Tian Gang looked at Li Dong with a strange expression.
’He just helped me, and now he’s already coming to me for something? Is he cashing in a favor the moment he gets it?’
He wasn’t in a hurry, though. He asked slowly,
"What is it?"
Li Dong gave a mischievous chuckle.
"Teacher Tian, I’ve been thinking about a research topic recently."
"And... I want to bring my high school teacher in to work on it with me."
Tian Gang glanced at Li Dong, then took a second look, making sure he wasn’t joking.
’A research topic?’
Tian Gang wasn’t surprised that Li Dong wanted to tackle a research project.
He would have even found it perfectly reasonable if Li Dong had said he wanted to work with Liu Ruochuan or other professors in the school.
After all, this first-year undergraduate had already produced two papers in analytic number theory that had sent shockwaves through the entire mathematics community.
None of the professors at the Yan University School of Mathematics treated him like a mere student anymore.
’But you want to bring in your high school teacher?’
It wasn’t that Tian Gang looked down on high school teachers.
In fact, he knew quite a few high school teachers who had published papers in journals like the *Mathematical Bulletin* or the *Journal of Computational Mathematics in Higher Education*, some of which were of decent quality.
But that was on a completely different level from what Li Dong had been doing.
Tian Gang’s expression became a little complicated.
"What’s the direction of your research topic?"
Li Dong didn’t beat around the bush and said directly,
"The generalization of local-global compatibility from GL2 to GLn."
The classroom fell silent in an instant.
Tian Gang thought he had misheard.
The handful of PhD students behind him were all completely stunned...
"You... say that again?"
"From GL2 to GLn," Li Dong repeated.
"To be precise, it’s about generalizing the local-global compatibility of automorphic representations of GL2 in cases where the ramification index does not exceed 2, to the general case for GL(n) where the ramification index is ≤ n."
Tian Gang rubbed his temples.
A fourth-year PhD student behind him asked, stammering slightly,
"Wait... are you sure you didn’t misspeak?"
Another third-year PhD student also chimed in.
"You said GL(n)?"
Everyone looked at Li Dong in disbelief. Even with his previous papers to back him up, they all thought he must be exhausted lately and talking nonsense.
Tian Gang raised a hand, signaling the students around him to be quiet.
He just stared at Li Dong.
One had to understand, what level of problem was the generalization of local-global compatibility from GL2 to GLn within the entire research framework of the Langlands Program?
Let’s put it this way.
The Langlands Program is known in the mathematics world as the "Grand Unified Theory of Mathematics." It attempts to unify seemingly unrelated branches of mathematics like number theory, algebraic geometry, and representation theory under one vast theoretical framework.
The most brilliant achievements in mathematics over the past half-century.
For instance, Wiles’s proof of Fermat’s Last Theorem and Wu Baozhu’s proof of the fundamental lemma were, in essence, just the tip of the giant iceberg that is the Langlands Program.
And local-global compatibility is the very foundation upon which the Langlands Program is built.
Over a decade ago, Jiang Yubai’s team spent a full three years just to prove local-global compatibility for the simplest GL2 case, with a ramification index not exceeding 2.
This result was published in the Duke Mathematical Journal and was considered the most important breakthrough in the field of algebraic number theory at the time.
And now Li Dong was saying he wanted to jump directly from GL2 to GLn?
What did this mean?
Going from GL2 to GL3 was equivalent to jumping from proving a theorem in two-dimensional space to three-dimensional space.
With each increase in dimension, the complexity doesn’t grow linearly, but exponentially.
The types of representations, ramification cases, and the structure of local factors you have to deal with all become unimaginably complex.
’If this thing could actually be done...’
Even Tian Gang found it a bit too staggering to comprehend.
It would directly give the foundation of the Langlands Program a complete upgrade, pulling the entire field from a stage where only the simplest special cases could be handled, all the way to the level of a general framework.
Mathematicians all over the world working on the Langlands Program, including Fields Medal winners like Laurent Laforgue and Wu Baozhu, would be shaken by this achievement.
