Top Student at Their Peak-Chapter 183 - 100: Those Genius Opponents and the Unpredictable Youth_6

Chapter 183: Chapter 100: Those Genius Opponents and the Unpredictable Youth_6

"Alright, as long as you have a plan in mind! It’s best if you start today, and don’t forget to take some time to look at the paper."

"Don’t worry, Mr. Xue."

"Good, I’m leaving now. You can wander around tonight, but make sure you’re back by ten."

"Alright, Mr. Xue."

...

Despite appearing humble, as soon as Old Xue left, Qiao Yu immediately searched online for the two names that Old Xue mentioned, especially Peter Schultz. After all, the other guy deals with computers and is not really his field.

And then he found Schultz to be really boring, having competed in the IMO four times.

But this didn’t particularly impress Qiao Yu, as he already had a general idea of the difficulty level of IMO problems. The key point was that this guy finished undergraduate courses in three semesters and completed the master’s curriculum in two semesters at Bonn University, which was indeed impressive.

But the most crucial thing was that this dude created Perfectoid Spaces by himself and became a W3-level professor, the highest rank at Bonn University, at the age of 24.

Damn! Is this guy cheating?

Qiao Yu didn’t even have the time to boast with his two friends surnamed Yu in their group chat. He didn’t rush to memorize those terms but instead seriously sought out videos on so-called Perfectoid Spaces, intending to understand what exactly it is that makes the mathematics community so focused on it.

Coincidentally, it turned out that this thing is closely related to prime numbers, which he was currently researching. It even gave him a tingling sensation in his brain.

The concept of Perfectoid Spaces is based on p-adic numbers, which Qiao Yu was somewhat familiar with. He had watched many videos about the analytic properties of the ζ-function, which mentioned analyzing p-adic ζ-functions and their relations to the distribution of prime numbers and L-functions. freēnovelkiss.com

The Perfectoid field created by Peter Schultz is a complete non-Archimedean local field with a p-adic topology, whose maximal ideal is generated by the prime number p.

So, you can also see Perfectoid fields as a kind of limit form of p-adic numbers, but they can only maintain their completeness under certain algebraic operations.

Thus, there may exist some geometric spaces with special structures on this perfectoid field, which can be used to tackle complex problems in geometry and number theory.

In summary, Perfectoid spaces are obtained by constructing certain types of completed geometric structures, and through infinite steps of p-adic completion, they can effectively handle complex geometric issues within p-adic number fields.

Moreover, Perfectoid spaces have a self-defined symmetry, allowing geometric information to be transferred between different extension fields and even permitting the infinite approximation of geometric objects when dealing with the cohomology problems of algebraic varieties...

This stuff... is something a human brain can think of?

They bring together parts of algebraic geometry to solve classical problems in number theory.

This kind of person actually participated in the IMO four times and only got first once? Could it be that Germany offers so much prize money for an IMO gold medal that it’s irresistible?

With his mind filled with frantic complaints, Qiao Yu casually logged into Yanbei University’s library system and then tried searching for Peter Schultz’s name, which indeed brought up a bunch of papers.

Without hesitation, Qiao Yu downloaded five papers related to Perfectoid spaces.

He then opened the first one in chronological order.

This was a paper published by Peter Schultz in 2011—"p-adic Hodge Theory for Rigid-analytic Spaces and Perfectoid Spaces".

Qiao Yu immersed himself in it, even though his phone kept vibrating. After glancing at it and finding out that it was just someone in the friends’ group expressing envy, he simply turned on "Do Not Disturb" and put it aside. Yu Wei’s weakness was no longer within his view, and he didn’t even get satisfaction from mocking him anymore.

Additionally, Qiao Yu suddenly felt a sense of urgency and naturally had no time to waste with the two of them.

A top student on the other side had already submitted a paper to a top conference during their freshman military training. If he wanted to be stronger than others, he had to submit a paper to a top mathematics journal before freshmen’s military training. With only half a year left, how could he waste his brain when it wasn’t tired yet?

Leisure had to wait until the brain could no longer hold out.

Not to mention Qiao Yu now desperately wanted to dive into Peter Schultz’s mind to see how this guy constructed all of this.

...

Outside Qiao Yu’s room, in the second-floor office of a building two blocks away, Tian Yanzhen had just returned to the office.

Originally planning to come back for dinner with Qiao Yu after the meeting and chat a bit, he couldn’t refuse the gracious invitation after the meeting and ended up staying for dinner over there.

He still had some project proposals with foreign collaborations to review.

The secretary knocked on the door, walked in, and handed over the printed proposals that needed confirmation. Before leaving, she smiled and said, "I just saw in the account backend that Qiao Yu just downloaded five papers by Peter Schultz, all related to the Perfectoid space theory."

"Oh?" Tian Yanzhen was visibly surprised and slightly puzzled.

This kid... Today, he had Mr. Xue give him the account with the thought that he would download papers related to Professor Robert, especially since the lecture was happening the day after tomorrow. It was essential to understand some of the speaker’s mathematical ideas in advance.

But this kid completely went off-script; why did he suddenly fixate on Peter Schultz’s Perfectoid space theory?

"Alright, I’ll check it out after finishing up here." Tian Yanzhen shook his head, choosing not to dwell on what this young guy was thinking, and instead focused on the collaboration contract details.

Once the approval process was roughly completed, he signed it, backed it up, and walked out of the office to end the workday.

"Let’s go, see what my new student is busy with."

Since the research center wasn’t that big, it only took dozens of steps from the office building to reach the room temporarily assigned to Qiao Yu. The kid hadn’t drawn the curtains, and from this angle, you could just see Qiao Yu’s profile through the glass.

At that moment, Qiao Yu was sitting at the desk, looking at the computer, with paper and pen placed beside him.

Tian Yanzhen motioned to stop the secretary who was about to knock on the door. He stood there for a moment, watching Qiao Yu stare at the computer screen, occasionally picking up the pen to jot down notes on paper, frequently tapping his head with the pen, and occasionally bursting into expressions of joy...

"Forget it, let’s go back for now and not disrupt the kid’s train of thought." After standing for a moment, Tian Yanzhen shook his head, then turned around and left.