Chapter 110 A new conjecture: Lin’s conjecture

Looking at Lin Xiao's stopped pen and the way he was thinking, everyone became confused. What was he thinking?

As a result, the applause started and stopped quickly.

People did not disturb Lin Xiao, just like they did not disturb Lin Xiao when he was thinking about the question raised by Wiles.

However, people discovered that this time Lin Xiao seemed to be thinking longer than before.

what happened?

One minute passed, two minutes passed.

At this time, according to the time, this report has already been completed for an hour.

However, the staff nearby did not bother him, because not far away, Professor Wiana, the chairman of the organizing committee, stopped him.

Any genius-like inspiration is born in an instant.

As a bystander, all we can do is give these geniuses more time and then believe in them.

For Professor Wiana, he did not trust Lin Xiao at first and thought that Lin Xiao was causing trouble. But after listening to this report, he had already changed his mind. Such a genius should never use Use common sense to figure it out.

In this way, about five minutes passed.

Everyone also waited quietly for five minutes.

At this time, Lin Xiao finally started to move.

He took out his pen and started writing on the blackboard.

But as his previous moves appeared, the eyes of Wiles and Deligne shrank.

Lin Xiao... also discovered it? !

"What is he doing?"

Professor Sarnak next to him couldn't help but ask.

"This is the layer."

Deligne stared closely at Lin Xiao's steps: "Yes, that's it...this step, my God, he can actually think of such a transformation! It's actually a model!"

"Incredible."

Even Professor Andrew Wiles murmured: "Why didn't I think of this when I proved Fermat's Last Theorem?"

Deligne had no intention of paying attention to Wiles's mention of Fermat's Last Theorem again.

His mind had already begun to follow Lin Xiao's steps.

And he had no other thoughts but wonder.

As for Lin Xiao, there wasn't much written on the blackboard, only six simple lines.

But at this point, he put down his pen, and then he quietly glanced at the last few lines.

【……Otop(E)Otop(BT2)k(E[p∞])】

He took a deep breath, then turned his head and faced the audience again.

The audience in the audience either frowned, thinking about the steps on the blackboard, or looked confused, as if asking "what happened?" Some people were already drowsy.

However, Lin Xiao just smiled, looked at Professor Wiles again, and said, "Professor Wiles, I have solved your problem."

"But yesterday when I listened to Professor Lahore's report on the geometry of curve modulus spaces, I think about this issue again now, and I came to a result that surprised me."

"As you can see, I formalized ψ(S0) into this function layer through modular formalization."

"However, this is clearly a unique situation."

"Therefore, I now have a guess. As long as we generalize this special case, that is, it can be established in the form of k=1, then any function can be converted into a layer form."

"Weil was eager to find the 'Rosetta Stone' between algebra and geometry. Today, his Rosetta Stone has become our Langlands Program of Geometry, and in the process of studying it, the 'layer' has become A wonderful approach, and if we can convert any function to a layer, I believe that we will bridge a small but strong enough gap in the geometric Langlands program."

"This is my vision for the future."

"Well, we've gone a little far, that's it. Does anyone else have any questions?"

He looked around the auditorium with a smile, but then he thought of Professor Wiles, so he turned around and said, "Oh, by the way, I'm sorry, Professor Wiles, do you still have questions about my proof?" "

At this moment, Professor Wiles in the audience was silent.

He quietly looked at the last six lines of expressions on the blackboard, and recalling what Lin Xiao said just now, he said: "No more, I'm very satisfied with your answer."

"Thank you then." Lin Xiao nodded.

But at this moment, Wiles said: "But, future Professor Lin, I think this guess you put forward is more attractive than this question. I originally proved Fermat..."

"Stop!"

When Deligne really couldn't stand this critical moment, Wiles actually wanted to talk about his shining moment again. It was as abominable as the author of the novel who immediately wrote the key point before writing it.

So he interrupted Wiles, stood up directly, and said directly without using a microphone: "This new guess you proposed has found a new direction for our algebraic geometry."

"In the past, we all believed that we could not naturally convert all functions into layers. Only certain functions allowed us to do so. And we all know that when functions are converted into layers, they will carry these functional forms that cannot be represented. A lot of information is coming out that will help us a lot.”

"Most of the functions in the Langlands Program can be converted into the form of layers, but there are still some that cannot be transformed. The guess you put forward will allow us to complete this part of the breakthrough."

"This is definitely a very important proposal for modern algebraic geometry. It will open up the direction of our algebraic geometry and make greater contributions to the unification of mathematics."

"So, I would like to ask you if you have any other thoughts on this issue?"

Lin Xiao looked at the professor. He didn't know who he was, but he seemed to be quite powerful.

He shook his head and said: "Sorry, as you can see, I only derived this question just now, and it is just a guess now. In addition, I don't do much research on algebraic geometry. If you let me If I solve it, there may be nothing I can do.”

"Even if I have a brilliant way to prove it, there's not much room on this blackboard, so forget it."

After hearing Lin Xiao's words, everyone couldn't help laughing.

Is this an homage to Fermat?

When Fermat proposed Fermat's Last Theorem, he wrote, "I am convinced that I have discovered a wonderful proof, but it is a pity that the blank space here is too small to write." So this question stumped three people in the mathematical world. It took more than 150 years for Wiles to complete the proof.

Deligne also smiled, without any regrets, and said: "Congratulations, young man, today you not only solved a problem that has stumped the mathematical world for more than two thousand years, but also solved a problem for us today. Once again, a new goal is proposed for the algebraic geometry community, and this goal will probably be called Lin's conjecture in the future."

"On behalf of my teacher Grothendieck, and Andre Weil, I would like to express my gratitude to you!"

Asking for a monthly ticket!