Glancing at Qin Yue suspiciously, Lu Zhou felt that this usually dull and honest guy seemed to be hiding something from him.
A girl with long chestnut hair immediately raised her hand.
Professor Fefferman is a researcher at Princeton University and the chairman of the Department of Mathematics at Princeton University. He is an old man who looks kind-hearted and greets everyone with a smile.
"...Based on the above conclusion, we can obtain the overall existence of smooth solutions to the three-dimensional incompressible Navier-Stokes equation under limited circumstances."
Hardy was stunned for a moment: "Probably... no."
Hardy and Jericho brought a two-person-high fishbone pine from outside and put it together with the cardboard boxes containing lights and ribbons in the corner of the office.
Standing on the podium, Lu Zhou spoke heartily.
About a third of the people in the classroom nodded.
This was already the last class, and Lu Zhou felt that he should still fulfill his duties as a professor.
"As for how to generalize this conclusion to a more general conclusion, further research is needed."
Regarding this unexpected question, Lu Zhou smiled and said.
However, this is not because of the shock brought by the tens of millions of dollars, but because there is nothing to discuss next.
Looking at the time on his watch, Lu Zhou saw that there was still a lot of time before get out of class ended, so he looked at his students and said.
…
Holding Hardy's mouth firmly, Qin Yue squeezed out a smile on his face: "Nothing!"
At Hardy's suggestion, everyone unanimously decided to decorate the office in a more festive atmosphere on Christmas Day.
“…can I use the whiteboard?”
"Professor, are you studying the NS equation?"
"Okay then," Lu Zhou erased the content on the whiteboard and wrote a new title. "In the second half of the class, I will talk about my personal understanding of the three-dimensional incompressible Navier-Stokes equation."
The entire engineering design plan has been clearly discussed in more than a month, and the complex physical details and engineering problems have also been solved during the discussion.
But he was surprised by this person's identity.
Lu Zhou asked again and again: "Really?"
But for the students in the audience, it is not so friendly.
After the theoretical work came to an end, Lu Zhou suddenly and unexpectedly found that in the last two weeks, the most stressful and critical period, he had become more relaxed. At least there was nothing more for him to do until the equipment arrived.
However, this does seem a bit like something a professor can do.
[B(μ,v)=-1/2P{(μ·▽)μ+(v·▽)μ｝]
Studying for a master's degree under the "legendary" Professor Lu is quite attractive to these geniuses who pursue climbing higher mountains in mathematics.
"In order to deepen your understanding, I hope that during the remaining time, you can think about a question. It is not difficult, but it should be interesting."
Anyway, he has time these days. If he delays it further, he may not have time anymore.
In the last class before Christmas, Lu Zhou took his textbook and came to the lecture theater for the first time in a long time.
Revisiting some basic content can reexamine whether the obvious questions are really obvious.
Lu Zhou smiled: "Of course, I will prepare a special Christmas gift for all of you."
For those students who have not yet started learning partial differential equations, or whose understanding is not in-depth, what Lu Zhou talks about is almost the same as the Bible.
I am ashamed to say that I am too busy this semester. Not long after I returned from being a visiting scholar at Columbia University, I immediately boarded a flight to Germany.
Hardy's face was filled with joy and he immediately asked enthusiastically: "Professor, do we have any Christmas gifts?"
Lu Zhou, who was writing at his desk, stopped writing. After thinking for a moment, he replied: "It should be possible unless something unexpected happens."
Lu Zhou glanced around the classroom.
After the research funding of 10 million US dollars was received, no one had any doubts about the project, and no one doubted whether Lu Zhou's mathematical ability could really process electromagnetic wave messages that looked no different from "noise".
Although they didn't know what it was, the expressions on everyone's faces were obviously looking forward to it.
Especially when expressing abstract concepts that are difficult to express in words, Lu Zhou himself was also reviewing the thoughts generated during the research.
With Professor Lu's ability, this promise can be easily fulfilled.
"Where P is the Leray projection of the divergence-free vector L... What we are asking for now is the equation Pμi with a square-integrable solution."
Looking at these students who were lost in thought, just when Lu Zhou was about to write down his email address on the whiteboard and leave this question until after class, a hand suddenly raised from the corner of the back row of the lecture theater.
…
In fact, even the sound of the meeting was much quieter.
This is really shocking!
There was a commotion in the office.
After entering the classroom, Lu Zhou felt a little embarrassed when he saw the unexpected expressions in the students' eyes.
Of course, there were also people with worried expressions on their faces.
But it doesn't matter, Christmas will be here in two weeks anyway.
