A genius? I just love studying.

Chapter 115 Classification of Higher-Order Topological Insulators
Yanbei University, north bank of Weiming Lake, Huaining Garden

"That's just how mathematics is; failure is always a constant."

Tian Yang strolled ahead, speaking softly without turning his head, his eyes filled with reminiscence.

He was the same way back then, struggling through countless failures and setbacks, and even wanting to give up at one point. In the end, with his passion, he made groundbreaking achievements and made amazing accomplishments.

The plan they had discussed a few days ago had been proven to be wrong, and he could sense the students' bewilderment without turning around.

Yuan Xinyi was absent-minded the whole way, clearly preoccupied.

"If you feel tired, take a break."

Tian Yang continued forward, his gaze passing over the tender buds of the weeping willows on the shore of Weiming Lake, and saw the CMO contestants emerging from the opposite side of Weiming Lake. "Yanbei University is currently holding a CMO event. Perhaps I can arrange a lecture for you. You can go and meet those young guys. Interacting with young people always makes people feel good."

He thought back to his own past, to the time when he took Yuan Xinyi as his student...

Yuan Xinyi, who had been silently following behind Tian Yang, also raised his head, a hint of anxiety flashing in his eyes.

The first day of exams is over!

Thinking of the matter hidden in his heart, Yuan Xinyi's heart stirred, and he finally spoke up, "Since the teacher likes these little guys, why don't you go and get to know them yourself?"

Tian Yang shook his head slightly, "More than ten years ago, I could still go out and pan for gold, but now, I don't have that energy anymore."

"What if there really are good prospects?"

Yuan Xinyi pressed further, "Isn't the teacher tempted either?"

"What, you've got your eye on a promising talent?"

Tian Yang, being a man of great stature, naturally understood the implied meaning.

Looking at the CMO contestants on the other side of Weiming Lake who had finished their exams and were rushing to the cafeteria, Tian Yang chuckled and shook his head. "I'm too old. I can still give lectures and enlighten young people, but as for training a disciple, forget it."

"Of course, if a genius of Gauss-Oula's caliber were to appear, I would still be tempted."

Tian Yang turned around and said with a smile.

Gauss-Oula was a man of immense stature, a genius one in a billion, so of course he had no hope.

"As for you, it's time for you to establish your own school of thought. If you encounter any promising talents, you should nurture them well and interact with young people more often. They might bring you unexpected inspiration."

An unexpected inspiration?

Yuan Xinyi pondered these words in his heart.

Someone has already brought it to him!

He hesitated, but ultimately didn't tell the teacher. The words that came out were, "Okay, teacher, I'll go then."

Tian Yang never expected that Yuan Xinyi would actually consider taking on a disciple.

This is different from teaching students at school. This kind of student is no different from the teacher and student in ancient times, just like him and Yuan Xinyi, just like him and his teacher who had broken off relations.

"Go."

After a brief moment of surprise, he was also happy for Yuan Xinyi.

At the same time, I was also curious about what kind of genius could catch Yuan Xinyi's eye.

However, once Yuan Xinyi accepts a disciple, we will eventually meet him, so there's no need to rush.

……

[Your math level increased from level 2 73% to 74%]

Turning to the last page of the printed paper and closing it, Chen Hui began to think about the direction of his paper topic.

These days he has also read a lot of papers related to condensed matter physics and has conceived a few directions in mind, such as the correlation effect in the moiré superlattice system, to explore the superconductivity, magnetism and other exotic phenomena in the moiré superlattice formed by stacking two-dimensional materials such as graphene and transition metal sulfides.

In recent days, he has also learned about controlled nuclear fusion. The two most promising methods are magnetic confinement and laser confinement, but Chen Hui believes that magnetic confinement is more likely to be achieved.

Magnetic confinement tokamak devices require the use of superconductors, and room-temperature superconductivity is the key to achieving magnetically confined controlled nuclear fusion.

He was also very interested in this.

However, this direction is more physics-oriented, requiring a large amount of experimental data to support it. Then, mathematical tools such as tight-binding models and renormalization group methods are used to build models, and finally, experiments are conducted to verify them. This process is then repeated continuously.

Such experiments require extremely high standards in material preparation processes, which is clearly beyond his current capabilities.

At the same time, the model parameters are extremely complex, making it difficult to find a unique and definite physical mechanism in these complex experimental data.

After learning how Einstein established the special and general theories of relativity, Chen Hui completely abandoned this outdated scientific research method. If he were to conduct research in this area, he would choose to first build a model through mathematics and then verify it through experiments.

However, it is clear that with his current level of physics, he is not yet capable of finding the symmetry necessary to build a model.

Physics is something you have to learn sooner or later. His goal is to fill the gaps in Yang-Mills theory. No scholar in mathematics or physics can help but be obsessed with unification, and Chen Hui is no exception.

