A genius? I just love studying.

Chapter 127 A Gathering of Powerful Figures, A Young Phoenix's Clear Cry

The Langlands program, through its deep number-theoretic structure of modular forms and automorphic representations, not only solved the problem of a rigorous definition of fractional Chern numbers, but also revealed the mathematical essence of the denominator selection mechanism observed in experiments.

This cross-disciplinary integration has elevated topological matter theory from a "phenomenological model" to a "natural manifestation of fundamental mathematics," and perhaps on this basis, we can explore the unification of quantum matter and number theory!

In a classroom on the first floor of Zhihua Building, fine beads of sweat still clung to Chen Hui's forehead.

He just reviewed his thoughts in the lecture hall and added some supporting evidence to make the argument more rigorous.

After doing all that, a new idea suddenly popped into my head.

It gave him the feeling of progressing through a technology tree. Originally, the whole tree was black, shrouded in a fog, but as he unlocked the prerequisite knowledge, the subsequent branches also became visible.

However, these branches are still gray, and he needs to water them with his sweat to light them up.

Your math level has improved from 2 (82%) to 83%.

Your English level has improved from 5% to 6% (Level 2).

Two more comments flashed by.

A faint joy welled up in my heart.

Every time a comment pops up, it brings him a great sense of satisfaction.

Writing papers was indeed the right path.

Learning is an input process, and in middle school, doing exercises is an output process. By doing exercises, we can master, consolidate, and organize the knowledge we have learned. Therefore, Chen Hui can clearly feel that his proficiency in doing exercises improves faster.

However, simply doing practice problems will not accelerate the improvement of proficiency; sufficient input is needed to produce output.

With Chen Hui's current knowledge base, solving problems is clearly no longer sufficient for this output process; instead, he needs to write papers!

His rapid increase in proficiency today is the culmination of his hard work and study over the past few days!
I checked the time; it was already 2:47.

I got up, tidied up the draft paper, and walked up to the third floor.

He had already eaten lunch in the classroom. Li Zehan had packed him some char siu and roast goose, which was quite delicious. He would like to eat there again next time he has the chance. He didn't know why he, a native of Chengdu, would like Cantonese food.

With a jumble of thoughts swirling in his mind, Chen Hui arrived at the door of conference room 303.

Several people were already seated in the meeting room; judging from their age, they were all students.

Ma Weiyang, who stole the show in the morning lecture, was also there.

"This is the conference room. If you want to study, please go to the first floor."

The arrival of Chen Hui and his two companions caught their attention. A classmate stood up and pointed out that the three were wearing rather conspicuous middle school uniforms.

"We are here to attend the seminar."

Chen Hui spoke first, then went straight to find a seat and sat down.

"?"

The students in the meeting room looked at each other, but didn't say anything more. The fact that Chen Hui could say the words "seminar" already spoke volumes.

But they couldn't understand what three high school students could possibly do here.
Ma Weiyang also saw Chen Hui. He remembered these high school students, but he didn't have time to pay attention to them. His mind was full of Langlands' program.

After receiving the news at noon, he didn't go back to catch up on sleep, but rushed to the library and downloaded several papers related to the Langlands Program.

But the time was too short, and he didn't even finish reading one of the papers.

His current knowledge of the Langlands Programme is limited to knowing the name.

After sitting down, Chen Hui began to look around the conference room.

The meeting room was small, only about 30 or 40 square meters. There was a round conference table in the middle, surrounded by chairs. Near the front door, there were two 1.5 x 1 cm whiteboards, indicating that the meeting room had been prepared in advance.

Soon, professors began to enter the conference room one after another.

"Chen Songxi, a full professor in the Department of Mathematics at Yanbei University, specializes in probability theory and statistics, and is a recipient of the China Thousand Talents Program."

As the professor walked in, Li Zehan whispered something in Chen Hui's ear, clearly indicating that he hadn't been idle while Chen Hui was refining his argument.

"Li Zhonghai, a full professor in the Department of Mathematics at Tsinghua University, specializes in differential geometry and mathematical physics, and is a recipient of the China National Science Fund for Distinguished Young Scholars..."

Soon, another professor came in, and Li Zehan continued playing with crickets.

When the professors entered the meeting room, they were somewhat surprised to see three young students in high school uniforms. It was rather strange to see such young faces in the meeting room.

Of course, they didn't ask any further questions, guessing that it must be a junior colleague of some professor who came to broaden their horizons.