Wiping the sweat from his forehead, Hardy straightened up and suddenly realized that Lu Zhou, who had rarely been in the office recently, was actually here today, so he said hello.
Jericho tilted his head, looked at Hardy and whispered: "Isn't the gift a math problem?"
Looking in the direction of the raised hand, Lu Zhou had a look of surprise in his eyes.
"Any questions?"
With that said, Lu Zhou picked up the marker and continued writing on the whiteboard.
[…]
While writing on the blackboard, Lu Zhou was giving a concise explanation at the same time.
Obviously this "problem" is not that simple to solve.
Lu Zhou smiled and nodded: "Of course."
So much so that the students who chose this course because of him have not seen him even a few times throughout the semester.
For these geniuses who can often question professors.
Hardy whistled, but was quickly held down by Qin Yue.
The most critical issue now is to implement what has been discussed.
"Professor, Christmas is coming soon, will you spend it with us?"
"...Today's course is about Mersenne prime numbers. I will mainly talk about the distribution rules of Mersenne prime numbers and the derivation and application of Lu-Zhou theorem. This part is not the focus. You can listen and relax. Anyway, I guess what you are thinking now It’s already flying to Santa Claus.”
It's not surprising that someone came up with an idea so quickly.
Although Lu Zhou said this in a joking tone, the students present obviously did not really take it as a joke.
Because these students had already previewed the lesson, and because it was the result of his own research, Lu Zhou spoke very quickly, finishing the entire course in less than twenty minutes.
She didn't care what the gift was. She stopped writing in her hand and looked at Lu Zhou expectantly: "Do I have one too?"
Because the holiday is approaching, the classroom is full of impetuous atmosphere.
He never treats his students favorably.
Lu Zhou asked, casting questioning glances at the two of them.
Perhaps because of the mysterious smile on his face, almost all the students nodded curiously this time.
Although Lu Zhou gave them a holiday, no one seemed to plan to go back this Christmas.
Of course, he did not expect these undergraduates to give an answer, but he hoped that listening to these students' ideas might bring some inspiration to his research.
Institute for Advanced Study in Princeton.
Strictly speaking, this is not a question, but a problem in the field of partial differential equations that he encountered while studying NS equations in the past two days.
Hearing the students' good-natured laughter, Lu Zhou wrote the title of the course on the whiteboard with a marker and continued talking to his students in a casual tone.
Most of the newly revised domestic textbooks use the term Zhou's theorem to replace Zhou's conjecture. However, after Lu Zhou came to Princeton, he found that he flipped through several number theory textbooks, and they all used the term "Lu-Zhou theorem" or "Zhou--" "Lu Theorem" is described.
[〈B(μ,v),w〉=-1/2∫R cube{((u·▽)v)w+(((v·▽)u)·w｝dx]
In order to avoid interference between the accelerator's confinement magnetic field and the plasma's confinement magnetic field, they had to drill a hole in the laboratory floor wall, extend the launch trajectory that allowed the particles to pass, and place the "magazine" of the atomic gun farther away. room to go…
"There is still a little time left in this class. If you have any questions, you can ask me."
[… Pμi=?]
"Many people are very curious," the girl blinked, and asked, "We are also very curious."
Lu Zhou nodded to her, indicating that she could get up and ask questions.
All the answers will be revealed that day.
It seems that whether students are in American or Chinese universities, whether they are mediocre or talented students, they all feel the same about the holidays.
Lu Zhou actually prepared Christmas gifts for them
The man sitting in the back row of the classroom is none other than Professor Fefferman, the chairman of the mathematics department of Princeton University whom he mentioned earlier.
After writing the last character, Lu Zhou gently placed the marker on the multimedia desk, looked at the students in the classroom who were deep in thought, and said in a joking tone.
"Are you curious?"
"If any one of you solves this problem, I will convince Professor Fefferman for him and allow him to graduate early and come directly to me to study for a master's degree or a doctorate."
Even though Princeton's undergraduate students are very strong, and many of them have completed all the undergraduate content in their sophomore year, it is still difficult for them to fully absorb the content written on the whiteboard.
"Why ask this question?"
Even Hardy, who always gave him a headache, he prepared a gift for him.
There was a dead silence in the lecture theater, and everyone was racking their brains for thinking.
But compared to his ease, it was a hardship for the engineers.
Her cheeks were slightly red, and Vera said sheepishly: "...I also prepared a gift for you."
emmm…
However…
This is again for students who have an in-depth understanding of partial differential equations.
Hardy, who was originally very excited, is now a little panicked...