However, this direction can only be considered as an alternative for the time being.

Countless topics swirled in Chen Hui's mind, only to be rejected one by one. Finally, only one topic remained in his mind: the classification and response theory of higher-order topological insulators.

This is also a popular area of ​​condensed matter physics, which mainly studies materials with high-dimensional topologically protected boundary states, such as hinged states and angular states, and establishes their mathematical classification, such as K-theory and symmetry indices.

This may seem unrelated to superconductivity, but classification theory provides clear prediction targets for experiments. For example, it can predict that specific materials, such as bismuthene and transition metal sulfide heterojunctions, may have higher-order topological states through symmetry analysis.

In recent years, experiments have observed higher-order topological states, such as angular localization, in photonic crystals, phononic crystals, and two-dimensional materials.

In other words, if a breakthrough can be made in this direction, this mathematical tool may shine brightly in the research of superconducting materials.

At the same time, this direction is more theoretical and has higher requirements for mathematics, which is suitable for Chen Hui's actual situation.

Chen Hui felt comfortable with this research approach of establishing theories first and then conducting experiments to verify them.

goooo...

Having eliminated his biggest threat, Chen Hui finally felt the protest coming from his stomach.

A thesis must be written step by step, just as a meal must be eaten one bite at a time.

After tidying up his materials, he slung his backpack over his shoulder, walked out of the study room he had randomly chosen, and headed towards the farm.

He had only been in Yanbei for a few days, but he had already fallen in love with this kind of life.

Every day, I would take my thesis, find a quiet place to immerse myself in the ocean of knowledge, and when I got hungry, I would go to the cafeteria to eat something before continuing to study.

No wonder so many people want to go to university.

University truly is paradise!
Letting the weeping willows gently caress his head, Chen Hui chose to stroll slowly along the lakeside path.

At this time, the CMO participants had already finished their meals, and the students of Yanbei University had all returned to their dormitories for a midday rest. Pedestrians strolled along the Weiming Lake in twos and threes, creating a truly pleasant atmosphere.

A dozen minutes later, we arrived at the farm. The huge canteen was only occupied by a few people. The aunties were pulling carts and clearing away the trays. The self-service food window had been removed, but fortunately, there were still two or three people queuing up for the Cantonese stir-fries on the first floor.

A bowl of stir-fried beef noodles arrives, the noodles glistening like amber, the beef slices slightly curled at the edges, the charred marks like gold trim, the teeth hitting the chewy noodles, the eardrums seeming to explode with the crisp sound of a spatula scraping against an iron wok, the vegetable stems so crisp you can hear yourself chewing, the salty and savory flavor of fermented bean curd mixed with the aroma of rice wine, soothing from the throat all the way to the bottom of the stomach.

Chen Hui's stomach was more satisfied than ever before. Five minutes later, the plate of stir-fried beef noodles was completely empty.

"Why did you come in person?"

“You think this is a small matter? Do you think those guys can handle it if I don’t come? Those guys in the admissions office are too slick; I don’t trust them to come.”

"They don't agree to the scholarship?"

"You don't need to worry about the scholarship. It will come from the research funding of the School of Mathematics. As long as that kid is as reliable as you say, I can make the decision."

After finishing his meal, Chen Hui looked up and noticed that two middle-aged men were sitting at the table in front of him. The one facing him was enjoying a plate of stir-fried clams with black bean sauce.

The person with his back to him was the professor from Jiangcheng University whom he had met just yesterday.

"Then hurry up and eat, and get this matter settled as soon as possible!" Yuan Xinyi urged.

After finishing the last clam, Wang Qiming sipped the broth from the shell three times before reluctantly putting it down. He then elegantly wiped his mouth with a tissue and asked, "So concerned? Tell me honestly, is that guy your illegitimate son?"

"I wish he were really my illegitimate child!"

Yuan Xinyi not only did not deny it, but also looked regretful, saying, "If I had a son like that, I would wake up laughing in my dreams."

"Is it really that strange?"

"His name is Chen Hui!"

"Chen Hui?"

Wang Qiming was puzzled. Why tell him the student's name?
"Chen Hui? Is that Chen Hui?"

But soon, he remembered the storm that had swept across the internet the day before.

Yuan Xinyi nodded.

"Then hurry up!"

Wang Qiming couldn't sit still any longer. He threw down the tissue, picked up his plate, and said, "I know Yanbei University well. Building No. 2, right? It'll only take a few minutes to get there."

"Teacher Yuan."

Chen Hui stepped forward.

Yuan Xinyi, who had just stood up, turned around and was immediately stunned, a blush creeping onto his face.

Seeing the plate Chen Hui was carrying, he roughly understood what was going on. It was also his fault for being too hasty earlier, only focusing on explaining the situation to Wang Qiming and not paying attention to his surroundings.

