universal data

Chapter 465 Minimal Model Program
468 chapter

The next day.

The first International Symposium on Geometry 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.

As the invited speaker of this conference, Cheng Nuo was arranged to appear third.

One of the two in front of him who came to the stage to give academic reports was a Fields Medal winner, and the other was a veteran mathematician who had won the Veblen Prize.

Since the number of participants was not too large, and all the invited mathematicians were in the field of geometry, no parallel sessions were arranged.

All academic reports are conducted in the same auditorium.

Each invited speaker has five to 10 minutes to make a report.

The conference lasted for four days in total.

The first two days are academic reports, and the last two days are academic exchanges in the form of discussions.

Without going into too much detail, the current president of the Swedish Mathematical Society gave the first academic report after a brief speech.

Cheng Nuo took out his notebook and wrote down with a pen while listening.

Life-long learning.

In the field of geometry alone, Cheng Nuo dare not say that he has understood seven or eight out of ten of it.

Cheng Nuo would cherish this opportunity to listen to the lectures of the Philippine award boss for free.

…………

There will be a short break between each presentation.

After the second lecture, Cheng Nuo was taken to the backstage of the auditorium by the staff.

To be honest, it was the first time for Cheng Nuo to give an academic report on such an important occasion. He didn't understand any rules, so he could only be led by the staff like a puppet.

After checking the PPT for the report, he put on some light makeup. After the staff asked Cheng Nuo if he had any other needs, he took Cheng Nuo to the entrance on the side of the stage.

Outside, the vice-president of the Swedish Mathematical Society, who was temporarily serving as the moderator, was 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 introduce his achievements to you."

"Proposer of Cheng Nuo's theorem, Cheng's complex ring conjecture, Jacobi's conjecture, Gushan Shimura's conjecture, and Cheng's complex ring conjecture! At the same time, he is also the youngest winner of the Veblen Award!"

"Next, we will invite Mr. Cheng Nuo, who is known as a 'mathematical genius', to give us an academic report. Let's see what kind of surprise he can bring us this time!"

clap clap ~ ~!

There was applause from below the auditorium.

At the entrance, Cheng Nuo took a deep breath to calm down his inner nervousness. Holding the microphone, he walked steadily onto the stage.

More than 400 people, at a glance, are all densely packed heads.

This is more than 400 mathematicians, not more than 400 Chinese cabbages.

Looking at those pairs of wise and penetrating eyes, Cheng Nuo felt like he was on his back.

The mentality still needs to be practiced!
Cheng Nuo smiled wryly in his heart, and hurriedly looked away, returning his attention to the academic content he was about to talk about.

The projector projected the topic of Cheng Nuo's report onto the screen.

"The Program Problem of Minimal Models in Dual Rational Geometries"

Seeing this topic, many mathematicians below were surprised.

Among the more than 400 mathematicians present, there were only a very small number of people who knew that Cheng Nuo was not going to tell the proof process of the previous two conjectures.

Among the very few people, Professor Fresnel was the only one who knew that the topic of Cheng Nuo's speech today was the minimal model program.

Therefore, everyone below was surprised at first, and then their eyes became playful.

To be honest, none of them thought of this.

However, they were not optimistic about Cheng Nuo.

To be precise, double rational geometry belongs to a branch of algebraic geometry, but it is relatively unpopular.

The minimal model program is one of the few unpopular directions in dual rational geometry.

The unpopular among the unpopular.

It is not an exaggeration to use this to describe the status of the minimal model program in the geometry 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 80s, there have been two mountains in front of it:

The first problem of the minimal model program, and the second problem of the minimal model program.

If these two mountains are not removed, the straight road that is most convenient for the study of the minimal model program will be completely blocked. If you want to study, you can only take a long detour, and it is a big circle.

This discourages many people.

In the last century, there was an endless stream of mathematicians who came to Yishan, but they found it difficult to pry even a corner of the mountain. After entering the millennium, it became a place where no one cares about it.

Cheng Nuo chose the extremely small model as the topic of his talk today. In their view, it was nothing more than researching by going around a circle of complicated formulas and theorems.

unless……

impossible!
They directly rejected that unrealistic guess in their hearts.

Such a short time!

For a moment, they thought of Cheng Nuo's monstrous experience, and the affirmative thoughts in their hearts became shaken.

If that person was Cheng Nuo, maybe, maybe, maybe, there would be that possibility.

On the stage, Cheng Nuo cleared his throat, and the loud voice spread throughout the auditorium, "For a given algebraic variety, we must be able to generalize the blow down operation or flip operation. After a limited number of operations, we can Get a geometric 'minimum model', this is the definition of the minimal model program."

"And we all know that there are two important issues in the field of the minimal model program." Cheng Nuo raised a finger, "The first question of the minimal model program is the existence of this kind of flip operation."

Cheng Nuo raised his second finger, "The second question is whether the flip operation will stop after a limited number of operations."

"These two problems have always been considered to be two mountains that hinder the continued research of the minimal model program."

"In the front-end time, I took a period of time to study it and found that the rumors were indeed exaggerated." Cheng Nuo smiled. "The two major problems of the minimal model program are not as terrible as the rumors."

Cheng Nuo's words made everyone below freeze.

Judging from Cheng Nuo's tone, this guy really didn't solve the minimal model program, did he?
Cheng Nuo ignored the reactions of everyone below, switched to the next PPT page, 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 not be easy for people before to answer, but I can clearly tell you here that this operation exists."

"Why?" Cheng Nuo spoke quickly, "Everyone can take a look at the formulas here."

"We first give a pair (X, △), assuming that there is a positive integer m, so that m (K+△) is the Kajiye divisor, then, Kawanmata is called the ultimate logarithm, if discrep=(X, △) >-1 and [△] ≤ 0."

"Next..."

(End of this chapter)