A genius? I just love studying.

Chapter 128 Inheritance
"amazing!"

Professor Adrien had no other thoughts; he was completely absorbed in Chen Hui's explanation until the deduction was finished, at which point he excitedly stood up.

"This is simply a perfect deduction method!"

The problem that had troubled him for more than half a year has been solved, giving him a feeling of relief like after constipation has been relieved. He is now eager to share this achievement with his team members and then continue with subsequent research.

That's truly exciting news!

"The Langlands Program is truly a magical tool; it seems I'll have to study it thoroughly from now on!"

Edriyan said excitedly that it wasn't until he listened to Chen Hui's speech that he realized the power of the Langlands Program, especially its interdisciplinary integration capabilities, which were quite ingenious in achieving great results with minimal effort.

By replacing complex physical phenomenological models with number theory tools, using the "rigidity" of mathematics to constrain the "softness" of physics, deriving experimentally observable topological responses from abstract symmetry, and achieving "counterintuitive precision" in theoretical predictions, weave the topological order of condensed matter physics, quantum field theory of high-energy physics, and number theory and geometry of pure mathematics into a single theoretical network, pointing towards the deep unity of natural sciences!
This is awesome!

Of course, this little Chinese guy who was able to do this is nothing short of amazing!

You're so amazing!

"Hui, you truly are the most brilliant mathematician I have ever met!"

"I would like to invite you to join my team. I am confident that you will be able to make groundbreaking breakthroughs in condensed matter physics!"

Edrian spared no praise, showering Chen Hui with compliments.

However, after a moment of excitement, he regained some composure and looked at Yun Wei and Tian Yang at the back of the conference room.

Although he was also a mathematician, there are differences between mathematicians. He did not find any flaws in the proof; he even thought it was perfect.

However, his research on the Langlands program was not in-depth, and he needed to obtain more evidence.

However, before the professors could speak, Ma Weiyang, who was sitting in the corner, raised his hand and stood up.

"Excuse me, I have a question I'd like to ask Chen Hui."

Seeing Ma Weiyang get up, Adelian's eyelids twitched violently. He recognized the little Chinese guy and suddenly had a bad feeling.

"please say."

Edrian wanted to shut Ma Weiyang up, but Chen Hui had already spoken.

“Hello Chen Hui, I am a student majoring in condensed matter physics. Your solution will eventually be applied to condensed matter physics, but we have not been exposed to the higher-order number theory tools involved in the Langlands program, such as automorphic representations, Gavarro groups, and modular forms, before. I can't even understand your proof, let alone apply it in my research.”

"Could you simplify the entire derivation process to the point that even students of condensed matter physics can understand it?"

Ma Weiyang had already adjusted his mindset. Professor Edrian's excitement had already explained a lot, so he was also looking forward to it. But as he said, he couldn't even understand the proof, so how could he apply it?
"can't read?"

Chen Hui was taken aback. He looked back at the proof he had written on the whiteboard and was somewhat puzzled.

The logic is clear, the arguments are detailed, and the proof is rigorous!

Why can't I understand it?
He turned his head and looked at the other professors in the conference room.

Seeing that confused look in her eyes, Ma Weiyang couldn't help but smile wryly; he was all too familiar with this kind of emotion.

What seems obvious to geniuses may take ordinary people a lot of effort to understand.

He had this feeling when he was explaining problems to his high school classmates, and he never expected that one day he would see the same reaction in someone else.

"Assuming the Riemann Hypothesis holds true, can you prove that all prime numbers p satisfy the imaginary part |Im(t_p)| of ζ(1/2 + it_p) > 1/2 log log p?"

Xing Jiguang spoke up to help Ma Weiyang out of his predicament. Since Chen Hui couldn't understand the difficulties Ma Weiyang was facing, he would give him an even more difficult problem so that Chen Hui could experience the same feeling and empathize with Ma Weiyang.

The other professors also smiled and looked at Xing Jiguang, some with a hint of mockery.

That old Xing, he really goes all out!

This question might be answered by a graduate student studying a related field, but that kid is good at the Langlands Program, so asking him this question is a bit too much.

However, in this situation, no one felt that Xing Jiguang's actions were inappropriate.

As expected, Chen Hui frowned and fell into deep thought upon hearing the question.

