Chapter 346 - 290: Joint Training

Chapter 346: Chapter 290: Joint Training

"They went to move the equipment."

"The upgrade parts for our vacuum chamber arrived today."

"After they bring the equipment up, they’ll have to recalibrate everything."

"We’ll probably be tied up with that for the whole next week."

Li Dong asked with a smile.

"So that means it’s all good? Shall we continue?"

Wu Kai nodded.

"Yeah."

"No problem."

"It’s all thanks to your ’Comment’ paper."

He chuckled.

"Although some people out there are still questioning it."

"Our funding, at least, should be secure now."

Li Dong asked another question.

"What about Le Pu?"

Wu Kai shook his head.

"Le Pu is still reviewing it."

"My guess is they’re waiting to see how the international inverse problem community reacts to your ’Comment’ before they decide whether to release the second round of funding, and when."

Li Dong nodded.

’He understood.’

’After all, there was still a large group of people out there opposing it.’

’A few had even made public statements over the past couple of days—’

"Until Engelhardt issues a formal response, we urge all our peers not to rashly trust Li’s criterion."

Li Dong nodded at Wu Kai.

"Then let’s just have Le Pu wait and see."

"As long as our vertical funding is secure, we can keep moving forward with our work."

Wu Kai smiled and clapped Li Dong on the shoulder.

"Kid."

"You go focus on your own stuff."

"I’ll call you over when we need you again."

"Of course, you’re always welcome to drop by on your own, too."

Li Dong said with a smile.

"Got it, Teacher Wu."

Wu Kai grunted in acknowledgment.

Li Dong turned and left the School of Chemistry.

He didn’t go back to his dorm.

Instead, he headed straight for the School of Mathematics.

Professor Wang Zhigang had called him twice in the last two days.

He said he thought the work Fu Chen had derived was just about ready for submission.

He wanted Li Dong to come by when he had a moment to go over the last few lines of details one more time.

Li Dong had originally wanted to just reply, "It’s fine as long as you’ve looked at it."

But he swallowed the words before they came out.

After all, this was Senior Fu Chen’s first paper that could make it into a major journal. 𝒻𝘳ℯℯ𝑤ℯ𝒷𝘯ℴ𝓋ℯ𝘭.𝑐ℴ𝑚

Li Dong wanted to take another look at it himself, too.

...

In the seminar room of Professor Wang Zhigang’s research group, on the second floor of the School of Mathematics building.

When Li Dong pushed the door open and entered, there were seven or eight people sitting in the seminar room.

Fu Chen was standing in front of a whiteboard covered in dense derivations. At the very top, a line of large text was written.

[The Persisting Correspondence Between Anomalous Residues of Cyclic L-Factors and the Local Dimension of Deformation Rings].

Apparently, with Gu Ming’s help, Fu Chen had already completed the final, crucial operator construction.

"Esteemed teachers," Fu Chen said, his voice steady as he pointed to the whiteboard.

"Regarding the ’persisting correspondence’ I mentioned last time, I’ve reorganized the logic."

"Assuming l is not equal to p and the residual representation is absolutely irreducible, we consider the properties of the special fiber of the framed deformation ring R..."

For the next ten-plus minutes, Fu Chen launched into a rapid-fire presentation.

He started with the construction of equidimensional schemes, delved into the closed subschemes corresponding to the inertial type τ, and attempted to establish a correspondence between a set of effective cycles C_θ and the Jordan-H?der multiplicities...

(The complex Algebraic Geometry derivations regarding the geometric form of the Bley-Mezaar conjecture are omitted here. The core logic involves explicitly calculating the local deformation ring and, by using the Cayley-Hamilton theorem, forcing the algebraic version of the conjecture towards the geometric end.)

"...And that is the complete framework after my revisions."

Fu Chen put down the chalk.

The feedback from the audience was even more intense than he had anticipated.

Associate Professor Liu was the first to speak up, firing off several questions about the compatibility of ρ?, drilling down from the classification of absolute irreducibility to the construction details of the pseudo-representation.

Immediately after, a postdoc from the group also couldn’t sit still, directly questioning the "computability" of this set of correspondence formulas from an engineering perspective, suggesting it might currently only exist on an abstract level.

Faced with this "bombardment" of questions, Fu Chen’s responses were extremely solid.

He first resolved the concerns about compatibility using a three-tiered classification method, then casually listed three explicit examples of cyclic classes on the whiteboard, pushing back against the "incomputable" accusation.

After a few rounds of Q&A, Fu Chen’s logic was so tight that his presence began to command the room.

Just as the seminar room fell into a brief silence, Li Dong, who was sitting in the back row by the door, slowly raised his hand.

"East God!" The students in the room were the first to spot him, blurting it out instinctively.

Only then did Fu Chen see Li Dong.

"East God! When did you get here?"

Li Dong waved a hand at him, gesturing for him not to be so formal, then threw out a question.

"Senior Fu Chen."

"I was following the direction of that new operator at the end of your derivation."

"Suppose I wanted to weaken the condition on ρ? from ’absolutely irreducible’ to the case of ’locally irreducible but globally reducible’..."

He paused, his gaze turning serious.

"In that situation, would your set C_θ still maintain its ’persistence’?"

"Or would a new class of anomalous residue appear that needs to be dealt with separately?"

The entire seminar room suddenly went quiet.

A few of the teachers instinctively exchanged glances, a shock running through them. ’That question is brutal.’

It struck directly at the weakest link in the concept of "persistence."

If he couldn’t answer, or if his proof’s logic collapsed, the entire paper would have to be rewritten from the ground up.

Fu Chen stared at the whiteboard, silent for a full three seconds.

Then, he smiled.

"East God, a new anomalous residue does indeed appear."

He picked up the chalk again and started a new line at the edge of the whiteboard.

"However, it has a simple algebraic relationship with the original residue."

"I’ve added a Lemma 3.8 here, which is just enough to absorb it..."

As Fu Chen wrote out the formula composed of a first-order perturbation and a correction term, Li Dong stared at it for a few seconds before finally nodding.

"Yeah, it holds. Very elegant."

Once those words were spoken, several of the teachers in the room simultaneously let out a long sigh of relief.

They knew that Li Dong’s "very elegant" had basically set the tone for the paper’s reception.

"East God, so... should I just submit it?"

Fu Chen was a little excited.

"Submit it."

Li Dong said succinctly.

"Compositio Mathematica. This paper has the weight for it."

Compositio is a top-tier journal, second only to the "big four." For a master’s student to be the first author on a Compositio paper...

That’s an achievement that would truly be "the most prominent item on one’s resume."

Fu Chen took a deep breath.

His shoulders trembled slightly.

"East God..."

"Is it really... good enough?"

Li Dong walked up and clapped him on the shoulder.

"Senior Fu Chen."

"You need to have confidence in yourself."

"You’re the one who wrote it. You know its quality better than anyone."

"Just submit it as is."

Fu Chen took another deep breath.

"Okay."

He nodded.

"I’ll finalize the draft next week."

"And submit it the week after."

Li Dong smiled at him.

"Sounds good."

He turned and walked toward the door.

Just as he reached the doorway, he heard the PhD students in the seminar room whispering among themselves.

"Holy shit."

"Fu Chen’s going for Compositio?"

"A third-year master’s student submitting as first author to Compositio?"

"If he actually pulls it off, Fu Chen’s name will go straight onto the ’Best Master’s Thesis of the Year’ list for the Yan University School of Mathematics!"

Hearing this, Li Dong smiled to himself.

’Well, people...’

’...always need something to look forward to.’