At that moment, a young man who looked to be in his thirties walked in.

Upon seeing this person, Li Zehan's voice trembled slightly, and his whole body quivered with excitement, "Yun Wei!"

"He's actually here too!"

"Yunwei?"

Chen Hui looked up at the young man, equally surprised.

This is a Chinese mathematical genius who is on par with Yuan Xinyi. He is one of the top figures in the Chinese mathematical community today. He won the Ramanujan Prize in 2012, the Breakthrough Prize in Science in 2017, and was invited to give a 45-minute lecture at the International Congress of Mathematicians in 2018!

He further established the overall Springer theory, providing a new research direction for the Langlands program!

He is already one of the few Chinese mathematicians who is closest to winning the Feinberg Prize, and the key point is that he is still very young!
Is this what a teacher's network looks like?

Chen Hui clicked his tongue in amazement and had even higher expectations for the upcoming seminar.

Not only them, but the other professors in the conference room were also surprised to see Yun Wei arrive. They all stood up to greet him and started chatting warmly.

At 2:55, Yuan Xinyi, Edrian, and Xing Jiguang walked into the conference room together, chatting and laughing.

"teacher."

Chen Hui stood up.

"?"

That one word, "teacher," immediately silenced the entire conference room.

what?
Are these high school students Yuan Xinyi's students?
But then another question popped up in their minds.

When Yuan Xinyi invited them, he said that his student would be giving the presentation at this seminar. Could he be referring to this high school student?
Edlian scrutinized Chen Hui carefully. He didn't know what the high school uniforms Chen Hui and the other two wore represented, but he felt that this kid was too young. Could the students Yuan Xinyi was talking about be these three kids?
"Wait a little longer."

After saying something softly, Yuan Xinyi began to greet the other professors in the conference room.

He didn't introduce Chen Hui to the professors because he knew that Chen Hui would introduce himself to them later, and the professors would probably remember him more clearly then.

"You're still here!"

"I knew you were coming!"

Yuan Xinyi looked at the middle-aged man at the back of the conference room with a broad smile. "You'd better give me a satisfactory answer, or you'll be in for a beating at Quanjude!"

Yun Wei wasn't very enthusiastic; he had skipped that person's meeting to come.

2: 59.

An elderly man with gray hair but a robust physique appeared at the conference room door.

"Haha, I'm not late, am I?"

Tian Yang said with a smile.

"Tian Lao."

The professors in the conference room all stood up and greeted Tian Yang.

Yuan Xinyi then came to Chen Hui's side, "Come here, this is your grandmaster!"

"Grandpa Master!"

Chen Hui greeted him politely.

He also investigated his teacher's background and learned that his great-grandfather was an academician of the Chinese Academy of Sciences, director of the International Center for Mathematical Research, and a whole host of other titles.

China is not like the West. In the West, academicians may be quacks, but the academicians of the Chinese Academy of Sciences are so important that even mentioning the title commands the respect of any Chinese person.

Chen Hui knew that his great-grandfather was very strong, but it wasn't until he saw the reactions of these highly respected professors in the conference room that he realized that his great-grandfather was even stronger than he had imagined!

"You're the student Xin Yi was talking about?!"

Tian Yang was also somewhat surprised. He had originally thought that the student Yuan Xinyi was referring to was the doctoral student he was supervising at Jiangcheng University.

Isn't this little guy a bit too young?
However, he quickly composed himself and said to Chen Hui with a smile, "Go!"

Chen Hui looked at Yuan Xinyi, and Yuan Xinyi nodded.

"The student Yuan Xinyi was talking about really is him!"

Watching the little guy stride towards the front of the conference room, the professors in the conference room were somewhat dazed. They could accept Yuan Xinyi praising his student, and even Academician Tian had come, so naturally they had no reason not to support him.

But even a graduate student would be acceptable.

A high school student?

Isn't that a bit too outrageous?

Yun Wei glanced at Yuan Xinyi, his pupils widening slightly, as if asking, "Are you joking?"

Why would a high school student be the main speaker at a seminar of this caliber?
Yuan Xinyi smiled slightly, said nothing, and simply looked at Chen Hui in front of him.

Xing Jiguang frowned, feeling as if he had missed something crucial.

This little guy is probably much, much stronger than he knows!

At this moment, he felt an emptiness in his heart, as if a piece was missing. He felt as if some opportunity that could have elevated his life had already passed him by.

