Simply put, this tool establishes a direct link between Algebraic Geotry and Representation Theory. To be honest, it’s a very difficult task."
"Uh... Great genius, what do you an?" Tang Jing asked.
Qiao Yu, in all seriousness, replied: "It ans that interactions between people are not like mathematics. If a connection needs to be established, it doesn’t have to be so complicated. For example, your friend could just ask for my WeChat directly. If there’s an interdiate step involved, many complex variables could arise.
For instance, maybe your friend is just being used as a shield by you, or perhaps you are playing truth or dare and teasing , so Senior Sister Tang Jing, next ti either let your friend ask directly for it or admit that you are my fan... Well, in any case, be sure to next ti!"
After saying this, Qiao Yu quickly took a few bites of his food, then stood up and ran off under the bewildered gaze of the senior sitting across from him.
It’s certainly not because he was afraid of the senior across from him; he just needed to quickly go back and jot down what was in his mind.
...
Tang Jing sat there dazed for a while before picking up her tray and returning to her friend’s side.
Zhao Xiaoyue asked, suppressing her laughter: "Tell , how did you manage to scare away the great genius?"
Tang Jing said gloomily: "They say the math departnt is the craziest of all, and it’s true. I just told that Qiao Yu you’re his fan and want his WeChat, and he spouted a bunch of nonsense. Stuff like Chevalley two-dinsional extension and Langlands Duality..."
"Wait, what did you tell him exactly?" Zhao Xiaoyue stopped laughing and looked at Tang Jing, both embarrassed and annoyed.
"You’re his fan! Didn’t you create a Weibo account just to follow him the other day?" Tang Jing said righteously.
"I’ve explained so many tis, that’s because I found the conversation about the Century Reconciliation in the math group quite intriguing, so I followed his Weibo. I just wanted to get the latest updates imdiately. How does that make a fan?" Zhao Xiaoyue said helplessly.
"But don’t you think it’s fate? This isn’t the math center, after all. We just randomly decided to eat here and ran into him? That... Xiaoyue, could it be that you’re upset because I told him you wanted to add him on WeChat and he ran away?" Tang Jing blinked, pondering as she spoke.
"I am not!" Zhao Xiaoyue replied resolutely.
Tang Jing nodded and said: "I figured as much. It’s okay; the great genius just said you could ask for WeChat yourself, and he’d definitely give it."
"Heh..."
...
"Let f be a global function: → C, where is a commutative heap."
"The transformation group G acts on the global function and is defined as: g⋅f(x) = f(g^−1⋅x), for all g ∈ G, x ∈."
"Define the Whitaker layer W, so that it remains invariant under the action of the algebraic group, i.e., W(x) = i∑aiϕi(x), where ϕi is the characteristic layer under the action of the algebraic group."
"Using the properties of the characteristic layer, the following mapping can be introduced: Φ: → W, such that: Φ(f) = g∈G∑g⋅f."
"Using the principle of categorical contraction, it can be proved that: ∀g ∈ G, g⋅Φ(f) = Φ(f). Therefore, Φ(f) is an invariant function and can be considered an automorphism of the Whitaker layer."
"Thus, it can be seen that f can be described through the automorphism of the Whitaker layer."
...
Back in his small room, Qiao Yu quickly opened LaTeX, wrote down the content above, saved it, and sent it to Professor Li at Huaqing on the other side.
It was a very brief proof process, but mathematics is sotis like this.
When you don’t expect it, it’s really difficult; but when inspiration strikes, the problem gets solved naturally.
Perhaps it’s because he’s been pondering this problem a lot lately, but Senior Brother Chen’s recent phone call that relayed Director Tian’s description of symtry sparked a geotrical intuition in him: viewing the global function as an invariant form under certain transformations.
After hanging up Senior Brother Chen’s call, his mind laid out a complete plan on integrating the characteristic layer theory with the principle of categorical contraction, constructing a transformation group to understand the properties of the global function, and considering the changes of the Whitaker layer under this transformation to reveal the relationships between them.
After sending the email and checking his proof process again, he picked up the phone and directly dialed Professor Li across the way.
Although he wrote it very briefly, Professor Li, who had been researching this issue for a long ti, would definitely be able to understand his ideas.
The phone was soon connected.
Qiao Yu got straight to the point and said: "Hello, Professor Li, I think I just proved that a global function can be described through the automorphism of the Whitaker layer, and these automorphisms have a direct relationship with the representations of the algebraic group. I just sent it to your email; could you take a look to see if my idea is correct?"
"You proved it completely?"
"Yes, but the write-up is a bit brief."
"Hold on a second, don’t hang up yet, I’m right by my computer; let check first."
The sound of keyboard and mouse movents echoed through the phone, and Qiao Yu decided to put it on speaker and placed it on the table.
There was no response from the other end for quite a while, so Qiao Yu’s thoughts began to wander.
Hmm, earlier a senior asked for his WeChat; it was probably the first ti such a thing happened to him at Yanbei University...
No, he shouldn’t have run away just now; it looked quite cowardly...
The senior probably thinks he was scared away?
Speaking of which, that fan senior seed quite pretty, but I wonder if she’s smart...
Mathematics is the most beautiful, though. Qiao Xi is second, Keke could be third...
"This... proof, this proof... How did you co up with it?"
The voice over the phone finally pulled Qiao Yu’s scattered thoughts back together.
"Well, it’s a long story. I have to start from when I attended a philosophy class about truth this morning. Hmm, Professor Li, are you sure you want to hear it now?"
"Never mind! I’ll verify it first. Pay attention to WeChat; talk about it during the team discussion session around eight tonight. Qiao Yu, you’re really a super genius!"
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