92. Neon Seventy-Nine
past life.
read at noblemtl.com
November 11, 2002.
Papers with the following titles are uploaded to the scientific papers repository, arXiv.org, operated by Cornell University in the United States.
＜The Entropy Formula for the Ricci Flow and its Geometric Applications>
Translated into Korean, it is a thesis titled ＜Entropy Formula for Geometry Application of Rich Flows>, and this was the thesis that completed the proof of the Poencare conjecture, which is one of the seven difficulties of the millennium.
Since the Millennium Seven has a $1 million prize for each problem, the American Clay Mathematical Institute tried to pay the prize money to Grigory Perelman, the owner of the paper, but Perelman declined the prize.
The official reason for his refusal of the prize was that he was not of great merit compared to Dr. Richard Hamilton, the founder of the rich flow theory.
In a way, it could be seen as an expression of humility, but this was not wrong.
It is true that the period of the Poincare conjecture proof was taken by Perelman, but the most important basis of the proof is Dr. Hamilton’s Rich Flow.
Let’s talk a little bit about rich flow.
To put it simply, the rich flow is like a botox injection.
In other words, the rich flow technique is to stretch the wrinkled and complex 3D manifold’s curved surface.
In other words, it simplifies the three-dimensional manifold. Based on this simplification principle, it played a decisive role in the proof of the Poincaré conjecture that ‘a single connected three-dimensional manifold is topologically equivalent to a three-dimensional sphere’.
Because the rich flow technique uses a concept of curvature called a rich tensor and simplifies the surface using the curvature value of the surface, the surface of the manifold where the curvature value is defined can be applied to the rich flow.
That is, for a manifold whose curvature values are defined, the Poincare conjecture holds.
However, if there is a point on the surface of the manifold where the curvature value is not defined, the application of rich flow becomes impossible at that point.
The point where the curvature value is not defined is called singularity. A typical example of a singularity is the tip of a sharp needle or the surface of a thin cylinder whose diameter converges to 0. Because the curvature becomes infinite, the application of rich flow is difficult it becomes impossible
So, the method proposed by the mathematicians is a surgical technique that cuts out these singularities and replaces the cut with a smooth surface with a finite curvature value.
However, this surgical technique needed verification, and what Perelman proved in his 2002 paper was the fact that the surgical technique had no problem mathematically, strictly speaking, scientifically.
As the surgical technique was scientifically verified in this way, the rich flow could be applied to singularity, and the proof of the Poincaré conjecture was completed.
* * *
The e-mail sent by the major sister, and the document attached to the e-mail.
The document contained the application of rich flow at the singularity in a completely new way rather than as a surgical technique.
It was a method to convert a rich tensor (that is, an infinite curvature value) into a new tensor function near a singularity and convert it into a finite curvature value.
To explain only the basic principle, it was similar to the principle that if x is infinitely divergent, multiplying x by 2/x results in a value of 2.
To this end, a new tensor function must be defined. This new tensor function converges to 0 at the singularity at a fixed time, gets closer to 1 as it moves away from the singularity, and after a set time, all tensor function values must converge to 1 again. should have
Using this feature, the curvature value at the singularity becomes a finite value, which in turn makes the application of rich flow possible.
This is the theoretical explanation, and now we need to find a new tensor function that satisfies these theoretical characteristics.
And in the document sent by my sister, a specific methodology for finding a new tensor function according to the type of singularity was laid out.
When Professor Park asked if I had received the major’s sister’s email, I said.
“Yes, I got it. What do you think, Professor?”
“The idea itself was fresh and good. Finding a new tensor function seems to be over soon, but the next process seems to be very difficult.”
Professor Park was right.
It was clear that the success of the proof would be decided in the process of generalizing the found tensor function.
The major’s sister was also aware of this, and she sent me an e-mail for my help in this area.
Over the past week, I have been thinking a lot.
My sister suggested that I do the Poincaré proof together, because I had absolutely no desire to do so.
But on the other hand, I wanted to help my older sister, and I also wanted to help Mike, who is in debt from the past.
On the way home after meeting with Professor Park.
I visited Namseocheon Park.
I walked there and gathered my thoughts.
I remembered a story told a long time ago by team leader Kim Jung-soo.
It’s about creating principles.
I walked home while pondering what the team leader said, and I arrived home late at night and sent a reply to the major sister.
+ +
So now I have to call you senior!
Major-senpai like the sky!
To be honest, I challenged the Poincare guess a long time ago.
But in the end, I gave up, and then I gave up and made this decision.
I’ll never make the Poincare guess again.
Instead, I will introduce you to a professor I know.
(By the way, he doesn’t know me.)
There is a professor named Des Hamilton in the Department of Mathematics at Yale University.
I think he will be of great help in the process of generalizing tensor functions.
Then, when you come to Korea in the summer, see you then!
From Jung-ho, a junior in public class.
+ +
Dr. Des Hamilton is my PhD advisor for a past life.
Just in case you’re wondering, Richard Hamilton is a different person than Richard Hamilton, who founded the Rich Flow technique.
