Chapter 468: Minimal model program

Chapter 468
The next day.
The first International Geometry Symposium was held at the headquarters of the Swedish Mathematical Society.
There were 412 mathematicians present, including three Philippine Prize winners and eight Veblen Prize winners.
Cheng Nuo, as the invited speaker of this conference, was arranged to appear in the third place.
The two in front of him who took the stage to give academic reports were a Fields Medal winner, and the other was a veteran mathematician who had won the Veblen Prize.
Since the number of attendees was not too large, and all mathematicians in the field of geometry were invited, no branch venue was arranged.
All academic reports are conducted in the same auditorium.
Each invited speaker will have 50 minutes to report.
The meeting lasted four days in total.
The first two days are academic reports, and the last two days are academic exchanges in the form of discussion.
Without going into too much detail, the current president of the Swedish Mathematical Society gave the first academic report after a simple speech.
Cheng Nuo took out his notebook and took notes while listening.
Life-long learning.
In the field of geometry alone, Cheng Nuo dare not say that he understood seven or eight of them.
To listen to the lectures of the Philippine award leaders for free, Cheng Nuo will still cherish this opportunity.
…………
There will be a short break between each report.
After the second lecture, Cheng Nuo was taken to the backstage of the auditorium by the staff.
To be honest, Cheng Nuo is really the first time to give an academic report on such an important occasion. He doesn't understand any rules and can only be led by the staff like a puppet.
I checked the PPT used for the report and simply drew a light makeup. After the crew asked Cheng Nuo if he had any other needs, they took Cheng Nuo to the entrance on the side of the stage.
Outside, the vice-president of the Swedish Mathematical Society who is temporarily serving as the host is still reporting.
"The next academic report is Professor Cheng Nuo from the Massachusetts Institute of Technology. Speaking of this, everyone must know him, but as usual, I still want to tell you about his achievements."
"The author of the Cheng Nuo theorem, the Cheng’s complex ring conjecture, the Jacobi conjecture, the Gushan Zhicun conjecture, and the prover of the three conjectures of the Cheng’s complex ring conjecture! At the same time, he is the youngest winner of the Veblen Prize!
"Next, we will invite Mr. Cheng Nuo, who is also known as a'mathematics ghost', to give us an academic report. See what kind of surprise he can bring us this time!"
Happiness~~!
There was applause from below the auditorium.
At the entrance, Cheng Nuo took a deep breath, calmed down his nervousness, took the microphone and walked calmly to the stage.
At a glance, more than 400 people were densely packed with human heads.
This is more than 400 mathematicians, not more than 400 Chinese cabbage.
Glancing at the pair of wise and thorough eyes, Cheng Nuo felt like a light on his back.
The mentality needs to be practiced again!
Cheng Nuo smiled bitterly, and hurriedly averted his gaze, returning his attention to the academic content he was about to tell.
The projector projected the subject of Cheng Nuo's report onto the screen.
"The Problem of Minimal Models in Birational Geometry"
Seeing this topic, many scholars below are surprised.
Among the more than 400 mathematicians present, only a handful of them got the proof that Cheng Nuo was not prepared to tell the previous two conjectures.
Among those very few people, only Professor Fresnel knew that the topic of Cheng Nuo's speech today was a minimal model program.
Therefore, the people below were surprised at first, and then their eyes became interesting.
To be honest, they didn't expect this one.
However, they are not optimistic about Cheng Nuo.
To be precise, birational geometry belongs to a branch of algebraic geometry, but it is relatively unpopular.
The minimal model program is one of several unpopular directions in birational geometry.
The unpopular among the unpopular.
It is no exaggeration to use this to describe the position of the minimal model program in the geometric world.
Moreover, the minimal model program is not only unpopular, but also very complicated.
Since the concept of the minimal model program was proposed in the 1980s, there have been these two mountains in front of it:
The first problem of the minimal model program, and the second problem of the minimal model program.
Without removing these two mountains, the straight road that is most convenient for the study of the minimal model program is completely blocked. If you want to study, you can only take a long way, and it is a big circle.
This discouraged many people.
In the last century, there were a steady stream of mathematicians who came to Yishan, but they found that even a corner of the mountain was difficult to move. After the millennium entered, it became a place where nobody cares.
Cheng Nuo chose the minimal model as the topic of his presentation today. In their view, it is nothing more than a round of complicated formula theorems to study.
unless……
impossible!
They directly rejected the unrealistic speculation in their hearts.
Such a short time!
For an instant, they thought of Cheng Nuo's enchanting experience, and their affirmative thoughts became shaken.
If that person is Cheng Nuo, maybe, maybe, maybe, there will be that possibility.
On stage, Cheng Nuo cleared his throat, and the loud voice spread throughout the hall, "For a given algebraic cluster, we must be able to generalize the blowon operation or the flip operation. After a limited number of operations, we can get A geometric "minimal model", this is the definition of the minimal model program."
"And we all know that there are two important problems in the field of the minimal model program." Cheng Nuo raised a finger. "The first question of the minimal model program is to ask about the existence of this kind of flip operation."
Cheng Nuo raised his second finger, "The second question is whether the flip operation stops after a limited number of operations."
"These two issues have always been considered to be the two mountains that hinder the continued study of the minimal model program."
"In the front-end time, I took a period of time to study it, and found that the rumors are indeed exaggerated." Cheng Nuo smiled, "The two major problems of the minimal model program ~EbookFREE.me~ are not as rumored. terrible."
Cheng Nuo's words made everyone below look stiff.
Listening to Cheng Nuo's tone, this guy really didn't solve the very small model program, right?
Cheng Nuo ignored the reactions of the people below, transferred to the next page of PPT, pointed to the projection on the screen and said, "Let’s first talk about the first issue of the minimal model program."
"The existence of the flip operation? This question may be difficult for people before, but I can tell you clearly here that this operation does exist."
"Why?" Cheng Nuo said quickly, "You can look at the formulas here."
"We first give the pairing (X, △), assuming that there is a positive integer m, so that m(K?? + △) is the Kajiye divisor, then the Kaanmata logarithm is called ultimate, if discrep=(X ,△)>-1 and [△]≤0."
"Next..."