seems to be kind of interesting. ”

Compared with the abstract proof method, the use of differential manifolds to study the NS equation is undoubtedly a novel idea. Introducing topological methods into partial differential equations seems to be a feasible idea.

But Professor Feverman has not done this research, so he can't immediately give Lu Zhou a yes or no answer.

From the beginning to the end of the paper on the manuscript paper, Professor Feverman raised his eyes and looked at Lu Zhou: "How did you come up with the idea?" ”

Lu Zhou: "I was inspired when I was running next to Lake Carnegie. ”

Professor Feverman glanced at Lu Zhou in surprise: "That was really surprising...... Looks like I'm going to have to go there more in the future. ”

Lu Zhou didn't answer, but asked straight to the point: "What do you think about this method?" ”

"I don't know, and I'll admit it's an interesting idea, but I'm leaning towards the abstract proof approach." Professor Feverman sighed, picked up the chalk and continued to write on the blackboard, "For more than a month, I have tried to improve the bilinear operator B that we constructed earlier, and this construction quantity is very close to Euler's linear operator B in μ(t). ”

【μ（t）=e^（t△）·μ0+∫e^（t-t）△B（μ（t‘），μ（t））dt】

【……】

The process of calculus is very similar to that of more than a month ago, and the framework of the whole calculation is still the same.

The only difference is in the construction of the B bilinear operator satisfying the elimination of 〈B(μ,μ), μ〉=0. Professor Feverman uses a very ingenious method, and the new construction B is already very close to the original operator B.

However......

It always feels like there's something missing.

Recalling the discussion more than a month ago, and then comparing the steps presented in front of him, Lu Zhou suddenly frowned slightly, and read a trace of unnatural disobedience from those calculations......

After staring at the blackboard for a long time, Lu Zhou suddenly spoke.

"I see, I know what's wrong......"

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