Academic genius: Arcane Invasion of America

So, another half hour passed.

Kayla Nolan remained hunched over the table, carefully searching for any potential pitfalls in Li Ang's manuscript.

The result was that it couldn't be found at all.

So much so that Li Ang, who was standing nearby, reminded him, "Professor Nolan, wouldn't you like to take a break? Or... have a cup of coffee?"

"Need not."

Kayla shook her head.

Drinking coffee is a trivial matter and should naturally take a backseat to more important matters, such as thoroughly understanding the core content of Li Ang's manuscript.

"Li Ang, let's get straight to the point. The first question is, in your article, you defined the 'Faltings height': hF(A):=1/[K:Q]deg^(ωA/S). You are trying to assign a real invariant to an abelian variety. The key is that this is highly dependent on the model choice. If the compactification is changed, will the deg^ you set change?"

Kayla bombarded her with questions in one breath.

Li Ang shook his head and replied slowly, "No. The key lies in Lemma 2.4. I proved that if L1 and L2 belong to the same projective space over the number field K and their continuous sections are the same, then deg^(L1) = deg^(L2) + O(log∣ΔK∣)... The specific derivation process is as follows."

Li Ang picked up a pen and began to perform calculations right in front of Kayla.

Li Ang quickly finished making his comments on the spot.

Kayla took a deep breath very subtly to calm herself down.

The completeness and technical skill demonstrated by Li Ang in his calculations have far exceeded the scope that undergraduates or even doctoral students can usually complete independently.

That's incredible.

However, Kayla understood that now was not the time to pop the champagne at halftime. She needed to further verify some of her guesses, then take Li Ang's manuscript out for peer review, or perhaps hold a grand mathematics exchange meeting.

"Okay." Kayla nodded, then pointed to the next point. "So, regarding your core lemma 3.7, for a fixed field K and an integer g, there exist constants c1(K, g) and c2(K, g) such that for any curve C of genus g on K, the Faltings height of its Jacobi variety Jac(C) satisfies c1 ≤ hF(Jac(C)) ≤ c2. For this proof of the two boundaries, you relied on the arithmetic analogy of the genus formula. So, what is the specific expression for the constant γ(g) in inequality (3.12) on page 18?"

Li Ang glanced at Kayla, a hint of doubt in his mind.

The new problem raised by Professor Nolan is quite fundamental in the field of number theory.

At least that's what Li Ang thought after he reached level 3 in mathematics.

However, he still patiently wrote down all the relevant information on the draft paper.

……

And so, Li Ang and Kayla engaged in an in-depth discussion about the Model Conjecture in the apartment.

At this point, Kayla finally confirmed one thing.

Li Ang's entire proof is clear, bold, and full of leaps in logic, yet each link is interconnected.

Although she may be reluctant to admit it, Li Ang's research in number theory may have surpassed hers in depth.

However, there was one thing that puzzled Kayla: during the proof process, Li Ang repeatedly mentioned some of the work that Grothendieck had just discussed in France. Much of this content was recorded by Kayla on-site when she went abroad to attend the conference, but she did not share it with Li Ang. So how did Li Ang know about it?

But upon further reflection, these questions seem minor compared to the proof of the Model conjecture itself.

There's no need to delve into it further.

Having grasped almost all the proofs of the Model conjecture, Kayla spoke up: "Leon, this really sounds like the work of a mature mathematician after careful consideration. I want to ask, did you really complete this proof independently? In just the past week?"

Li Ang thought to himself, "This is a theorem I got from the system."

However, it took a lot of time to gain experience, so I guess it was completed independently.

"I had been thinking about many of these ideas for a year, but the core parts were actually completed after I came to the University of Chicago."

Upon hearing this, Kayla gave Li Ang a deep look.

His eyes revealed an undisguised appreciation for her talent, and even a hint of something more.

In the past few days, Kayla has helped Leon complete his enrollment procedures, solve his tuition problems, and publish his first paper. She knows that Leon has a talent for mathematics and is smart and hardworking.

But the manuscript before us reveals a vision far beyond that of an undergraduate, doctoral student, or even many established mathematicians.

This is less a talent and more a gift from the god of mathematics.

"Very good! Also, I'd like to take this manuscript with me. It needs to be carefully and repeatedly checked. Every definition, lemma, and corollary needs to be reviewed by a professional mathematician. You know, this area is actually beyond my area of ​​expertise. This process will be lengthy, and there will be people who question and nitpick. Is that alright?"

Li Ang was not too surprised by Kayla's request.

Something of the magnitude of the Model Conjecture could not possibly be decided by Kayla alone.

As for whether there will be plagiarism or academic misconduct during this process, Li Ang cannot guarantee 100%.

After all, in 1960, the concept of preprints didn't even exist, let alone a platform like ArXiv.

Academic misconduct can only be restrained by the ethical bottom line of scientists.

Li Ang is not afraid. If anyone dares to copy his writing, he has ways to make the plagiarist confess in front of everyone and cause a social death.

With that thought in mind, Li Ang nodded, "No problem."

"Okay, if everything goes well, you may need to attend a mathematics conference. I will arrange the specific details for you. You just need to share the proof process of the Mordell conjecture with everyone."

"Yes, thank you, Professor Nolan."

Kayla smiled slightly. "Professor... no, if things go smoothly, we'll soon be colleagues."

"colleague?"

Kayla said matter-of-factly, "Now that you've proven such a mathematical conjecture, which professor would dare to teach you if you continued your studies? I think the Board of Trustees would agree to let you graduate early, find a way to award you a doctorate, and eventually recruit you as a professor in the Department of Mathematics at the University of Chicago."

Emmm...

All Li Ang could say was, "Isn't this a bit too fast?"

Is the foundation weak?

How can a college student who has been enrolled for less than a month not only skip several grades to graduate, but also directly obtain a doctoral degree and become a mathematics professor?

An 18-year-old mathematics professor—that's probably the first of its kind at the University of Chicago, and even in the entire United States.

But upon further reflection, Model's conjecture is undeniably valuable.

In Li Ang's previous life, a young college student proved the Seetapan conjecture and was exceptionally appointed as a professor by the university.

In terms of influence in the mathematics community, the Mordell conjecture is even greater than the Seetapan conjecture, so it seems reasonable that he could be considered a mediocre professor in the mathematics department at the University of Chicago.

Becoming a professor naturally has many advantages.

With that in mind, Li Ang responded, "Thank you, Professor Nolan."