Chapter 204 - 152: Qiu Chengtong’s Question
"Come, sit down, sit down."
Qiu Chengtong had Chen Lin sit on the sofa in the reception area, then sat across from him. He studied Chen Lin from top to bottom, his gaze filled with undisguised admiration and curiosity.
"Impressive, very impressive. The younger generation is truly something to be reckoned with." He smiled and nodded, then added half-jokingly, "For the past month, I’ve heard nothing but news about you."
Chen Lin smiled humbly. "To be honest, I never expected to cause such a commotion. I just wanted to publish a paper quietly."
"Hahaha, that wasn’t up to you." Qiu Chengtong laughed heartily. "Talent will always shine through."
He paused, took a sip from the teacup on the table, and continued, "Speaking of which, Academician Liang Tianshi and I are old friends. He was the one who showed me your paper on Differential Geometry before it was officially published in JAMS."
’So that’s how it was.’
Chen Lin nodded in understanding.
When he had finished the first draft and sent it to Professor Gu Ming for review, he had also sent a copy to Academician Liang.
A nostalgic look appeared in Qiu Chengtong’s eyes as he spoke slowly. "I remember it clearly. The afternoon I received your paper, I spent the entire time personally verifying every single mathematical proof and calculation in the main body, from beginning to end."
As he spoke, the admiration in his gaze toward Chen Lin grew even stronger.
"The results left me utterly astonished. Not only was your entire proof process logically rigorous and irrefutable, but it was also filled with ingenious ideas. There were several key steps handled in ways I had never considered myself."
Hearing such undisguised praise from a Fields Medal winner, even Chen Lin, who was not easily flustered, felt a bit embarrassed.
He could only demur once more. "A part of the paper actually drew from and applied some of your own research from back in the day."
"Ah, no need to be so modest." Qiu Chengtong smiled and waved his hand dismissively. "My work only provided you with a foundation, at best."
"The core deductive portion of your paper, the mathematical ideas and techniques it showcases, are absolutely in the highest echelon of all the papers I have reviewed in my decades-long career!"
He leaned forward slightly, his expression growing more serious. "And that is precisely why, when I learned you would be attending this mathematics conference, I specifically asked Academician Liang to make sure you came to see me."
A flicker of curiosity crossed Chen Lin’s mind. He asked, "Professor Qiu, is there something in particular you wanted to see me about?"
"Of course." Qiu Chengtong nodded as if it were obvious, his sharp eyes glinting with the excitement of a player who has met their match. "The fact that you could write that paper shows you must have a very deep understanding of the field of Differential Geometry. As it happens, I’ve also been pondering some related problems recently, and I’d like to discuss them with you."
With that, he dropped the pleasantries and posed his first question.
"Chen Lin, regarding the Ricci Flow on a Calabi-Yau Manifold, what are your thoughts on the geometric structure near the singularities?"
’Here we go.’
Chen Lin tensed, knowing the real test had begun.
His ’Little Mathematician’ title had already quietly activated the moment he began to think.
Countless scattered, abstract concepts from Differential Geometry first flooded his mind, only to be instantly activated, linked, and reorganized in the next moment.
Innumerable complex formulas, theorems, and lemmas converged and collided like a torrential flood deep within his brain, ultimately forming a crystal-clear logical pathway.
Without the slightest hesitation, Chen Lin blurted out, "Professor Qiu, I believe that to understand the geometric structure near a singularity, the key lies in analyzing its tangent cone formation under limit conditions."
"We can attempt to construct an auxiliary function based on Perelman’s entropy and constrain the possibilities of singularity models by proving its monotonicity. Ultimately, it should converge to a Ricci soliton with non-negative Ricci curvature."
Although his answer, due to time constraints, lacked any detailed derivations or calculations, it precisely identified the core approach to solving the problem and the key mathematical tools that could be used.
Upon hearing this, Qiu Chengtong’s eyes instantly lit up. He slapped his thigh, a look of delighted surprise spreading across his face. "Exactly! Using Perelman’s entropy to construct an auxiliary function—that’s an incredibly clever approach! Why didn’t I think of that before?"
It was as if a door to a new world had swung open for him. He immediately pressed on, "Then what about the relationship between the stability of minimal submanifolds of high codimension and the second variation formula? Do you think it’s possible to generalize the Almgren-Pitts min-max theory to non-compact background Manifolds?"
Chen Lin’s brain was still operating at high speed, his thoughts perfectly clear.
"Theoretically, it’s feasible, but several technical difficulties need to be resolved. First, the nature of a non-compact Manifold at infinity might cause the energy functional to be unbounded below. We would need to introduce a suitable weight function to ensure its coercivity."
"Second, when constructing the replacement surfaces, we must control their asymptotic behavior at infinity more finely. This might require some of the more profound tools from geometric measure theory..."
And so, in this exchange of questions and answers, time slipped by unknowingly.
Professor Qiu Chengtong seemed to have forgotten the time, forgotten even his usual stern and unsmiling demeanor.
He had finally found a kindred spirit. One by one, he brought up the most cutting-edge and intractable problems he had encountered in the field of Differential Geometry in recent years.
And Chen Lin, always within moments of him finishing his question, would provide an answer that was not just satisfactory, but downright astonishing.
Although each answer was merely a highly condensed conceptual framework, the profound insights and brilliant ideas contained within them left Qiu Chengtong feeling a deep sense of shock and admiration time and time again.
Before they knew it, an hour had passed.
When Chen Lin finished answering the final question about "self-similar solutions of the mean curvature flow," Qiu Chengtong let out a long breath and leaned back against the sofa.
His face showed clear signs of fatigue, but his eyes sparkled with an unprecedented, exhilarating sense of fulfillment.
He quietly watched the young man before him for a good ten seconds before slowly speaking, his tone filled with an indescribable mix of emotions.
"Academician Liang Tianshi once told me you were a rare mathematical genius."
Qiu Chengtong shook his head, a look of disbelief on his face.
"Now, I see he was wrong. He was far too conservative."
He stared into Chen Lin’s eyes and said, with the utmost solemnity, articulating each word with care, "You are the kind of person who has the ability to change the course of mathematical development in the world—or even the course of development for all of Science!"
With that, he stood up and gave Chen Lin an encouraging smile.
"I will definitely be there for your presentation the day after tomorrow. I am certain you will deliver a presentation that will stun everyone."