Time ticked by, and Xing Jiguang smiled, not intending to linger for too long. After only a few minutes, he spoke again, "So..."

“We can try to construct a proof by contradiction framework. Suppose there exists a prime number p0 such that |Im(tp0)|≤21loglogp0, and then derive a contradiction.”

Before Xing Jiguang could finish speaking, Chen Hui had already spoken.

The professors' smiles froze on their faces, and Xing Jiguang opened his mouth wide, swallowing back all the words he was about to say.

He even studied the Riemann Hypothesis?

Is he really only sixteen years old?
Condensed matter physics and the Langlands program are inherently very complex fields of knowledge, involving multiple disciplines and fields. Many doctoral students cannot even understand one of them, and even many professors need to spend a lifetime studying them to make any progress.

But this little guy just solved a difficult problem in condensed matter physics by introducing the Langlands program, and now he has shown in-depth research on the Riemann Hypothesis.

Even if you started learning math from the womb, you couldn't possibly master this much knowledge, right?

“Following the work of Guth and Maynard, the problem of zero distribution is transformed into matrix analysis of Dirichlet polynomials. First, a Dirichlet polynomial related to the zeros is constructed, the magnitude of which reflects the degree to which the zeros deviate from the critical line. Then…”

As he spoke, Chen Hui turned around and began to work out the remaining blank space on the whiteboard.

"Alright, no need for proof."

Sitting at the very back, Tian Yang smiled broadly and waved.

He certainly understood what Xing Jiguang meant; this method worked most of the time. Unfortunately, they ran into Chen Hui.

He's really growing to love this little guy more and more!
Chen Hui stopped writing, turned to look at his grandmaster, and understood Xing Jiguang's intention in setting this question, but...

Do you know which structural materials C30 concrete is suitable for?

Tian Yang asked with a smile.

Ginger is indeed old and spicy!
Upon hearing this, everyone in the conference room looked at Tian Yang, as if they had been enlightened.

Including Chen Hui.

He really couldn't answer that question.

"The higher the grade of concrete, the stronger its compressive strength. Therefore, high-grade concrete is usually used for columns, walls, and shear walls. However, low-grade concrete is used for ordinary beams and slabs because beams and slabs are mainly subjected to bending. High-grade concrete has limited effect on improving the load-bearing capacity, but it will increase the reinforcement ratio and the risk of cracking."

Tian Yang explained, then looked at Chen Hui, "Do you understand?" Chen Hui certainly understood.

You can never truly learn from someone else, but you can learn from experience. This is the same principle; many things are truly difficult to understand without personal experience.

He himself had climbed his way up from being a poor student, and he never imagined that one day he would fall into such a trap.

After the sudden realization, everything became clear.

"I will spend some time building the Langlands dictionary to translate the key properties of automorphic representations into physical language. This will take some time, but it is not difficult."

Chen Hui said to Ma Weiyang.

Your math level has improved from 2 (83%) to 84%.

"So, you also believe that this implementation method is fine, right?"

Professor Edrian's focus, however, was not on that at all, and he asked again as if in a dream.

This time, the other professors, including Tian Yang, all nodded.

Indeed, Chen Hui's implementation method is not only flawless, but also perfect, ingenious, and full of clever ideas!
At this moment, Yun Wei, who was sitting next to Yuan Xinyi, stood up and said, "In the experiment, it was observed that the fractional Chen number with n=3 may correspond to multiple modulo forms, which requires additional physical criteria. If the experiment measures σxy=e2/(3h), it may correspond to different combinations of coefficients of multiple modulo forms, which requires higher precision to distinguish."

Have you considered these issues?

Yun Wei looked at Chen Hui, and before Chen Hui could answer, he continued to ask, "The Langlands program is mature in two-dimensional number theory, but fractional Chern numbers of three-dimensional and higher topological phases lack a corresponding modular form theoretical framework, and a completely new high-dimensional automorphic form theory needs to be developed."

The connection between number-theoretical structures and physical phenomena is more of a "mathematical coincidence" than a mechanistic explanation, making it difficult to guide the design of new materials and impossible to directly predict the manipulation of non-Abelian anyons in materials from modal properties.

A barrage of questions made Chen Hui's forehead sweat slightly. He only considered solving the problem Professor Adrien encountered and providing a differential geometric implementation of fractional Chern numbers.

Indeed, the issues raised by Yunwei were not taken into account.