He wasn't one to mince words, and quickly recovered, saying, "Perfect, no need to go to the dormitory, let's sign the contract here!"

"Hello, Chen Hui!"

Wang Qiming smiled and extended his hand to Chen Hui. "Let me introduce myself. I am Wang Qiming, the vice dean of the School of Mathematics at Jiangcheng University."

"Hello."

Chen Hui also extended his hand, though he was still a little unaccustomed to this way of greeting. But when facing his sugar daddy, he wouldn't reject things that were dispensable.

"Truly, heroes emerge from among the young!"

Wang Qiming gently shook Chen Hui's hand, put down his plate, took out a tissue from his pocket, wiped the table, and then sat down opposite Chen Hui. He then took out a stack of contracts from his briefcase and placed them on the table.

"Old Yuan has already told me about your situation. Here is the contract. Take a look at it first. You can ask me any questions at any time. If there are no problems, you can sign it here."

He was also a straightforward and decisive person, and without saying much, he began to explain the contract details to Chen Hui.

"Ah."

Chen Hui gave a soft "hmm" and, without being polite, began to carefully read the contract terms.

He had heard Li Hai mention that a professional League of Legends player commented on other players' contract disputes, saying that if someone signed a document, then it had to be accepted.

Not long after, this professional player retired and was unable to earn money through live streaming due to contract issues.

He certainly wouldn't make the same mistake again.

"I heard from Lao Yuan that you have done a lot of research on the Langlands program in geometry? And that you even provided him with crucial inspiration!"

While Chen Hui was reading the contract terms, Wang Qiming spoke up again, "I've also been working on a related project recently—the construction and duality of automorphic D-modes of finite-order local systems on projective curves. I'm also stuck on a key issue. Could you help me think about it?"

He only heard Yuan Xinyi say that Chen Hui had provided him with inspiration, but he didn't know that the inspiration was related to condensed matter mathematics. He just subconsciously thought that Yuan Xinyi was studying the Langlands program, so Chen Hui should also be good at this field.

"Within the geometric Langlands framework, how can we explicitly construct the automorphic D-module corresponding to a local system with a finite single-valued group on a projective curve X, and verify its duality?"

Perhaps this is the case for all researchers: no matter how eloquently others describe it, the truth ultimately lies in what they see with their own eyes. They can only judge for themselves by witnessing it firsthand.

Even though he knew Chen Hui had won the Asai Gold Award, he didn't know how deep the waters were in Asai.

He believed in Yuan Xinyi's academic ethics, but no one knew exactly how significant his contribution was.

Chen Hui looked up from the voluminous contract terms and asked Yuan Xinyi with a puzzled expression, "When did he say he was good at the Langlands Program?"

Yuan Xinyi couldn't help but roll his eyes; he hadn't expected Wang Qiming to pull such a stunt.

However, before he could speak, Chen Hui replied, "Perhaps we can try to bypass the explicit construction by using the duality between the modulus space of the Higgs bundle and the Langlands of quantum geometry, and simplify the problem by utilizing symmetry."

He understands the importance of inspecting the goods.

Just a few days ago, I studied Yang-Mills theory and realized that with my current mathematical ability, it would be too difficult to solve this problem, so I decided to turn to the study of condensed matter physics.

But when he heard Wang Qiming's question, he immediately thought of the method Higgs, the supplementer to Yang-Mills theory, used to solve symmetry breaking.

Upon hearing his answer, Wang Qiming narrowed his eyes slightly. This was a problem they were actually facing, and there was no way Chen Hui had prepared in advance.

When he raised this question, he didn't expect Chen Hui to be able to provide an answer.

It's already quite remarkable that a high school student can understand this question.

Yuan Xinyi, however, frowned.

He wasn't doubting Chen Hui, but rather seriously considering the feasibility of the method Chen Hui had described. He knew that this was indeed a research project for Wang Qiming's graduate students, and he had been one of the reviewers when the project was proposed, so he had some understanding of it afterward.

But the solution they offered at the time was clearly not like that.

Chen Hui frowned slightly, also deep in thought. "First, we can try to embed the local system L into the Higgs mode cluster space MHiggs and use non-Abel Hodge theory to connect it with the construction of D-modes."

"Yes!"

Chen Hui's face lit up with joy. "By introducing quantum parameters and using the duality of quantum geometry's Langlands, we can transform the original problem into the construction of quantum D-modes of the dual group LG. We can then transform the finite single-valued group conditions into discrete parameters of the dual group. Finally, by utilizing the symmetry of the mode space, we can reduce the problem to a fixed point set. At this point, the automorphic D-mode can be explicitly expressed as a generator of the same kind on the equivariant!"

He himself did not expect that when he heard Wang Qiming's question, he only had a general idea in mind.

But when he thought about the idea carefully, the solution appeared in his mind automatically, like fireflies in the dark.

(End of this chapter)