Scholar's Advanced Technological System Chapter 381


Chapter 381 The Last Number Theory Lecture Before Christmas

Translator:Henyee TranslationsEditor:Henyee Translations

After the US$10 million research fund was received, no one else had any doubts about the project or Lu Zhous mathematical abilities.

Even the project meetings were quieter.

However, it wasnt quite because of the sudden US$10 million; it was because they didnt have anything to discuss.

The entire engineering design had been clearly outlined; all of the complex physics and engineering problems were already solved.

Right now, the most important problem was implementation.

The theoretical work was complete. Suddenly, Lu Zhou realized that in these two most crucial and intense weeks, he had somehow relaxed. There was nothing else for him to do, at least not before the equipment arrived.

However, the engineers had no time to relax.

In order to prevent the accelerator magnetic field from interfering with the magnetic field of the plasma, they had to drill a hole in the laboratory wall and place the atomic gun further away from the orbit path

Princeton Institute for Advanced Study.

Hardy and Jerick dug out a two-meter tall Christmas tree and placed it next to the decoration boxes in the office.

Although Lu Zhou gave them a Christmas holiday, no one wanted to take a vacation.

Everyone agreed to Hardys proposal of decorating the office for Christmas.

Hardy wiped the sweat off his forehead and stretched his back. He suddenly noticed Lu Zhou, who rarely came to the office, was in the office. Therefore, he greeted him.

Professor, will you spend Christmas with us?

Lu Zhou was writing at his desk, and he stopped writing and said, I should.

Hardy was delighted, and he immediately asked, Then professor, do we get Christmas presents?

Lu Zhou smiled and said, Of course, Ill prepare a special Christmas gift for all of you.

The office was suddenly intrigued.

Lu Zhou would prepare a Christmas gift for them?

Although they didnt know what the gift was, everyone was obviously looking forward to it.

Of course, some people also looked worried.

Jerick turned to Hardy and whispered, The gift isnt a math problem, right?

Hardy said, Probably not.

However, this seemed like something Professor Lu Zhou would do.

Hardy wasnt so excited anymore

Vera stopped writing and looked at Lu Zhou as she asked, Do I get one as well?

Lu Zhou smiled and said, Of course.

Lu Zhou would never cheap out on his students.

He even prepared a gift for the troublemaker Hardy.

Vera was blushing slightly as she said, I also prepared a gift for you.

Hardy started to whistle but was stopped by Qin Yue.

Lu Zhou looked at them and asked, Is there a problem?

Qin Yue covered Hardys mouth and said, Nothing!

Emm

Lu Zhou looked at Qin Yue suspiciously and felt like this normally honest guy was hiding something from him.

But that didnt matter; Christmas was in two weeks anyway.

All of the mysteries would be revealed.

On the last lecture before Christmas, Lu Zhou brought his textbook to the lecture hall.

It was almost the holidays. Therefore, the classroom was full of energy.

Just like the Chinese students, it seemed that American students felt the same way about holidays as well.

Lu Zhou walked into the classroom and when he saw the surprised looks on his students faces, he felt a little embarrassed.

Lu Zhou was very busy this semester. After he returned from Columbia University, he had to fly to Germany.

Therefore, the students that chose this course because of him barely got to see him.

Since this was the last lecture, Lu Zhou felt like he should perform his duties as a professor.

He had some free time anyway.

Todays lecture is about Mersenne primes, I will mainly talk about the distribution of Mersenne primes and the derivation of the Lu Zhou theorem. This isnt the main course material, so you can just relax and listen. Im guessing your minds are on Santa Claus right now.

The students chuckled, and Lu Zhou wrote down the title of the lecture on the whiteboard. He continued to talk with his students in a relaxing manner.

Most of the Chinese textbooks replaced Zhous conjecture with Zhous theorem. However, after Lu Zhou came to Princeton, he found several American textbooks that used Lu-Zhou theorem, or Zhou-Lu theorem.

Because these students had already studied the lecture material beforehand, and because Lu Zhou was talking about his own research, Lu Zhou spoke very quickly. It took him less than twenty minutes to finish the lecture content.

Lu Zhou looked at the time on his watch and saw that there was a lot of time left. Therefore, he looked at his students and said, Theres still a little time left, feel free to ask me any questions.

A girl with maroon hair immediately raised her hand.

Lu Zhou nodded at her, indicating that she could speak.

Professor, are you researching the NavierStokes equations?

Lu Zhou smiled at this unexpected question.

Why do you ask this?

A lot of people are curious, the girl blinked and said, and were also curious.

Lu Zhou looked around the classroom.

Are you guys curious?

A third of the students in the classroom nodded.

Lu Zhou asked again, Really?

Perhaps it was because of Lu Zhous mysterious smile because everyone in the classroom nodded this time.

Okay then, Lu Zhou said as he wiped the whiteboard and wrote down a new title. He then said, For the second half of the class, I will talk about my personal understanding of the three dimensional incompressible Navier-Stokes equation.

Revisiting fundamental concepts was a good way of finding obvious problems.

Lu Zhou was reminiscing about his research ideas, especially those abstract concepts that were difficult to express in words.

Lu Zhou lectured his heart out.

However, the students didnt have such a good time.

Princeton undergraduate students were talented, and most of them had completed all of the undergraduate content while they were in their second year. However, it was still difficult for them to understand the concepts on the whiteboard.

Even students that had a deep understanding of partial differential equations had trouble understanding them.

For those that hadnt learned about partial differential equation yet, it was as if Lu Zhou was speaking in a different language.

These students were geniuses that often went hand to hand with professors.

This really humbled them!

According to the above conclusion, we can calculate the global existence of the smooth solution of the three-dimensional incompressible Navier-Stokes equation in a finite case.

As for extending this conclusion to a more general case, more research is needed.

I hope that you can think about this problem in your spare time. It isnt difficult, but it is very interesting.

Lu Zhou picked up a marker and wrote on the whiteboard.

[

[B(,v) = -1/2P{()+(v)}

[]

Strictly speaking, this wasnt a practice question; this was a partial differential equation problem that Lu Zhou ran into when he was studying NavierStokes equations.

He obviously didnt expect the undergraduate students to give an answer. Instead, he wanted to listen to the students thought process for inspiration.

Lu Zhou wrote and explained at the same time.

Where P is the Leray projection without the divergence vector L We now asking searching for the equation Pi with a square-integrable solution.

[ Pi=?]

Lu Zhou finished writing the last symbol and placed the marker on the lecture stand. He then looked at the students as he spoke in a joking tone.

If anyone one of you can solve this problem, I will recommend them to Professor Fefferman for early graduation, or you can study a masters or even a PhD under me.

Professor Fefferman was not only a researcher at the Princeton Institute for Advanced Study, but he was also the head of the mathematics department at Princeton University.

Although Lu Zhou spoke as if he was joking, the students didnt take it as a joke.

Professor Lu definitely had the ability to let them graduate early.

Studying a masters degree under the legendary Professor Lu was an attractive option.

The lecture hall went dead silent; everyone was thinking.

However

This question obviously wasnt easy to solve.

Lu Zhou looked at the students and wrote down his email on the whiteboard. Suddenly, in the back corner of the lecture hall, someone raised their hand.

Can I use the whiteboard?

Lu Zhou looked at the raised hand and was surprised.

He wasnt surprised that someone was attempting to solve the question.

He was surprised at who this person was.

The person sitting in the back row of the lecture hall was none other than Professor Fefferman.