But now that I think about it, these problems must be solved.

Otherwise, simply realizing the differential geometric representation of fractional Chern numbers would not be of much significance.

Only by thoroughly solving these problems can we gradually establish the standard model of "topology-number theory", develop experimentally measurable "modal probes", and construct high-dimensional Langlands-topology theory.

The flaw in the Langlands approach is essentially a "dimensional gap" between mathematical tools and physical needs, but its solution points to a profound revolution in mathematical physics.

By redefining the interaction between theory and experiment, the abstract beauty of number theory can be transformed into a blueprint for controllable quantum technology. The success of this approach may give rise to a new paradigm of "number theory-driven materials design," the significance of which goes far beyond the fractional Chern number problem itself.

In other words, in the past, the properties of a certain structure were determined through experiments, and then the structure was represented using mathematical language. The materials were then analyzed, and new materials were discovered or constructed.

However, if these key pathways are broken through, then the logic of future materials science research will undergo a radical change.

The approach has shifted to a mathematics-driven model, where mathematical models are first used to design and predict material properties, which are then verified through experiments.

This kind of change is similar to Einstein's revolution of theoretical physics research through symmetry!

Its impact is comparable to that.

It is easy to imagine how difficult it is.

Therefore, when Yun Wei raised these questions, the other professors in the conference room did not look very happy, especially the professors from the Department of Mathematics at Yanbei University.

They felt that this brilliant mathematician from the Tsinghua Mathematics Research Center was deliberately making things difficult for younger generations and was suspected of bullying them.

Yuan Xinyi, however, did not think so. He knew Yun Wei well; if he hadn't completely accepted Chen Hui, he wouldn't have bothered to say another word.

These questions were not meant to make things difficult for Chen Hui; on the contrary, they were guidance, or even pointing him to a bright future.

"Wow, what a brilliant idea!"

The conference room was filled with Professor Edriyan's exclamations of amazement; he seemed to already see the glorious future that would come after all these problems were solved.

"But none of that matters. Chen has already shown us a broad road ahead. With the differential geometric realization of fractional Chen numbers, we can continue our research!"

Adelian looked at Chen Hui again and extended a sincere invitation to him, "Chen, a genius like you should come to Stanford!"

"I have no plans to study abroad at the moment."

Chen Hui shook his head.

He doesn't have it now, and he doesn't have it in the future either.

"What a pity!"

Adelian sighed in disappointment. His mind was no longer on the seminar; he just wanted to get back to his team as soon as possible, share the brilliant methods he had learned at the seminar with his team members, and then use these methods to study their next ideas.

His eyes were filled with a bright light, and the world would be wonderful again tomorrow!

"Extending this conclusion to higher dimensions is indeed quite difficult. Perhaps we could try to use quantum computers to assist in developing quantum algorithms to quickly calculate the Fourier coefficients in high-weighted modulus forms, such as a variant based on Shor's algorithm..."

Xing Jiguang, however, kept staring at the formulas on the whiteboard. He frowned, glared at Edrian, and interrupted his rambling.

"How can we adapt the high-dimensional representation of strongly correlated systems using tensor network compressed modular forms?"

Chen Hui asked a question in return, then frowned and fell into deep thought.

For a module form of N=100, quantum algorithms can compute ap in polynomial time, while classical algorithms require exponential time.

Times have indeed changed, and the logic of mathematical research is also changing. For example, Schultz has been collaborating with Microsoft for a long time, trying to use computer-aided mathematical research, which he also mentioned in his liquid tensor experiment. They have now made considerable progress.

Not to mention that many mathematical studies nowadays require verification using supercomputing, so he could consider this path, embracing the new era and new technologies.

"We could consider interpreting the modal form as the generator of the topological response function, reconstructing topological field theory, such as the quantum correction term of the Chern-Simons action..."

Yunwei also joined the discussion.

Soon, the professors in the conference room also offered their insights on these existing problems, and then, based on the opinions of other professors, the content was continuously revised and adjusted...

A seminar, of course, cannot be a one-man show by Chen Hui alone.

Yuan Xinyi organized this seminar not only to expand Chen Hui's network, but also to use this format to solve bigger problems and save Chen Hui's research effort, just like what his teacher did for him a few days ago.

Perhaps, this is what inheritance is!

(End of this chapter)