Top Student at Their Peak-Chapter 198 - 103: The Proud Young Man, Commanding with Vigor_3

He could feel his heartbeat accelerating.

"Thump thump thump..." like a war drum being beaten.

What kind of comprehension speed is this? He initially thought it would take at least half an hour to simply explain quantization to Qiao Yu, because it involved many complex mathematical concepts, many of which he wasn’t sure if Qiao Yu had encountered before.

After all, Qiao Yu hadn’t received systematic education in mathematics, but as he spoke, and spoke, this guy suddenly clarified a rough idea from yesterday to this extent? And looking at the process, it seemed not wrong, rather quite rigorous.

There are issues, but for a fifteen-year-old child, he really couldn’t ask for more!

"Have you encountered Symplectic Geometry before?" Suppressing the excitement in his heart, Tian Yanzhen asked with as steady a tone as possible.

"No." Qiao Yu shook his head.

"Have you specifically studied quantum physics?" Tian Yanzhen pursued.

"No, just know a little bit, like wave functions and that the microscopic world doesn’t have certainties, only probabilities. Haven’t conducted specialized research, just read some popular science, understand things like wave-particle duality." Qiao Yu shook his head again.

"And you understood?"

"I understood, yeah. The principle is to incorporate quantum variables, or quantum structures, into curves to perform micro-manipulations, expanding their operability. You explained it so clearly. If I still didn’t get it, wouldn’t that be quite foolish?"

Having said that, Qiao Yu suddenly felt something was wrong, realized it, and cautiously asked, "Ah... is my deduction process incorrect?"

Tian Yanzhen took a deep breath, shook his head, and suddenly felt that some of his previously thought-to-be smart students now indeed seemed a bit dumb.

Then he opened his mouth slowly and responded, "Mathematics exams are about right or wrong, but frontier research in mathematics really isn’t." Judging the correctness of a deduction process only depends on whether you can reason it within the given theoretical framework without leaving any logical loopholes.

At present, I haven’t seen any logical loopholes in your deduction process, but I can’t represent the mathematical community. At least, my knowledge of Peter Schultz’s research is limited to understanding, which also includes the homology theory of p-adic geometry, but I am not proficient. You can record all these into the seminar report for the afternoon, and analyze them together with everyone else."

Qiao Yu nodded hastily and said, "Understood, Director Tian."

As they were talking, the door suddenly opened, and Professor Xue appeared at the door with two lunch boxes in hand.

"Qiao... uh, Mr. Tian, you’re here too?"

"Yes, at noon I asked a few school leaders to accompany Professor Robert for lunch. I was thinking about explaining some things to Qiao Yu since it’s his first time holding a seminar."

"Oh, you haven’t eaten yet, right? How about you guys eat first?"

Tian Yanzhen hesitated for a moment, then nodded and said, "Okay, then I will eat here. Don’t run back and forth, I’ll send a message to Xiao Li to bring a portion back for you."

Originally, he hadn’t planned to eat here.

But there’s no way around it, teaching a student like Qiao Yu really easily becomes addictive because it’s particularly easy to gain a sense of achievement.

Especially since this child’s foundational knowledge in mathematics is almost like a mixed abstract painting, yet he can find his own patterns within this abstraction. This talent is probably not inferior to Peter Schultz’s.

Tian Yanzhen believed that no matter who had such a student, they wouldn’t mind interacting a bit more.

"No need for so much hassle; I’ll just ride a bike to the cafeteria, have a meal, and come back afterward."

"That works too. Make sure to come back quickly after you finish eating to help Qiao Yu sort out his things and enter them into the computer. Meanwhile, I’ll teach Qiao Yu something in advance." Tian Yanzhen nodded and said.

Xue Song nodded with a complex feeling and replied, "Alright. I’ll be quick." After speaking, he immediately turned around and left, while Tian Yanzhen opened the lunch box and said, "Finish your meal quickly; you still have a few propositions, and I’ll briefly talk about them with you."

"Okay, Director Tian."

Many times, truly liking someone is actually shown in similar ways.

...

"...If X is an algebraic curve of deficiency g, its moduli space Mg parameterizes all curves of deficiency g and imposes geometric constraints..."

"But haven’t you considered, this would add yet another index related to the properties of the homology group of modular forms, greatly increasing the complexity of the result."

"Director Tian, how do you think this should be handled?"

"I think it’s better to directly introduce Schultz’s p-adic Hodge theory, to gain further geometric constraints by analyzing the behavior of the curve in the p-adic number field Qp."

"You mean globalizing local properties? But local information is usually associated with a specific prime p, and different primes may lead to different local behaviors, which is more challenging, right?" freeweɓnovel.cѳm

"But it was your suggestion, so you need to think about it. However, as far as I know, in p-adic geometry, the local properties of an algebraic curve can be described using the étale homology group. And as you just mentioned, completeness condition has already ensured that we can derive global results from the local geometric structure, so this path is definitely feasible."

"Oh, then I need to think carefully about this... But we still have to introduce a constant, right?"

"Indeed, think about it thoroughly. Qiao Yu, you have to remember, the greatest gain for a mathematician in proving any mathematical conjecture is the method of proof, not merely the result..."

After eating a quick meal, Xue Song took over to begin the entry work from Qiao Yu, while the discussion and guidance from the mentor and student constantly flowed into his ears.