Chapter 157 The Most Valuable Report

"Old friend, are you sure that today's lecture will be special? I was originally planning to attend another one."

Friday, August 2006, 8, IFEMA.

Outside the main lecture hall No. 1 in the conference venue, Professor Wells of the Clay Mathematics Institute had a puzzled look on his face, and there was some disbelief in his eyes when he spoke to Deligne.

He had originally booked a one-hour lecture in the lecture hall next door, thinking that this lecture would be more valuable.

However, he was persuaded by his old friend Deligne and finally changed his mind to listen to the report in the No. 1 main lecture hall. However, he still doubted the value of the content of the report.

The entire mathematicians' conference will last seven days, and in addition to the one-hour reports, it will also include 45-minute group reports.

With so many papers accepted by the conference, it would be impossible to listen to all of them.

What's more, for these older mathematicians, their energy is limited.

It would be good if I could attend two reports every day.

Therefore, faced with so many reports every day, it is important to choose which one to attend.

The key is to see if there is anything of higher value worth listening to.

Otherwise, it would be a waste of time to some extent.

Deligne had a smile on his face at the moment, and he responded as the two of them hurried to the lecture hall.

"Are you still not confident in my judgment? The speaker at today's conference is the winner of this year's Gauss Prize."

"I still remember that the last time he attended an academic conference, he proved Qiu Chengtong's conjecture on the spot."

"That's the math genius from China." Wells had an impression of him and took over the conversation.

Deligne: “You talked about it on the day of the opening ceremony.”

When Wells heard this, he suddenly remembered that if it was a lecture by this Gauss Prize winner who made significant progress in the twin prime conjecture and proved Qiu Chengtong's conjecture, it would definitely be worth his while to go and listen.

However, he did not take Deligne's next words to heart.

Xu Yuan tried to prove Qiu Chengtong's conjecture on the spot and successfully solved it, putting an end to the Calabi conjecture. He had seen this news before.

I admire this courage and determination.

This is also the reason why he wanted to invite the other party to join their Clay Mathematics Institute.

However, there are indeed many unproven conjectures and difficult problems in the mathematical world, but not everyone can solve them easily.

Otherwise it wouldn’t have remained unresolved for so many years.

When Xu Yuan was in his early twenties, he published several papers in the Annals of Mathematics.

This is already a very terrifying thing, and he can definitely be called a genius among mathematical geniuses.

But if he were to say that the other party could solve another difficult problem in the field of mathematics during today's lecture, he would definitely not believe it.

The thought stopped here, and he nodded and said, "I have previously invited him to join our Clay Mathematics Institute. I should definitely go and listen to his lecture now."

After he finished speaking, he no longer hesitated and even quickened his pace.

Upon hearing this, Deligne naturally knew what his old friend was thinking, but he did not explain too much.

After all, he was not clear about the specific content of Xu Yuan's report today, and could not be sure whether he could still bring surprises to everyone.

If I say too much, it will be embarrassing if Xu Yuan's report turns out to be mediocre.

But having said that, he was still very much looking forward to it.

After all, ever since I met Xu Yuan, I have been constantly surprised.

Moreover, ten months have passed since Xu Yuan last proved Qiu Chengtong's conjecture on site. According to the speed at which Xu Yuan published papers in the past, he should have had new academic achievements.

Thinking of this, he and Wells soon walked into the main lecture hall together.

The main lecture hall in the conference venue is the one that can accommodate the largest number of people. The report delivered by the Fields Medal winner yesterday was also given in this lecture hall.

It wasn't that long since Xu Yuan first made his mark in the mathematics world with his proof of the Carmichael number spacing problem and has now won the Gauss Prize in Mathematics.

But he is quite popular in the mathematics community.

It is estimated that apart from famous mathematicians such as Deligne, Witten and Qiu Chengtong, the appeal of others is simply incomparable.

Therefore, the number of people who chose to attend Xu Yuan's lecture can be said to be very large.

When Deligne and Wells first entered, they were also very surprised to see the dark scene inside.

Even at a glance, I spotted a familiar figure.

At this time, the people who came earlier saw that it was Professor Wells from Deligne and Clay Mathematical Institute.

He also stood up out of courtesy.

Those sitting in the front row even took the initiative to greet him.

"Professor Deligne."

……

Deligne smiled and responded to the greeting, then walked up to a short-haired man.

"Mr. Combe, are you here too?"

"After all, he is the first winner of the Gauss Prize, so he still has to come for this one-hour report." Kang Kebi stood up and said with a smile on his face.

As a representative of the German Mathematical Association, he personally presented the Gauss Prize to Xu Yuan.