Ma Weiyang struggled to open his swollen eyes.

While others may not know, he personally witnessed Chen Hui only starting to read Professor Edrien's paper about twenty minutes before the meeting began, and at that time Chen Hui was even still looking up words.

Now you're telling him that this little guy solved a problem that had been troubling Professor Edelman's team for more than six months?

Are you kidding me?
Chen Hui was unaware of what the people in the conference room were thinking; only countless formulas and inspirations surged in his mind.

Stepping between the two whiteboards in the conference room, Chen Hui looked at the nine professors and thirteen students in the room. When he actually stood in front of the whiteboard, the tension in his chest slowly dissipated and turned into a surge of pride that soared to his head.

"Hello everyone, I've been studying papers related to the Langlands program these past few days. This morning, during Professor Adelian's lecture, he mentioned that when generalizing the traditional Chern class to rational coefficients, it cannot explain why only specific denominators, rather than all rational numbers, were observed in the experiment."

"I was thinking, why not introduce the Fourier coefficients from the Langlands program? The Fourier coefficients of the modular form are often rational numbers. For example, the coefficients an∈Q of the modular form f(z) with weight 2, and the denominator is constrained by the modulus N. n=3 corresponds to N=27, which naturally fits the denominator selection mechanism in the experiment!"

"So I started to try to introduce the mature conclusions of the Langlands program to solve the differential geometric realization of fractional Chern numbers. What follows is my derivation process. If there are any inappropriate points, please correct me."

As he spoke, Chen Hui turned around, picked up the marker on the whiteboard base, and began to write down his deduction process.

"First, we need to select the correct model form... and obtain its Fourier expansion..."

Chen Hui wrote rapidly on the whiteboard with a marker, explaining his thought process as he wrote.

Tian Yang sat at the back of the conference room, looking at the eloquent little guy in front of him. His smile grew brighter and brighter. Only someone with a deep understanding of the world could show such confidence, and only a little guy like him could possess such brilliance.

This little guy looks just like him when he was young!

When Ma Weiyang heard Chen Hui speak, he also put aside his distracting thoughts. Regardless of whether this idea came from Chen Hui or not, he valued the result more.

And it's quite impressive that a high school student can retell these things.

However, he soon lost track of time and realized that he was starting to fall behind the other person's story.

"So how was that high school student able to understand it?"

A great deal of doubt arose in his mind.

So engrossed in his work, he didn't notice that not only him, but also the other professors, who had initially seemed to be watching the show, had all become serious.

"By embedding the modular form f(z) into the high-dimensional Chern-Simons theory, we define the fractional curvature form..."

At this point, Chen Hui had already written the formula on the second whiteboard.

Yun Wei, who had been somewhat lazy, sat up straight, his eyes shining brightly.

"The discreteness of fractional Chern numbers corresponds to the algebraic property of modular coefficients, and the stability of topological phases corresponds to the irreducible representation property of Galois groups. Establishing a correspondence between topological order in condensed matter physics and automorphic forms in number theory, and discovering this non-obvious correspondence, requires extraordinary insight!"

"Unifying physical symmetry and number theory symmetry through the Langlands dual group requires a solid foundation of knowledge!"

If this is really something the little guy made, then that's really interesting!

"By combining the curvature form Ω^m/n with the modular form f(z), a hybrid geometry-number theory object is constructed, and the analyticity of the modular form automatically guarantees the quantization condition of fractional Chern numbers!"

"Prove the duality between gauge field theory and Galois representation, and deduce the representational characteristics of the topological charge of non-Abelian gauge fields corresponding to the Galois group."

Is this the kind of ingenious idea that a high school student could come up with?
As Xing Jiguang looked at Chen Hui's proof process on the whiteboard, he suddenly felt a little uncomfortable.

Unlike the other professors in the conference room, he believed, without any reason, that Yuan Xinyi was not trying to promote Chen Hui; these things were really just the little guy's own ideas.

At most, Yuan Xinyi only offered some pointers.

"Finally, using the properties of modulus transformation, we prove that the modified curvature satisfies the generalized Bianchi identity!"

After writing the last formula, Chen Hui turned to the professors in the conference room and said, "These are all my thoughts for now. I don't know if there are any omissions. Please give me your guidance."

The entire conference room was so quiet you could hear a pin drop; for a moment, only Chen Hui's clear voice echoed in the room.

(End of this chapter)