The Science Fiction World of Xueba

Mochizuki said, "It's almost finished. I'll send the electronic version to your email after I get back. If there are no problems, we can arrange publication as soon as possible."

Pang Xuelin nodded and said, "Yes."

At this time, Perelman suddenly said: "Pang, I may not go to the seminar during this time."

Pang Xuelin was taken aback for a moment, and asked doubtfully, "Why?"

At present, the Ponzi geometry seminar is mainly hosted by Perelman and Mochizuki Shinichi. Pang Xuelin will go there two to three times a month, and most of the time is to answer questions for everyone, or listen to some valuable research reports.

If Perelman didn't go, Mochizuki would be struggling alone.

Perelman said: "In the past few months of research on Ponzi geometry, I found that I have some new ideas on Hodge's conjecture, and I need to retreat for a while."

Pang Xuelin couldn't help being stunned.

Mochizuki Shinichi, on the other hand, looked calm, obviously knowing Perelman's decision long ago.

Pang Xuelin asked curiously, "Are you inspired by Hodge's conjecture?"

Perelman said: "Maybe, further research is needed."

Pang Xuelin nodded.

The Hodge conjecture is a great unsolved problem in algebraic geometry. It is a conjecture about the association of the algebraic topology of nonsingular complex algebraic varieties and its geometry expressed by polynomial equations defining subvarieties.

In the 1930s, mathematicians discovered powerful ways to study the shape of complex objects.

The basic idea is to ask to what extent we can form the shape of a given object by gluing together simple geometric building blocks of increasing dimensionality.

This technique has become so useful that it can be generalized in many different ways, eventually leading to some powerful tools that allow mathematicians to make great achievements in classifying the wide variety of objects they encounter in their research. Progress.

Unfortunately, in this generalization the geometric starting point of the program becomes blurred.

In a sense, certain parts without any geometric interpretation must be added.

The mathematician William Valence Douglas Hodge thus asserted that, for a particularly perfect type of space called a projective algebraic variety, the parts called Hodge closures are actually geometric parts called algebraic closures (rational linear) combinations of .

To put it another way.

Now there are two pipes, one denoted 1 and one denoted 2, which represent two regions. We assume that all tubes can be stretched and bent at will.

Connect the two tubes end to end and you have a car tire like ring with two regions.

Let's use another straight pipe to mark it as 3, and install it in the middle of this ring, one end is connected to area 1, and the other end is connected to area 2. Now it is a double ring with two holes, and three areas are connected two by two.

Now we use a "T"-shaped trident tube, marked as area 4, and the three ports are connected to area 1, area 2, and area 3 respectively. So now there are 4 areas connected in pairs; we use a four-pronged tube to mark it as area 5, and 4 ports are connected to areas 1, 2, 3, and 4 respectively, and now there are 5 areas connected in pairs.

This step can go on indefinitely, using five-pronged tubes, six-pronged tubes,... Construct infinitely many regions, all of which are connected in pairs.

This construction method is the Hodge conjecture.

The four-color theorem, Goldbach's conjecture, Fermat's last theorem, and Riemann's conjecture are all unified under the tool of Hodge's conjecture.

When we make geometric topological superstructures the way Hodge conjectures them: a manifold.

The whole of this manifold is Fermat's last theorem, and the Riemann conjecture is used to calculate the part of this structure.

Like the BSD conjecture and the Poincaré conjecture, the Hodge conjecture is one of the seven millennium problems.

But until now, the research on Hodge's conjecture in the international mathematics community has been in a very preliminary state.

It was once reported that Schultz had made some progress in this field,

But no articles have been published.

Pang Xuelin did not expect that Perelman had an inspiration for this question.

After pondering for a moment, Pang Xuelin said: "Okay, then you don't have to worry about the seminar for the time being, and study your Hodge conjecture carefully. By the way, you won't be returning to China right now."

Perelman glanced at Pang Xuelin: "I have stayed here well, why should I go back to China?"

"That's good!"

Pang Xuelin smiled and said with a sigh of relief.

As long as Perelman doesn't leave.

After Perelman came to Jiangda, Jiangda arranged for him a relatively quiet apartment, just across from Mochizuki's family.

Pang Xuelin went to see it once.

Perelman's life is simple, except for three weekly Ponzi geometry seminars, he spends most of his time at home.

The diet is even more simple to outrageous, cold and hard rye bread, plus whole milk, is his main diet.

Occasionally he also goes to the supermarket to buy some tomatoes, lettuce and other foods to make salads.

Pang Xuelin took him to dinner several times, but he didn't seem interested in Chinese food.

The only time he had breakfast in the school cafeteria was a leek box, which became another of his favorites.

He often went to the cafeteria in the teaching area, packed twenty or so leek boxes and put them in the refrigerator.

Serve two in one meal and heat them up straight in the microwave.

It wasn't until Mochizuki Shinichi's wife came to take care of Mochizuki, and then often invited Perelman to their house for dinner, that Perelman's food gradually improved.

At this time, Mochizuki said, "Pang, if there is nothing else, Grigory and I will leave first. By the way, I will send you the discussion paper on Ponzi geometry when I get back."

"Okay, let's get in touch if there is anything else."

Not long after Mochizuki and Perelman left, Mochizuki sent the electronic version of the discussion draft of the Ponzi geometry seminar.

In the next few days, Pang Xuelin has been studying this discussion paper.

This discussion paper is regarded as the latest collection of papers on Ponzi geometry-related research in the international mathematics community. Every article included has very high theoretical value.

After confirming that there were basically no problems with the discussion draft, Pang Xuelin handed over the "Ponzi Geometry" textbook and the discussion draft to Liu Tingbo for processing.

The appearance of these two works is equivalent to officially announcing to the mathematics community that the Ponzi School of Geometry centered on Jiangcheng University has established a sect.

Liu Tingbo cared more about this than Pang Xuelin himself.

This is the world's top textbook written by Chinese, which is rare in China in the field of colleges and universities.

With Pang Xuelin as a great god and these two books, the Department of Mathematics of Jiangcheng University will greatly enhance the attractiveness of the world's top scholars.