Tian Gang was getting old; his heart couldn’t take this kind of shock.
He let out a long breath and took a moment to compose himself before speaking:
"Li Dong, you know that Jiang Yubai only managed to push the ramification index from 1 to 2, right?"
"That single step was already considered the limit in this direction."
"And from what I understand, the research group he’s leading now is only aiming to push the ramification index from 2 to 3."
"And he’s a top expert in this field."
"Besides, even if you really have this idea, aren’t there enough professors here at Yan University for you to choose from?"
"Liu Ruochuan in algebraic number theory, Zhang Wei in representation theory, Chen Hao who works on L-functions... which one of them isn’t a top expert in the country?"
"A high school teacher... can he even keep up with your pace?"
Li Dong shook his head.
"Teacher Tian, I know this project is huge, and it’s also relatively difficult."
The PhD students standing nearby felt their eyes twitch in unison.
’Relatively difficult?’
’Dude, your idea of "relatively difficult" is completely off.’
Li Dong continued.
"But this high school teacher of mine, he has actually done research in this area."
"He has a very deep understanding of the local structure of automorphic representations, not just some superficial knowledge."
He was actually very certain in his heart.
That paper on the analysis of the GL2 ramification index was written by Old Yang.
His Logic attribute was already 0.4. If he were in Detective Conan, he’d be solving cases left and right.
Li Dong just hadn’t exposed the truth.
Old Yang was good at hiding it, but he couldn’t hide it from him.
Tian Gang smiled and shook his head.
He didn’t believe it.
’A high school teacher doing this level of research... while not exactly an amateur scientist, how good could he possibly be?’
But since Li Dong had already asked, he wasn’t going to refuse and cause his future student to lose face.
’It might be good for him to hit a wall for once. The kid’s had it too easy.’
Of course, it wasn’t that he didn’t believe in Li Dong’s ability.
It was just that for this particular topic, some things were limited.
Trying to prove the local-global compatibility from GL2 to GLn within the existing mathematical framework... there were just too many missing intermediate steps.
Too many theoretical tools were lacking.
This wasn’t something you could just brute-force your way through, even if you were a genius.
"So what do you want my help with?"
Li Dong grinned.
"I want to get my high school teacher a position... like, an external researcher for a project group? A visiting scholar? The kind of status that would let him share the university’s academic resources, access the library databases, and use the school’s computing platform."
Tian Gang shook his head. "Don’t come to me for this."
Li Dong was taken aback. "Huh?"
He hadn’t expected that even Tian Gang couldn’t solve this.
Tian Gang shot him a look and said,
"If he wants to have the status of a visiting scholar, he first needs to join a formal research group."
"And can’t you apply for a research group yourself? When the time comes, you can go through the university’s formal procedures: propose the project, form the group, apply for a spot for external personnel, and I’ll just sign off on the approval for you."
"So, you can just handle it yourself."
It was only then that Li Dong realized.
’That’s right!’
He could totally apply to establish a research group himself, and then, as the project leader, apply for an external researcher position for Old Yang.
That way, Old Yang could formally enter Yan University’s academic system, share the library’s journal databases, use the school’s high-performance computing cluster, participate in the school’s academic seminars...
If it were any other undergraduate, the application would most likely be rejected.
But Li Dong was confident that as long as it was an application related to mathematical research submitted by him, there was no reason the university wouldn’t approve it.
Having figured this out, he sidled up with another grin.
"In that case, Teacher Tian, I’ll come find you for help next time."
Tian Gang: "..."
’So you’re saving the favor for later, are you? This kid.’
After the class ended, Li Dong was in a good mood, his mind already churning with how to break the news to Old Yang.
He planned to go to the cafeteria to grab a bite first, then head back to his dorm to organize the materials for the project application.
Unexpectedly, his phone vibrated when he was halfway there.
It was a call from Li Qin.
He answered the phone.
"Xiaodong."
Li Qin’s voice came through.
"In a little while, Mom might be coming to Kyoto, too. I’ll come and see you then."

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