He was a very warm-hearted person, and he was like a father to me.
To be honest, I had a lot of conflicts of mind until I introduced Professor Des Hamilton to my major sister.
If I introduced him, it would seem that I was doing something bad to Grigory Perelman, and I felt sorry for my sister for pretending not to know.
So, the principle I made while walking the Namseocheon Stream is as follows.
If you can’t decide what’s right, do as your heart tells you.
A week later.
Gimpo Airport Departure Hall.
“If I go to language training, will my Japanese improve a lot?”
At my words, Incheol smiled and said.
“Well… Do you have any more Japanese?”
“Then what are you going to do for language training?”
In response to my question, Incheol showed a meaningful smile and said.
“I want to play a big game!”
What… Incheol’s words sound a little unsettling.
In-cheol turned his head to greet his mother, and then spoke to Ji-eun.
“I’ll come back with good news.”
Ji-eun said with tears in her eyes at In-cheol’s words.
“Always take care of yourself and stay healthy.”
In-cheol said, wiping the tears from Ji-eun’s eyes with his hand.
“don’t worry. And I will call you often.”
Ji-eun nodded at In-cheol’s words, took out a thick envelope from the bag and handed it to In-cheol.
“This is what my mother told me to give you pocket money… .”
“no! I have enough money.”
Despite In-cheol’s rejection, Ji-eun was stubborn.
Eventually, he folded the envelope in half and put it in Incheol’s pants pocket.
“It has already been exchanged for yen, so I can’t even use it here. Keep it.”
In-cheol nodded as if he had no choice but to tell Ji-eun.
“Yeah, be sure to say thank you.”
After a while, In-cheol waved to us and entered the immigration hall.
* * *
Klitschko Airlines flight from Gimpo to Narita.
After checking the seat, Incheol shoved his passport and ticket into his bag.
Incheol pulled out an envelope from his pocket, and stopped trying to put the envelope into the bag.
It was because there was a small note reflected inside the envelope.
Incheol took out a piece of paper folded in half and unfolded it.
+ +
In Chul-ah.
With only your heart, this woman says that you are so special and that she is grateful to you.
So, don’t do the hacking we talked about last time, and I hope you have a good time in Japan.
built mom.
+ +
ten days ago.
author’s house.
“Wow! I really enjoyed the meal. It’s my first Korean food in four days, so I think I’ve eaten properly now.”
At In-cheol’s words, Ji-eun’s mother, who was sitting across from the table, said:
“Would you like one more bowl?”
“no. I ate two bowls, and now I am so full.”
In-cheol got up and moved the rice and soup bowls he ate to the sink, and Ji-eun’s mother arranged the side dishes on the table.
When the table was finished, Ji-eun’s mother opened her mouth to In-cheol with a slightly stern expression.
“Do you know why Auntie told me to come?”
“Yes, I know.”
Incheol nodded and continued speaking.
“I should have told you earlier, I’m really sorry.”
“Mom, this is not In-cheol’s fault. I asked Incheol. So… .”
In-cheol interrupted Ji-eun and told Ji-eun’s mother.
“no. This is something I prepared and planned from the beginning. In fact, the author also told me about it a while ago.”
There was a moment of silence, and at the end of the silence, Ji-ji’s mother opened her mouth.
“In-cheol, I don’t know how you find out, but I hope you don’t.”
“Mom!”
Ji-eun’s mother said to Ji-eun with a stern expression.
“You stay still!”
She spoke to Incheol again.
“It was an organized cover-up. The more I dug into the case, the more dangerous it became, so I ended up running away from Japan with Ji-eun.”
“… .”
“Did you see it too? The author’s application for a Japanese visa was rejected for no reason.”
“Mom, that’s because I don’t have a job!”
“Students are jobs! Why don’t you have a job?”
Even the author did not lose and raised his voice and said.
“Your mom said that. Dad might be still alive! Doesn’t Mommy want to see Daddy?”
At Ji-eun’s words, Ji-eun’s mother said with a bitter expression.
“Of course I want to see you. By the way… ”
She turned her head and spoke to Incheol.
“I can’t let someone else’s precious child do such a dangerous thing just because I miss him.”
At her words, Incheol waved both hands and said.
“Mother, this is not dangerous at all. It just connects to the internet and fetches only the information you need. I have no fear of getting caught.”
“If it’s that easy, there’s no need to go all the way to Japan, right? Can we find out by connecting to the internet here?”
In response to Ji-eun’s mother’s question, In-cheol opened her mouth by touching the back of her nose with her left hand.
“actually… The reason I went to Japan this time was to find out.”
“What do you mean?”
“It’s a bit complicated to explain in detail, but I’ll check it out tomorrow. So, if you want to be able to access from Korea, you can cancel your trip to Japan.”
“Really?”
“sure. But if the internet speed is too slow, you have to try several methods, and it will be faster if you do it yourself in Japan.”
Incheol continued to speak while touching the back of his nose again.
“And even in Japan, there will never be anything dangerous. Because the internet is anonymous, you have no idea who took what information.”