Chapter 290 Coming to Hodge’s Conjecture

For Oleyevich, he knew very well that Lin Xiao's report was of great importance to the study of the Hodge conjecture.

In the past, both forms of the integral Hodge conjecture had certain errors, which meant that mathematicians had found counterexamples. Therefore, mathematicians are still pursuing a brand-new integral Hodge conjecture that can perfectly combine the Hodge conjecture.

Guess it in a nutshell.

Now in Lin Xiao's report, he used a very rigorous discussion process to propose this new motivated cohomology person, and then came up with this new integral Hodge conjecture. From this point of view, it is enough for Ole

Yevich trusted it very much, and later Lin Xiao also used a proof by contradiction to prove that his integral Hodge conjecture was completely correct and carried all the information of the original Hodge conjecture.

"Loss of information" is a common situation that hinders the development of mathematics, and it usually occurs during changes in form.

For example, Lin Xiao's Lin's theorem solves the transformation from function to layer. In the past, not all functions could be transformed into layers because during the transformation process, some information would be lost, that is to say, some of the information would be lost.

Information will be lost after transformation.

The incomplete form of information will naturally have an impact on the process of solving mathematical problems. Therefore, how to solve this problem requires the development of new tools.

For Lin's theorem, it is a tool to achieve lossless transformation between functions and layers.

In the process of transforming the Hodge conjecture into the integral Hodge conjecture, it is necessary to take advantage of the fact that cohomology can be converted into differential form. However, due to the limitations of tools, this conversion process will lead to the loss of some information, so it is

This led to the errors of the two integral Hodge conjectures in the past.

But now, Lin Xiao's new motivation cohomology has once again solved such a fatal problem, allowing the original "information" to be transformed in two forms without loss.

Therefore, Orejevich was very amazed by Lin Xiao's report. Undoubtedly, this was a very remarkable achievement.

The importance of this report cannot be overstated.

"I'm really looking forward to Professor Lin's report."

Oleyevich shook his head, then looked at the end of the report, and suddenly he was stunned.

At the end, there are several lines of mathematical formulas.

"Huh? Why is there something at the end... Professor Lin hasn't finished it yet?"

With some doubts, he looked at it a few more times.

After a while, his eyes suddenly showed a solemn look.

"Is this...Professor Lin actually starting to prove this conjecture?"

The few steps at the end clearly prove the beginning of the integral Hodge conjecture.

But even though it was just a few simple steps, it was enough to arouse the imagination of mathematicians like Oleyevich.

According to the steps given by Lin Xiao, if we continue, maybe we can achieve some important phased results?

At least for now, Lin Xiao's last few lines of expressions already have such potential.

Not to mention the actual proof, but the staged results are also very important in mathematics. For example, Perelman was able to prove the Poincaré conjecture because of a mathematical tool called Ricci flow, which played a very important role in it.

Important, this also led Perelman to publicly state that the mathematician who created the Ricci flow, named Richard Hamilton, made a greater contribution than him.

But even so, but——

"Why are there only so many steps?"

For the first time, Olejevich felt the abomination of the broken dog, and even felt like sending a razor blade to Lin Xiao.

This can obviously be written in the future. At least with Lin Xiao's ability, I think it is definitely possible to write in the future.

But he got stuck at such a crucial step and stopped writing.

Olejevich scratched his hair, feeling itchy.

I believe that no mathematician can resist the temptation to prove the Hodge conjecture, or in other words, any of the seven millennium problems. The US$1 million reward offered by the Clay Institute alone is enough to convince many mathematicians.

I'm so greedy.

Mathematicians are often not that wealthy, so they were surprised when they learned that Perelman did not even accept the $1 million.

And beyond that, not to mention the fame it brings and the need for self-actualization, which is a millennium problem after all.

So Oleyevich really wanted to know how to write after this crucial step.

"What is this Professor Lin doing?"

But no matter how confused he was at this time, no matter how hard he thought about it, he probably never imagined that Lin Xiao wanted to recreate the process of Andrew Wiles proving Fermat's last theorem.

If you can’t figure it out, then don’t think about it.

