I was a top student in America.

Chapter 119 Homecoming Day (Please Subscribe)

"Weak solutions, Sobolev spaces, and local energy estimation—partial differential equations are indeed a branch of mathematics that is naively described but exceptionally difficult to study."

In a classroom at Wyndham High School after school, Li Ao sat in his usual spot by the window and muttered to himself.

A book on partial differential equations by Strauss lay open in front of him, and a basketball training bag was at his feet.

When summer vacation ended, he returned to his high school campus.

Although there wasn't much left for him to learn in high school, he still sat in class diligently in order to get his diploma, but he focused his main energy on self-studying university-level material.

After returning from the University of Chicago, he first took the time to incorporate the derivation of the discrete curvature correction term into the draft of his paper, and then sent the revised version to Professor Rudy and Amber for review.

He had assumed that such a long article in a top journal in computational physics would likely be criticized for many flaws and require repeated revisions.

The next day, they received very positive feedback, and Professor Rudy even specifically praised his rigorous and clear expression of the algorithm in the email.

Clearly, the other party had not expected him to be so good at writing academic papers.

With the physics project nearing completion, Li Ao shifted his focus back to mathematics.

Aside from studying functional analysis, I spent most of my time researching partial differential equations and harmonic analysis.

Among them, the subtle relationship between regularity, boundary conditions and energy concentration in partial differential equations is what interests him the most.

Many basic definitions and models of partial differential equations are often just a single line long, without the need for complex symbol stacking.

Taking fluid equations as an example, as long as one understands basic physical concepts such as velocity field, pressure, and time evolution, even a high school student can roughly understand what the question is asking.

This intuitive mathematical expression has been widely used in fluid mechanics, materials science, and financial models.

Even those famous world-class mathematical problems do not seem mysterious when viewed in isolation.

For example, the regularity problem of the three-dimensional Navier-Stokes equations essentially asks:

Given a sufficiently smooth initial velocity field, will the solution of fluid motion collapse in a finite time?

However, this core branch at the intersection of mathematics and physics, which once attracted the attention of many top mathematicians such as Hilbert, Poincaré, and Lere, still has many key problems that remain unresolved.

Besides the regularity problem, partial differential equations also include different research paths such as elliptic, parabolic, and hyperbolic forms, making them the most important tool in modern analysis and physical modeling research.

As he turned the pages, he gradually absorbed the knowledge of partial differential equations, and timely notifications popped up on the system panel:

[Under intense study conditions — Intelligence attribute +0.1]

Li Ao only snapped out of his reverie after turning to the last page of the chapter in front of him.

He casually picked up his phone to check the time, then looked up at Lin Jinni sitting opposite him. "I'm getting ready to go to training," he said casually. "Are there any AP Calculus questions you still don't understand?"

During this period, in order to prepare for the AP Calculus exam, Lin Jinni would always stay a little longer after school.

When they encountered problems they didn't understand, they would ask Li Ao for help. Over time, the two became familiar with each other.

Hearing Li Ao's words, Lin Jinni's eyes lit up, and she asked with a smile, "Not for now. Can I come to the gym to watch you train?"

"Sure, it's just routine training, not as exciting as a formal competition. As long as you don't get bored."

Li Ao had no objections. He swept the textbooks on the table into his backpack, picked up his training bag from the ground, and went downstairs. Lin Jinni also quickly packed her things and followed him.

As September arrives, it gets dark earlier and earlier each day.

Pushing open the doors of the teaching building, the chilly air of early autumn hit me, instantly making me feel much more awake.

The white streetlights on campus were already lit up early.

Walking down the street, Lin Jinni suddenly remembered something, took out a beautifully packaged little box from her bag, and handed it to Li Ao.

Perhaps it was the cold wind, but her cheeks were slightly flushed.

"Um—I went shopping with my student council friends at the mall last time for back-to-school," she explained softly, "and I happened to see this color is our school's official blue. You've been helping me with AP Calculus problems lately, so consider this a thank you gift."

"What's this?" Li Ao asked casually, taking the item.

"Open it and take a look, it's a wristband, you should be able to use it when playing ball."

Li Ao opened the box, his gaze lingering on the blue wristband for a moment.

The inside of the wristband has a barely noticeable letter "L" sewn on with white thread. The stitches are a bit crooked, and it's obvious that it was sewn on by hand.

Looking at Lin Jinni's slightly evasive eyes, Li Ao naturally understood what was going on.

Although he didn't have any particular feelings for Lin Jinni, he couldn't very well turn down the girl's good intentions.

So he carefully put the box away and placed it neatly into his backpack.

"Thank you, it's very useful."

Seeing that he accepted it, Lin Jinni breathed a sigh of relief and smiled happily: "I'm glad you like it."

The two quickly arrived at the entrance of the gymnasium. Lin Jinni took the initiative to start a conversation, chatting about the school's arrangements: "The Homecoming dance is in a few days. Your team will probably go after practice, right? I heard from the student council that the budget is plentiful this year, and the music and venue setup are quite good."

"I'll ask them later," Li Ao nodded.

Although the homecoming dance is an annual tradition, it is usually a perfunctory affair at Wyndham High School, with few students willing to participate in this old-fashioned and restrictive event.

On the contrary, the homecoming sports competitions after the dance often attract a lot of people.

In previous years, a rugby match was usually scheduled, but because the Wyndham Eagles basketball team performed exceptionally well this year, the school specially arranged a basketball scrimmage.

And their opponent is none other than Simon Vocational College, their old nemesis whom they faced in the first match of last year's Southern League.

The announcement of this competition schedule immediately whetted the appetite of all the students in the school.

After all, the team lost to Simon Academy last year, although by only three points, and naturally no one wanted to repeat the same mistake at home this year.

Moreover, the fall semester has just begun, and the new captain and the new lineup need an opportunity to prove their abilities.

It would be really unacceptable if this back-to-school match were played too poorly.

After training, Li Ao did not return to the classroom to study.

After changing his clothes, he came out and found that everyone was still there, sitting in twos and threes in the locker room resting.

Jamal was frantically tapping on his phone with his head down, probably texting his new girlfriend; Jaylen, on the other hand, was carefully wiping down the shoes and protective gear of several new teammates.

Li Ao casually mentioned the homecoming dance, assuming that these rough guys who played basketball wouldn't be interested in such an event. However, everyone expressed their desire to join in the fun.

"I definitely have to go to the ball this year!"

"I heard that the school has secured a lot of sponsorships this year, so the funding is particularly abundant. Not only have they prepared a lot of delicious food, but they've also spent money to hire a famous DJ to liven things up."

"Our school is usually very stingy, so I don't know why they've suddenly become so generous this year."

"Brother Leo, you have to come with us!" Jamal raised his head and shouted.

At his urging, the locker room instantly became lively.

Everyone chimed in, saying they absolutely had to get the team leader involved too.