Mochizuki Shinichi: "It's almost sorted out, I'll send you an email when I get back later, if there are no problems, we will arrange for publication as soon as possible?" ”

Pang Xuelin nodded and said, "Yes." ”

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

Pang Xuelin was slightly stunned, and wondered: "Why?" ”

At present, the Ponzi Geometry Seminar is mainly chaired by Perelman and Shinichi Mochizuki, and Pang Xuelin goes there two or three times a month, most of the time to answer questions or listen to some valuable research reports.

If Perelman doesn't go, Shinichi Mochizuki will be a little struggling to be alone.

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

Pang Xuelin couldn't help but be stunned.

However, Mochizuki Shinichi looked unfazed, and obviously knew Perelman's decision for a long time.

Pang Xuelin was curious: "Are you inspired by the Hodge conjecture?" ”

Perelman said: "Perhaps, further research is needed. ”

Pang Xuelin nodded.

The Hodge conjecture is a major unsolved problem in algebraic geometry. It is a conjecture about the correlation between the algebraic topology of a nonsingular complex algebraic cluster and the geometry it is expressed by the polynomial equations that define the subclusters.

In the thirties of the twentieth century, mathematicians discovered powerful ways to study the shape of complex objects.

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

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

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

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

The mathematician William Valens Douglas Hodge thus asserts that for a particularly perfect type of space called a shadow algebraic cluster, the components called Hodge closed chains are actually combinations of geometric parts called algebraic closed chains.

Let's put it a little more figuratively.

Now there are two tubes, one denoted as 1 and one denoted as 2, and they represent two areas. We assume that all tubes can be stretched and bent at will.

Connecting the ends of the two pipes is a ring like a car tire, which has two areas.

Let's use a straight pipe to mark 3, which is installed in the middle of this ring, with one end connected to area 1 and one end connected to area 2, and now it is a double ring with two holes, and there are three areas connected by two.

Now we use a "D" shaped three-pronged tube, denoted as zone 4, and the three ports are connected to zone 1, zone 2, and zone 3 respectively. So now there are 4 areas connected by two; We use a four-pronged tube to mark area 5, there are 4 ports connected to areas 1, 2, 3, 4, and now there are 5 regions connected in pairs.

This step can be carried out without restrictions, with a five-pronged tube, a six-pronged tube,.....。 Construct an infinite number of areas, all of which are connected in pairs.

This method of construction is known as the Hodge conjecture.

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

When we use the method of Hodge's conjecture to make a geometric topological superstructure: a kind of manifold.

The whole of this manifold is Fermat's theorem, and the calculation of this part of the structure requires the Riemann hypothesis.

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

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

There was once news that Schultz had made some progress in this area, but no article has been published.

Pang Xuelin did not expect that Perelman would have an inspiration for this issue.

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

Perelman glanced at Pang Xuelin: "I stayed here well, why do I want to go back to China?" ”

"That's good!"

Pang Xuelin smiled and said with a sigh of relief.

It's good if Perelman doesn't go.

After Perelman came to Jiang University, Jiang University arranged a quieter apartment for him, just opposite Mochizuki Xin's family.

Pang Xuelin once went to see it once.

Perelman's life was simple, except for attending Ponzi geometry workshops three times a week, and he spent most of his time at home.

The diet was outrageously simple, with cold, hard rye bread and full-fat beef being his main diet.

Occasionally, he would go to the supermarket and buy tomatoes, lettuce and other foods to make salads.

Pang Xuelin pulled him to dinner a few times, but he didn't seem interested in Chinese food.

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

He often went to the cafeteria in the teaching area and packed more than 20 leek boxes directly and put them in the refrigerator.

Eat two at a meal and add directly in the microwave.

It wasn't until later that Shinichi Mochizuki'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 Shizuki: "Pang, if there is nothing to do, Grigory and I will leave first, by the way, I will send you the Ponzi geometry discussion draft when I go back." ”

"Okay, we'll get back in touch when there's anything."

Not long after Shinichi Mochizuki and Perelman left, Shinichi Mochizuki sent an electronic version of the discussion draft of the Ponzi Geometry Workshop.

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

This discussion paper is the latest collection of papers on Ponzi geometry in the international mathematical community, and every article included in it has very high theoretical value.

After confirming that there was basically no problem 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 mathematical community that the Ponzi geometry school centered on Jiangcheng University has been established.

Liu Tingbo is even more concerned about this than Pang Xuelin himself.

This is one of the few world-class textbooks written by Chinese in the field of colleges and universities.

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