Then he definitely couldn't miss Xu Yuan's lecture.

Their main purpose was to see the content of Xu Yuan's report. If the content of the report was not of high quality or even contained errors, it would have some negative impact on them and the Gauss Prize established by the International Mathematical Union.

It will reduce the value of the Gauss Prize in the mathematics community. In simple terms, the better Xu Yuan performs, the more valuable it is for them to award the Gauss Prize to him.

Deligne understood the situation to some extent and said nothing more.

Just sat in the empty seat next to him with Wells.

In the following time, as more people walked into the lecture hall, Wells couldn't help but pay more attention to this lecture.

The main reason is that even the three winners of this year's Fields Medal chose to attend this lecture, which really arouses expectations for the content of the lecture.

nine in the morning.

Xu Yuan appeared at the podium in the lecture hall on time.

Standing on the stage, you can have a panoramic view of the layout of the entire lecture hall. On the right hand side is a waist-high podium with a laptop on the table.

Behind it is a huge screen used to display the report content.

Xu Yuan lowered his eyes and looked around, and naturally saw many familiar figures.

In addition to Deligne, there were Wells from the Clay Mathematical Institute and Combe who presented him the award.

Because Ma Zhiming and Zhang Yitang had to give group reports, there was a conflict in the conference schedule, so the two of them could not come to attend his report.

What surprised him a little was that in addition to Terence Tao, two other Fields Medal winners were also called over.

However, he was confident about his thesis and did not feel any pressure.

He signaled to them with his eyes and then officially started the one-hour report according to the procedure.

“First of all, I would like to thank the conference committee for giving me this opportunity to stand here and give a one-hour report.”

"My speech is about the study of singularities in differential geometry..."

……

At the same time, the content of the report he had previously submitted to the conference also appeared on the large screen behind him.

As Xu Yuan continued his speech, many mathematicians sitting in the audience were somewhat surprised, and many of them even couldn't help but frown slightly.

Differential geometry can be said to be a branch of mathematics that is basically covered, so even if you are not particularly good at it, you will be very clear about some situations in the field of differential geometry.

Among them, singularity is the core problem of differential geometry recognized by the international scientific community.

Normally, when giving a report at a mathematician's conference, one would choose the area in which one is best at.

In everyone's opinion, Xu Yuan should choose twin prime numbers, or content related to Qiu Chengtong's conjecture.

This at least ensures that no mistakes are made.

Otherwise, it would be extremely embarrassing and humiliating if you were invited to give a one-hour report at a conference and then had your mistakes pointed out by others during the report.

Although the proof of Qiu Chengtong's conjecture also intersects differential geometry, it is different from the study of singularities.

Deligne was not too surprised that Xu Yuan chose this content. After all, he had known that Xu Yuan would always come into contact with new content.

However, given the difficulty of the singularities in differential geometry, the report would appear mediocre if no research results were produced.

If this is true, Xu Yuan would not choose to report with such content.

Since he was able to stand on the stage and give a report with confidence, it meant that he must have achieved results in the study of singularities in differential geometry.

"Has he proved the strangeness of differential geometry?"

As this speculation came into his mind, he couldn't help but feel excited and happy.

You must know that singularities cannot be differentiated and have no differential structure.

To solve this problem, we need to develop new theoretical tools based on the work of our predecessors.

And also ensure that the logic performance is successfully verified.

If it is successful, the mathematical community's research on differential geometry will be more in-depth in the future.

But before confirming his guess, he calmed himself down for the time being and listened carefully to Xu Yuan's report.

As time passed, the expressions of many mathematicians in the lecture hall became serious.

As the saying goes, an expert can tell whether something is good or not at one glance. After seeing the content of Xu Yuan’s report, one naturally understood that there was something there.

At the same time, Wells, who was sitting in the front row, had brighter and brighter eyes, and he was looking forward to it.

I want to see if Xu Yuan can really prove the singularity of differential geometry.

It was not until this moment that he realized how wise it was to listen to Deligne and attend this lecture.

As for Kang Kebi who was standing next to him, he even informed the conference staff in advance and asked them to move the next report meeting to the spare hall, because he could see that only one hour might not be enough.

At this moment, Xu Yuan was completely immersed in the report, still speaking at his own pace.

I completely forgot there was a one-hour limit.

Another half hour passed.

With only the last page of the report on the screen left, the proof of the singularity of differential geometry also came to a critical point.

“H(S(X)∩B)<C(n,v)”

"Rx C(S…"

Xu Yuan looked at the proof formula on the screen and gave the final conclusion.

"This shows that in a certain geometric background, the singularity is not random, it has a specific structure."

……

(End of this chapter)