The top student must be diligent

Chapter 77 Maynard: Am I going to learn far Abelian geometry?

Professor plans to go to China?

Upon hearing this news, Maynard's students were a little stunned.

Why did they suddenly plan to go to China?

As researchers of mathematics, they did not have a very deep impression of China. It was only recently that the mathematical genius of China emerged that made them a little surprised that such a talented young man could appear in this country.

"Professor, are you going to China to attend a mathematical conference?"

Li Qiman asked.

Maynard waved his hand and said, "Forget it, let's not talk too much for now. This matter has not been decided yet. I just have this idea. Let's make a decision later."

He decided to communicate with Xiao Yi first and further discuss his ideas on far Abelian geometry and automorphic forms. If he had to talk face to face, he would go to China in person.

Then, he took out paper and pen and prepared to study it according to the theory in Xiao Yi's attachment.

But at this moment, he suddenly remembered something, and then said to Li Qiman: "By the way, since your thesis has been completed, let's start the defense in a week, is that okay?"

Li Qiman was stunned and said in disbelief: "What? Professor! The defense will be in a week... I'm not ready yet! At least... at least one month, right?"

Maynard said helplessly: "I'm doing this for your own good. In a month, whether you can graduate is a question."

"Why?" Li Qiman didn't understand at all, he pushed the θ value to 0.617!

Maynard sighed. He didn't want to hit his student, but after thinking about it, if he didn't explain, Li Qiman might still ask questions.

So he explained: "Because someone has further improved my method and pushed the θ value to 0.65."

"Wang Defa?"

Li Qiman's eyes widened immediately.

How is this possible? !

Maynard's three papers were published in June, and only three months have passed. Who can improve his mentor's method so quickly?

It improved by 0.05 at once!

He was able to improve from 0.6 to 0.617 based on Maynard's work. That was because Maynard was his mentor after all. So before these three papers came out, he had studied this method with Maynard, and combined with his own understanding, he was able to achieve this level.

For their analytic number theory community, improving by 0.017 is also a huge breakthrough.

As a result, now...

"Professor, who is he? Has his paper been published? Where did you see it?"

Litchman asked three questions in a row.

It's about graduation, he has to be anxious!

"Hmm..." Maynard said, "Since you want to know, I will reveal it to you for now."

"This person is the 17-year-old Chinese mathematical genius, named Xiao Yi. He has not published a paper yet, but just sent me an email. In the email, he mentioned that he would not publish this result in a short time... I guess, maybe he doesn't think highly of this result."

Xiao Yi could send this result to him without any scruples, so he must not think highly of this 0.65. Perhaps, what this genius boy really wants is to complete the combination of far Abelian geometry and automorphic form, which can easily advance to 0.7 or even higher.

Maybe...

It is to prove the Elliott-Halberstam conjecture?

He came back to his senses and looked at Lichtman in front of him.

At this time, his student was completely stunned. Maybe he was shocked to learn that the result he worked so hard for so long was completely worthless in the eyes of others?

Especially that person was only a 17-year-old young man.

Of course, it was not just Li Qiman. Several other students who heard the news also showed disbelief in their eyes.

It seems that it is still too early for these young people to accept this news.

After all, even Maynard himself was a little unbelievable in his heart.

"Okay, don't think too much, go back and prepare for the defense. Even if Xiao Yi may not publish it in a short time, it's better to be on the safe side. If he publishes it on arxiv in advance, then your graduation thesis will be outdated, and the college will most likely not pass your graduation thesis."

Patting Li Qiman on the shoulder, Maynard stopped persuading him, turned around, and began to carefully study the PDF sent by Xiao Yi.

Although the content of these 15 pages is small, he really has to study it carefully.

"Am I going to start learning far Abelian geometry?"

Such thoughts came to his mind involuntarily.

...

Time passed quickly.

The second day in China.

When Xiao Yi got up early in the morning, he looked at the time and it was exactly six o'clock.

He should have gone to bed around 10:50 last night.

He slept for a little over seven hours.

"Huh~"

He stretched out in bed and then did a few math problems in his mind out of habit.

[Find lim(x→0)[tan(tanx)-tan(sinx)]/ln(1+x^3).]

"Hmm... it should be equal to 1/2."

After a brief thought, he got the answer.

He didn't think about the answer carefully, and it was not worth thinking about. Anyway, it must be right.

He thought about two more questions.

Today's "brain warming exercise" for getting up was completed.

And the [Ruthless Lianxue] buff was also shown to be renewed.

"Done."

He got up, dressed, washed up, took the breakfast coupon, went to the restaurant on the first floor of the hotel for breakfast, and then returned to his room to start his study. The next day would probably be spent in study - this is his normal schedule.

"It seems that the military training is still going on at HKUST?"

Xiao Yi thought about it. According to the plan, after attending the meeting in Germany, he could return to school to catch up with a few days of military training.

But who would have thought that after returning home, he would have to stay in Beijing for another ten days.

According to the time agreed with the leaders of the School of Mathematics yesterday, his report on returning home will start in 10 days, that is, on September 26. The venue for the report is a large conference hall in the School of Mathematics, which can accommodate more than 300 people.

He definitely doesn't have to go back in these 10 days. Anyway, the school directly stated that he can go back if he has time, and it's no problem if he doesn't go back.

The military training will end on the 20th. If I had known, he wouldn't even see the instructor after school started!

As for going to class after the military training?

That's even more of a problem.

"In this case, am I a bad student or a good student?"

He thought so in his heart.

Forget it, don't think too much, start studying!

After opening the computer and checking the mailbox, Xiao Yi raised his eyebrows: "Huh? Professor Maynard sent an email?"

Chapter 78 Mysterious Functor

After opening the mailbox, Xiao Yi saw that he had received a new email, and the sender was Professor Maynard's email.

The reply was quite fast!

Enter the email.

[Mr. Xiao, hello!

I am very happy to receive your letter. I am very interested in the ideas you mentioned in the letter, especially the possibility of combining far Abelian geometry and automorphic forms that you described. I must say that this seems to be a very bold move, but I have to admit that it is in line with the idea of ​​the Langlands Program.

So, I think there is a good chance.

My specific thoughts are mainly presented in the attachment. It should be noted that I don’t know much about far Abelian geometry, so it is difficult to discuss with you from the perspective of far Abelian geometry. However, I do have some understanding of p-adic Hodge theory. Grothendieck once mentioned a conjecture that since the crystal homology H1(X/W(k))Qp of special fibers and the p-adicétale homology H1(X, Qp) contain the same information, it is believed that there is a "mysterious functor". Although I can’t find out whether this mysterious functor is helpful to your thoughts for the time being, I always have a hunch that it should have some relationship.

Please believe in the intuition of a number theorist:)

Finally, I look forward to your reply. 】

The attachment is also a PDF file with a title called "Kuznetsov Trace Formula and p-adic Hodge Theory".

After reading the other party's email, Xiao Yi immediately fell into deep thought.

"Mysterious functor?"

He really didn't know about this thing.

But after seeing Maynard's proposal, he immediately had an intuition in his mind that this thing might really have a great impact on his current research!

Mathematicians' intuition is sometimes very accurate, and this is even more so for particularly outstanding mathematicians.

In the discussion at the Max Planck Institute of Mathematics, Xiao Yi was able to sensitively perceive the problems in Mochizuki Shinichi's proof, which was inseparable from his intuition.