The report meeting was held at two o'clock sharp, and it was impossible for Xu Chuan to be on stage at two o'clock.

Going on stage a little early is the necessary etiquette and respect for the audience who come to listen to the report in any formal report meeting.

As he appeared on the podium, the crowded Alexandria Auditorium instantly fell silent. Everyone stopped their discussion and turned their attention to the young man on the stage, leaving the camera alone to make a quiet noise.

Being stared at by hundreds of pairs of eyes in the audience, Xu Chuan didn't feel too nervous.

After all, he has experienced all this before.

Not to mention giving a speech in front of hundreds of people, when he discovered dark matter and dark energy in his previous life, it was called madness.

If there hadn't been adequate security to control the crowd, everyone would have wanted to jump in his face.

Compared to the craziness of that time, the scene here was nothing.

.......

On the podium, Xu Chuan opened the notebook he had prepared and clicked on the pre-compiled ppt text.

A slide was projected onto a silver-white curtain.

The picture above shows a golden ball on the bottom line of the grid, with various blue, purple, red and black lines zigzagging through the ball.

This picture comes from the background of the Hodge conjecture. In the twentieth century, mathematicians discovered powerful methods for studying the shapes of complex objects. The idea is to what extent a given object can be

The shapes are formed by gluing together simple geometric building blocks of increasing dimensions.

】

The grid plane and sphere, as well as the curves that can shuttle and interweave in the sphere, can express this idea, so it is widely used in the introduction of Hodge's conjecture.

Above the picture, there is a line of bold characters: "Hodge conjecture".

This is today's topic.

Clicking on the homepage of the ppt, Xu Chuan turned to look at the crowd in the Alexander Auditorium, and said calmly:

"Thank you very much for traveling thousands of miles from all over the world to come here. I would like to express my most sincere gratitude to you here."

"The theme of today's report is the proof paper of Hodge's conjecture."

"I believe that everyone has already read my paper, so I will not repeat the entire paper here. I will focus on two aspects in the following explanation."

After a pause, Xu Chuan gently clicked the control pen in his hand.

The picture on the projection screen suddenly jumped.

The first official picture in the speech ppt document popped up.

[Algebraic Varieties and Group Mapping Tools]

[The proof process of Hodge’s conjecture]

Two lines of text, presented in a concise ppt document.

Xu Chuan glanced at the slide and continued: "As shown in the picture, in the following explanation, I will focus on the two aspects of 'algebraic varieties and group mapping tools' and 'the proof process of Hodge's conjecture'

.”

"The former is the key to solving the Hodge conjecture, a bridge connecting algebraic geometry and topology, and the most essential part of this proof paper. The latter is the complete proof idea of ​​the Hodge conjecture."

"I will focus on these two aspects, and as for other things, I will briefly mention them."

"Of course, if you have any questions about this proof paper, you can ask them in the subsequent question session, and I will do my best to answer them."

Highlighting the theme of the report meeting is something that every competent academic speaker will do.

After all, everyone's time is precious, and attending a report meeting is not just about watching the speaker repeat what is already in the paper with a ppt.

It is also a common practice and a necessary etiquette in the academic community to preview the speaker's paper before the start of the academic seminar.

Everyone comes here to learn and understand the knowledge that they do not understand.

There is no need to talk about the verification process and other things that have been clearly written in the paper again at the report meeting.

If you want to go through the proof paper of more than 100 pages in detail, you probably won't be able to do it if you don't have a few days.

And for most people who attend the lecture, such as students who follow the professor to gain knowledge, or professors who take the initiative to participate in the lecture, they are here to witness history.

A report meeting of a few hours is fine, but for a report meeting that lasts for several days, I am afraid that most people will not have the patience.

.......

Turning over the ppt page, Xu Chuan entered the theme of this report meeting.

"Algebraic varieties and group mapping tools are the core mathematical tools for proving Hodge's conjecture. If you want to understand the proof process of Hodge's conjecture, you must have a sufficient understanding of it."

"This mathematical method originated from the mapping and torsion of the Weyl group. Its core idea is the mapping of algebraic varieties through the Weyl group, and then through the introduction of Bruhat decomposition and field theory..."

Following his explanation, the pictures on the ppt continued to play.

