Top Student at Their Peak-Chapter 187 - 101: The Crazy Math Novice_4

If all of the above difficulties can be overcome, then the theory of tilting involved in a complete space really makes one scratch their head. This concept, by introducing a new perspective of algebraic geometry, relates a p-adic complete body with a perfect body of characteristic p.

But this connection is very abstract, involving algebraic closure, whole closure, and other extremely abstract mathematical techniques...

In other words, this theory cannot be understood through the existing mathematical framework, and to understand Peter Schultz’s ideas, one needs to establish an entirely new mathematical system in their mind.

Qiao Yu just casually glanced at a paper on this topic that he downloaded yesterday, and today he seems to already understand it?!

Is this the advantage of having a weak foundation? No, if the foundation is weak, such papers should be incomprehensible in the first place.

To be honest, Xue Song finds it hard to grasp exactly how Qiao Yu manages to understand the concepts created by Peter Schultz.

Xue Song actually heard what Tian Yanzhen said earlier, but he couldn’t offer any opposing opinion; he just silently placed Qiao Yu’s draft paper back on the desk.

This probably belongs to a kind of free-range strategy. But the resources prepared for Qiao Yu are top-notch, just watching him tinker every day, it seems like a very exciting thing to see what kind of results he can come up with.

"Professor Xue, do you have any opinions?" Tian Yanzhen asked.

Xue Song shook his head, showed a faint bitter smile, and said, "I think this arrangement is quite good. Anyway, it’s just half a year. Let’s give him enough freedom first, and then let the results speak for themselves."

Tian Yanzhen nodded, looked at Qiao Yu, and said, "Then it’s settled. Do you have any questions?"

Qiao Yu quickly asked, "Oh, by the way, is there a Senior Brother Chen in this building?"

Tian Yanzhen nodded and replied, "Yes, his office is arranged on the third floor. Did you meet him?"

Qiao Yu kept nodding, saying, "Yes, yes, yes, I just wanted to ask what Senior Brother Chen’s PhD research topic is?"

Tian Yanzhen looked Qiao Yu up and down, amused: "Why, addicted to guiding fellow students? Previously helping Professor Xue’s master’s students with their papers wasn’t enough to showcase your level, and now you want to guide the PhD students?"

Qiao Yu repeatedly denied, "No, no, I just want to hear how difficult Senior Brother Chen’s topic is, to have a psychological preparation for my future PhD topic."

Tian Yanzhen shook his head and said, "Your situation is different from Senior Brother Chen’s. His topic has no reference for you at all."

However, after he said this, seeing Qiao Yu’s eyes full of curiosity, he still opened up and revealed, "His research direction is geometric analysis on complex manifolds, specifically the existence and stability of minimal surfaces on Kähler manifolds.

For instance, how to use the variational method to construct minimal surfaces, the stability of the energy functional of minimal surfaces, and the evolution of minimal surfaces under the action of Ricci flow, and so on." freeweɓnovel.cøm

"Oh!" Qiao Yu nodded, with an expression of sudden realization.

"What? You’ve studied these too?" Tian Yanzhen asked.

"No!" Qiao Yu shook his head and said, "I just feel that there’s a reason Senior Brother is still not graduated at 29. I watched a video before where a big shot mentioned that anything involving functional analysis is quite difficult."

Beside him, Xue Song couldn’t help it and said, "Functional analysis is difficult? As difficult as it is, it cannot be more difficult than Schultz’s complete space! As long as you can fully understand Hilbert spaces and Banach spaces, studying functional analysis is very simple."

Qiao Yu looked at Xue Song blankly and responded, "Huh? So, the methods of analyzing infinite-dimensional spaces involving p-adic numbers in the paper are techniques from functional analysis? Many places in the paper use p-adic Banach spaces."

Tian Yanzhen nodded and answered, "Indeed, when doing topological properties of p-adic numbers, function spaces and p-adic representation theory related analysis, the structure of Banach spaces often appears. But p-adic numbers are quite special, and the Banach spaces involved are different from those in real number analysis, which is what you call p-adic Banach spaces.

Don’t get tangled up in these, once you broaden your knowledge, you’ll understand. In the frontier of mathematical research, many mathematical tools overlap. This is also why mathematicians need a well-rounded foundation. But I want to see to what extent you can reach on your own. Any more questions?"

Qiao Yu immediately shook his head and said, "No more."

"Then we’ll go first. Tomorrow, Professor Xue will take you to attend Professor Robert’s lecture." After saying this, Tian Yanzhen and Xue Song left together.

Qiao Yu watched the two professors leave, stood up to stretch his body, and looked at the paper again.

Director Tian said that starting this afternoon, it’s fine to start reading Professor Robert’s paper.

With an hour or so until mealtime, Qiao Yu thought he should be able to almost fully absorb the essence of Peter Schultz’s first paper.

...

Under the warm sunshine, the two mathematics mentors walked quietly for a while. Xue Song couldn’t help but ask, "Mr. Tian, I don’t see any problem with giving Qiao Yu the freedom to learn over the next six months, but how should we arrange things after the start of the school year next year? Should he still learn with the talent class?"

Tian Yanzhen thought for a moment and said, "No rush to make a decision, let’s first see what this kid can achieve. To be honest, I don’t really know how to teach him now, but I feel that letting him actively explore problems on his own might be more suitable."