So Orejevich stopped taking care of it and put the report in the archives. After it is reviewed later and it is completely determined that there are no problems with the report content, it can be uploaded to their 2022ICM official website.

Orejevich could even imagine that when other mathematicians downloaded Lin Xiao's report and read it, they would be like him and hate Lin Xiao's step that was stuck at a critical point.

Maybe, after Lin Xiao finishes his report in his speech, the audience will make a fuss.

Oleyevich is already looking forward to that time.

Shaking his head and putting this matter behind him, he was about to start other work, but at this moment, someone suddenly called him.

When he saw it, he saw that it was his friend Zorelovsky, who was a professor of mathematics at St. Petersburg State University.

St. Petersburg State University is second only to Moscow State University in Russia, and its status is equivalent to Qingbei in China.

Although in the so-called international university rankings, St. Petersburg State University's ranking can only compete with the 985 schools outside Qingbei, China, its own strength cannot be objectively expressed by those international rankings, because these international rankings are all

Paying attention to internationalization, in layman's terms, is the requirement for English. Therefore, in the QS university rankings, for example, universities in English-speaking areas are basically at the forefront.

Because of this, the strength of St. Petersburg State University is actually very strong.

At the same time, Russia’s basic mathematics education is also very strong, and St. Petersburg State University has naturally inherited this strength. Even Perelman graduated from St. Petersburg State University.

It is precisely because of this that Zorelovsky is also quite famous in the mathematics community.

After answering the phone, he smiled and said, "Brother, why are you in the mood to call me?"

Zorelovsky on the opposite side did not greet him, but said directly: "Did you know? Lin Xiao from China has decided to hold a report on the proof of Lin's conjecture at their Beijing University. Do you plan to go?"

Oleyevich was stunned, "Proof of Lin's conjecture?"

Of course, he is also very interested in this matter. As someone who studies algebraic geometry, he is certainly not unfamiliar with Lin's theorem. In some of his recent studies, he has used research on Lin's theorem.

But then he said helplessly: "I am currently in charge of the International Congress of Mathematicians, so I probably won't have time."

"That's right, that's true." Zorelovsky said: "This report is scheduled to be held on June 30th. I guess you really don't have time."

"Hmm...wait a minute, you mean June 30th?"

Suddenly, Olejevich sat up directly. When he heard Zorelovsky say that Lin Xiao planned to give a report on June 30, he suddenly felt that something was wrong.

A week after June 30th, it will be the International Congress of Mathematicians, and there will be a one-hour report by Lin Xiao.

So what is Lin Xiao planning to do?

Two reports in ten days?

No, there is also the Fields Lecture.

Although he, the chairman of the organizing committee, cannot evaluate the Fields Medal, which is decided by the International Mathematical Union, he can still get some information. Lin Xiao has a 10-10 chance of winning the Fields Medal.

big.

This made him daydream even more.

Lin's conjecture? Integral Hodge conjecture?

There are also several steps that Lin Xiao will try to prove Hodge's conjecture at the end of the report.

Olejevich always felt that Lin Xiao wanted to make something big happen.

"It's June 30th, what's wrong?"

On the other end of the phone, a question came from a friend.

Oleyevich came back to his senses, and then said with a smile: "Nothing, I just think that this year's mathematics world may be unusual."

Zorelovsky said with a smile: "In January, Professor Lin proved his own Lin's conjecture. This alone is enough to make this year's mathematics world extraordinary."

Olijevich shrugged: "Well, what I want to say is that this year's conference should not be too ordinary."

"Really? Then I'm looking forward to it."

"Well, look forward to it." Oleyevich said, "I'm looking forward to it too."

…

Time flies.

April and May were spent in peace, and June arrived on time.

In Lin Xiao's room.

After being in seclusion for almost three months, Lin Xiao's hair now reaches her eyebrows, collar and ears, and even her beard has grown out.

The young man who was originally twenty-two years old seems to have turned into a sloppy uncle.

Of course, this is also because his classes at school have been completed before the ninth week of the semester, so he has not been able to go out.

However, despite being in seclusion for so long, he still has not completed the final proof of Hodge's conjecture.
To be continued...