"...Suppose gz=gl(n,c) is a general complex linear group, and b∈gz is an upper triangular subgroup. Then, gzbruhat decomposition is a double-performed set decomposition bg1/b=nb is n*n

Linear isomorphisms of transformation matrices.”

“…..a maximum ring t of unitary group u(n):={diag(d,d2,…,dn):|dj|=1)…then the subgroup g?

The double-trained set decomposition of u(n) is tg1/t=nbwb.”

"..."

In the entire paper that proves the Hodge conjecture, there is no doubt that this algebraic variety and group mapping tool is the most important and essential thing.

It is based on the algebraic group, subgroup and torus structure methods proposed by Professor Mirzakhani, but it is completely reborn. It can be said that it is completely separated from the original foundation and structure and has become a completely new mathematical method.

As for a brand-new mathematical tool, the mathematical community has always been cautious in accepting it.

This chapter is not over yet, please click on the next page to continue reading! So at today’s report meeting, Xu Chuan focused on explaining this tool.

On the one hand, it is to let more mathematicians understand it.

On the other hand, it is a report on the subsequent proof process of Hodge's conjecture.

After all, if the algebraic varieties and group mapping tools cannot be understood, the subsequent proof process of Hodge's conjecture will be even more unclear.

Regarding this part, Xu Chuan spoke very seriously, starting from the principles and going into details on how to map, reverse, and expand the group domain.

The audience in the auditorium also listened very carefully.

Even the math students who had begun to understand it were staring at the stage with their eyes wide open.

Students who can be tutored, or can follow professors to participate in such large-scale mathematics seminars, are basically interested in making further progress in mathematics.

For studying mathematics, it is definitely much better to listen to the explanations of problems by such top experts than to read textbooks alone.

Even if they don’t understand the process, there are always some concepts and ideas that can be recorded, and these things can often bring inspiration to them when combined with the knowledge in their own minds.

For students or professors who are interested in making further progress in mathematics, the proof report of this major conjecture will be something not to be missed.

...

On the stage, Xu Chuan explained algebraic varieties and group mapping tools in an orderly manner.

In the corner of the auditorium, Hu Xingjian, who had come to attend the mathematics exchange meeting with his tutor Zhang Weiping, looked at the chattering peer on the stage with complicated eyes.

More than two years have passed since we said goodbye at the Morning Star Mathematics Prize awards night.

Two and a half years were not enough for him to complete all his studies in school, but the young man who was already so dazzling before was now at the pinnacle that was far away from him.

Proof of Hodge's conjecture.

This was a difficult problem that ordinary people would spend a lifetime studying and could not break through, but it was solved by that person in only two years.

"Professor, do you think he has really solved the Hodge conjecture?" Finally, he couldn't help but whispered to his instructor Zhang Weiping.

Although he had been listening hard and had read the more than 100 pages of the paper in advance.

But sitting here today, he still can't keep up with the opponent's rhythm, and now, he can no longer understand the algebraic varieties and group mapping tools that are being explained.

Whether it works or not, mathematics is such a realistic thing.

Upon hearing the inquiry, Zhang Weiping turned to look at his student. Seeing the complicated expression on his face, he smiled and said, "What's wrong? Are you hit?"

He can naturally guess a certain amount of his disciple's thoughts and emotions.

After a pause, he continued to comfort him: "You don't have to, and there is no need to compare with him. If you are a genius, then he is a real monster."

“If we look at the entire history of the development of mathematics, we can count such evil figures on one hand.”

.......

The reporting time passed very quickly. During Xu Chuan's explanation, half of the scheduled one-hour reporting session passed in the blink of an eye.

At this time, he had just completed the explanation of algebraic varieties and group mapping tools.

Of course, the real report meeting cannot end in an hour. Everyone present, whether it is Xu Chuan or the audience in the auditorium, are ready to stay here until the end and then eat dinner directly.

No one cared about this long time. Those who cared about it had already gotten up and left. Everyone who stayed wanted to explain it in as much detail as possible, even if they couldn't understand it.

On the stage, Xu Chuan finished explaining algebraic varieties and group mapping tools and looked at the audience.

Next, is the proof of Hodge’s conjecture.

Although theoretically speaking, the proof of Hodge's conjecture is far more important than algebraic varieties and group mapping tools. But whether it is for Xu Chuan or the audience in the audience, when this tool is made and learned to use
To be continued...