"Maybe... algebraic geometry?" When he said this, Zhang Wei's voice was full of uncertainty.
Zhang Wei's areas of expertise are similar to those of his mentor Zhang Shouwu, mainly focusing on representation theory, the Langlands Program, and also research on the Dirichlet L function.
The audience was completely silent.
Noticing the change in expression on his old friend's face, Deligne asked casually.
Faltings said expressionlessly: "Just so so."
It’s better to leave boring questions to others.
Thunderous applause resounded instantly, and lasted for a long time in this spacious and crowded lecture hall...
Also sitting in the back row of the venue, the corners of Faltings' originally tense mouth suddenly raised an unusual angle.
"That's not necessary."
Looking at the second hand getting closer and closer, he put on a serious look on his face and cheered up.
"Why don't cars traveling at high speeds decompose themselves? Why don't stationary lakes suddenly explode?"
"It's about to begin!"
Lu Zhou's speaking speed became faster and faster, and his thoughts became clearer and smoother.
Because as soon as he said these words, he remembered that Lu Zhou's mentor was Deligne, and his ancestor was the legendary "Father of Modern Algebraic Geometry" and "The Pope of Mathematics" Grothendieck!
And the source of that magic power is knowledge.
"Returning to the original question, why don't high-speed cars decompose themselves? Why don't stationary lakes suddenly explode? Is there such a mysterious singularity on an infinite time scale that allows our equations to diverge in a finite time? ?”
"Do you understand?"
At most, we haven’t researched that yet, and the results are still in the making…
"How does it feel?"
After all, it is impossible for everyone to be as talented as Terence Tao, who can prove the weak conjecture of Goldbach's conjecture while studying the abstract proof of NS equations, and even find time to read Mochizuki Shinichi's paper...
"Now, it's time to answer that question."
What he didn't expect was that when he stood here, he still couldn't control the surging emotions in his heart.
Everyone is staring at the pictures and calculations on the curtain. Everyone is listening carefully, unwilling to let go of any detail or miss any moment.
…
Anyway, I already understood everything.
After the brief opening remarks, the PPT on the curtain turned to the next page.
Whether he uses the abstract proof method to construct the abstract bilinear operator B', or he uses the "L-manifold" method, this part is essential.
There is nothing special to explain in the previous part.
After a while, he whispered to Zhang Wei sitting next to him in a voice that only two people could hear.
In the back row of the venue, feeling the heat in the atmosphere, Vera clenched her right hand, and her originally calm heartbeat began to accelerate. At this moment, she was genuinely proud of her mentor...
Lu Zhou originally thought that he was used to this feeling.
Although it is not loud, it has a convincing magic power.
"Even as early as the 19th century, we have summarized the equations that summarize the laws of fluid motion and made it look simple enough. However, to this day, we are still at a loss to understand the deeper mathematical and physical connotations behind the equations. "
Looking at the calculations on the curtain, Xu Chenyang couldn't help but sigh: "It's unbelievable..."
Almost at the moment Professor Faltings left the lecture hall, the entire lecture meeting came to an end.
The introduction of L-manifold played a decisive role in solving the entire proposition.
The core theories of modern algebraic geometry are basically derived from several of Grothendieck's works that have not been lost.
Almost at the moment the words fell.
Nine o'clock sharp.
On stage, the presentation will continue.
Xu Chenyang: "Number theory, abstract algebra, functional analysis, topology, differential geometry, partial differential equations... Are there any other areas that he is not good at?"
That voice was clear and sure.
Under the spotlight, a clear title appeared on the silver-white curtain.
Zhang Wei: "What's unbelievable?"
While the PPT was being shown on the screen, Lu Zhou, holding a laser pointer in his hand, was explaining at a steady pace.
In response to the glances from the audience, Lu Zhou slowly spoke and began the opening remarks of the report meeting.
But it’s even rarer than the giant panda…
Standing on the reporting platform, Lu Zhou took a deep breath and let his heart rate gradually calm down.
Terence Tao, who was on the other side of the venue, muttered "That's it" in a low voice, with excitement shining in his eyes.
And this is exactly the core of the theory of "using topological methods to study partial differential equations"!
However, the next part is the key to the entire proof idea!
"When we give a Schwartz divergence-free vector field μ0 to the equation and set the time interval IC [0, +∞), we can continue to define a generalized solution H10 of the Navier-Stokes equation as an integral equation μ(t ), that is, μ→H10df(R3)…”
"... Combining all the above inferences, the results are obvious. The solution to the three-dimensional incompressible Navier-Stokes equation exists and is as smooth as we expected!"
“For too long, we have been troubled by the obvious, because the truth we desire has always been disguised as obvious.”
[μ(t)=e^(t△)·μ0+∫e^(t—t')△B(μ(t'),μ(t'))dt']
Deligne: "It's going to end soon, don't you want to see the end?"
The audience stood up from their seats.
He looked at his watch for the Nth time.
"Aren't you blushing when you say this?" Deligne smiled faintly and returned the gift he had given him before, intact.
[Proof of the existence and smoothness of solutions to the three-dimensional incompressible Navier-Stokes equation]
[…]
"Mathematics is a rigorous subject, and propositions involving numbers should not be described with ambiguous words like maybe or maybe."
In the world of mathematics, there are many all-rounders.
When the last line of calculation came into view of the audience, there was almost no need for Lu Zhou to give any more explanation.
The corner of his mouth twitched, Faltings ignored his old friend's teasing, looked at his watch, and stood up slowly.
At the same time, the atmosphere in the venue was also pushed to a climax.
He will introduce the concept of differential manifolds into problems of partial differential equations.
The report meeting also got down to business.
With the arrival of this moment, the originally confusing situation became clear in an instant.
There was no need for anyone to maintain discipline. When the time reached the hour, the venue, which was originally noisy and chaotic due to the low-pitched discussions, instantly became quiet.
It was like a hammer, blasting a gap in the unbreakable maze wall.
Zhang Wei would never believe it if he said he didn't know algebraic geometry.
Under the stage, Xu Chenyang's face was solemn, and the pen tip in his hand was tapping gently on the notebook.
After leaving these words, Professor Faltings did not stop, passed through the crowd sitting on the floor in the aisle, and went straight to the exit of the venue.
…
Partial differential equations are not his area of expertise, and he has only learned about NS equations out of interest.
Different from the lecture in Lecture Hall 1 of the Institute for Advanced Study in Princeton, this time he faced not only the number theory community, but the entire mathematical community...
In three seconds, Lu Zhou quickly sorted out the ideas for his speech in his mind. Then he faced the entire audience and gave a brief summary of his proof ideas in one minute.
Zhang Wei shook his head: "My research on partial differential equations is not much more than yours. If you start to feel difficult, then I am almost done."
Sitting in the corner of the venue, Fefferman had a smile on his face. From this moment on, he had seen the end.
Because as the entire audience can see, the final answer is already ready to come out.
Similar things can be seen in many papers on the study of NS equations.