Scholar’s Advanced Technological System

Lu Zhou originally thought that he was used to this feeling.

The unexpected thing was that when he stood here, it was still difficult to restrain the surging tide.

Unlike the report of the Auditorium of the Princeton Institute of Advanced Studies, this time he faced not only the theory of numbers, but the entire mathematics world…

Standing on the report desk, Lu Zhou took a deep breath and calmed her heart rate.

The Nth looked towards the watch.

Looking at the second hand that is getting closer and closer, his face is replaced with a serious expression, and his spirit is uplifted.

“Get started!”

Nine o’clock.

There is no need for people to maintain discipline. When the time reaches the hour, the venue that was originally noisy and confusing because of the whispering discussion will be quiet in an instant.

Under the eyes of the public, a clear line of headlines emerged in the silver white curtain.

[Proof of the existence and smoothness of solutions for three-dimensional incompressible Navier-Stokes equations]

In response to the pair of sights, Lu Zhou slowly opened his mouth and began the opening remarks of the report.

“Why doesn’t the high-speed car disintegrate itself, why doesn’t the static lake suddenly explode?”

“For a long time, we have been plagued by obvious things, because the truth we are craving is always covered with obvious disguise.”

“Even as early as the 19 century, we have summed up the equations that generalize the laws of fluid motion and make it seem succinct enough. However, to this day, we are still unable to understand the profound mathematical and physics connotations behind the equations. ”

“Mathematics is a rigorous subject that involves the proposition of numbers and should not be described in words that may or may not be so ambiguous.”

“Return to the original question, why does the high-speed car not self-decompose? Why does the stationary lake not explode suddenly? Is there a mysterious singularity on an infinite time scale that allows our equation to diverge in a limited time? ?”

“Now, it’s time to answer this question.”

At the end of the brief opening, the PPT on the curtain opened the next page.

The report meeting also entered the topic.

In three seconds, Lu Zhou quickly sorted out the idea of ​​speaking in the brain. Then he faced the audience and made a brief overview of his proof of the idea in a minute.

The audience listened to absolute silence.

Everyone stares at the photographs and calculations on the screen, and everyone listens carefully, not willing to let go of any details, and is unwilling to miss any moment.

[μ(t)=e^(t△)・μ0+∫e^(tt”)△B(μ(t’), μ(t”))dt”]

[…]

“When we give a Schwarz-free divergence vector field μ0 to the equation, set the time interval I?[0,∞), and then we can continue to define a generalized solution of the Navier-Stokes equation H10 as an obeying integral equation μ(t Continuous mapping of μ→H10df(R3)…”

The PPT in the curtain was shown on the side, and Lu Zhou, holding the laser pointer in his hand, explained it at a uniform speed.

There is nothing special to explain in the previous section.

A lot of similar things can be seen in thesis on the study of NS equations.

Whether using the abstract proof method to construct the abstract double Linear operation B”, or the “L manifold” method he uses, this part is essential.

However, the next part is the key to the whole proof!

He introduces the concept of differential manifolds into the problem of partial differential equations.

And this is the core of the theory of using topological methods to study partial differential equations!

……

Under the stage, Xu Chenyang was dignified, and the nib in his hand was lightly lit on the notebook.

After a while, he whispered to Zhang Wei, who was sitting next to him, with a voice that only two people could hear.

“Do you understand?”

Zhang Hao shook his head: “My research on partial differential equations is not much more than you. If you start to feel strenuous, then I am almost the same.”

Zhang Wei is good at his direction and is similar to his mentor Zhang Shouwu. He focuses on the theory of representation, the Langlands program, and his research on Dickley Lfunction.

The partial differential equation is not an area he is good at. He has only learned about the NS equation because of his interest.

After all, it’s impossible for everyone to be as genius as Tao Zhexuan, and to prove the weak proof of Goldbach’s conjecture, while studying the abstract proof of the NS equation, and even taking time to read the new sis of the moon…

In the mathematics world, all is not without.

But it is even rarer than the giant panda…

Looking at the calculations on the curtain, Xu Chenyang couldn’t help but feel: “It’s incredible…”

Zhang Wei: “What is unbelievable?”

Xu Chenyang: “Number theory, abstract algebra, functional analysis, topology, differential geometry, partial differential equations… and what direction is he not good at?”

“Perhaps… algebraic geometry?” When he said this, Zhang Wei’s voice was full of uncertainty.

Because this sentence he just said, he thought of Lu Zhou’s mentor is Pierre Deligne, the ancestor is the legendary “father of modern algebraic geometry”, “the pope of mathematics” Alexander Grothendieck!

The core theory of modern algebraic geometry is basically derived from several books that have not been lost by Alexander Grothendieck.

To say that he does not have algebraic geometry, Zhang Wei is killed or not believed.

At most, I haven’t researched that piece yet, and the results are still brewing…

……

On the stage, the report will continue.

Lu Zhou’s speed of speech is getting faster and faster, and his ideas are getting clearer and clearer.

The introduction of the L manifold has played a decisive role in the resolution of the entire proposition.

It is like a hammer with the same handle, and a gap is opened on the unbreakable labyrinth wall.

With the arrival of this moment, the confusing situation has become clear and clear.

At the same time, the atmosphere in the venue was pushed to the high chao.

Sitting in the corner of the venue, Fefferman smiled on his face, and from this moment he had seen the last.

Tao Zhexuan on the other side of the venue whispered “originally is this way” in his mouth, and his eyes sparkled with excitement.

In the back row of the venue, I felt the enthusiasm in the atmosphere. Vera pinched the right hand, and the originally calm heartbeat began to accelerate. At this moment, she is proud of her mentor from the heart…

Also sitting in the back row of the venue, Faltins’s tight mouth, suddenly evoked an uncommon angle.

I noticed the change in the expression on the face of the old friend, Pierre Deligne asked casually.

“how are you feeling?”

Faltins expressionlessly said: “General.”

“Do you not blush when you say this?” Pierre Deligne faintly laughed, and he sent his own meeting before, and returned it intact.

The mouth twitched a bit, Fartings ignored the old friend’s teasing, looked at the watch, and slowly stood up.

Pierre Deligne: “It’s almost over, don’t you see the last?”

“Nothing is necessary.”

Anyway, I have fully understood.

Bored questions, or leave it to others to say hello.

Leaving this sentence, the Faltins Professor did not stop, and the crowd who sat on the aisle and walked straight to the exit of the venue.

And almost at the moment when Faltins Professor left the lecture hall, the whole report also ushered in the final end.

When the last line of calculations was reflected in the audience, almost no further explanation was required from Lu Zhou.

Because as the audience heard, the final answer is already coming out.

“… Combining all the above inferences, the results are already obvious, the solution of the three-dimensional incompressible Navier-Stokes equation exists and is as smooth as we expected!”

That voice, clear and sure.

Although not Hongling, it carries a convincing magic.

And the source of the magic is knowledge.

Almost in the moment when the voice falls.

The audience stood up from the seat.

The thunderous applause, which echoed in an instant, was endless in this wide and crowded lecture hall…