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Chapter 171: Chapter 167: The Value of 2/5 of a Newton

In the international conference hall, Li Dong was still on stage, speaking with great enthusiasm.

He had now reached the core of his third paper: the proof of equivalence between the Fourier transform of the zero pair correlation function and the GUE predictions.

The whiteboard was already covered in dense formulas.

The definition of the normalized imaginary part of the zeros, γ̃ⱼ; the separation of the main term for the pair correlation function F_T(α) in the interval |α|∈[1, 2]; the refined form of Σ log p ~ X given by the Prime Number Theorem; the strict control of the remainder term O(log⁻¹T)...

14.134725...

21.022039...

25.010857...

These zeros were no longer just cold numbers.

In Li Dong’s derivation, they had transformed into musical notes.

And when the limit of the pair correlation function F(α) converged precisely to the GUE prediction in every interval...

...that was the final movement of the entire symphony.

All the sections came together as one.

Beneath the chaos, order was eternal.

「In the audience.」

Guan Yi sat motionless in the third row.

His palms were drenched in sweat.

He finally understood why Professor Xu Hongwei had wanted him to attend this lecture.

And he finally understood just how vast the gap was between his own first-author paper in the Duke Mathematical Journal and the man on the stage.

Before, he had thought Li Dong might be just a little more impressive.

Now, he wanted to take that back.

This wasn’t ”a little bit.” Not by a long shot.

But strangely, Guan Yi didn’t feel discouraged.

Instead... he felt a strange sense of excitement.

It was as if something had begun to sprout in his mind.

The key points in his research on the convergence of curvature flow that he’d been stuck on were now, astoundingly, starting to spark faint glimmers of inspiration.

What Guan Yi didn’t know...

...was that at this moment, it wasn’t just him.

Everyone in the conference hall was experiencing a similar feeling.

The graduate students, though they could only follow about seventy percent of the content, found that seventy percent taking root in their minds ten times deeper than usual.

Even Lin Xue, a graduate student who considered herself completely removed from the world of number theory...

...felt as if something was flowing into her mind.

Of course, how much of what flowed in would actually remain depended on each person’s aptitude and comprehension.

Some retained a great deal.

Others, only a little.

As for Li Dong on the stage, he just felt that today’s lecture was going especially smoothly and that the audience was being particularly respectful—not a single person seemed distracted.

’The students at Zhejiang University are such high-caliber,’

he marveled to himself.

He was completely unaware...

...that the passive aura, ”Inheritance of the Torch,” which he had received from Fields, had been active ever since he stepped onto the stage.

...

”Alright, that concludes today’s public lecture.”

Li Dong set down the chalk and gave a slight nod to the audience.

Applause erupted.

But after the applause died down, not a single person moved.

Several hundred people sat there quietly, lost in thought.

Li Dong had actually seen this kind of scene before.

The reaction had been the same when he gave his academic report at the International Congress of Mathematicians.

So he spoke up directly, ”If there’s anything you didn’t understand, you can ask now.”

Still, no one spoke.

”Well... if there are no questions, I’ll be going?”

The moment he finished speaking, a tall, thin young man in the third row shot to his feet.

”Li Dong... Teacher Li Dong.”

Guan Yi’s voice was a bit faltering.

Calling someone younger than himself ”Teacher” was, to some extent, a little awkward.

But he couldn’t be bothered with that now.

Li Dong looked at him and smiled.

”Feel free to ask about anything you didn’t understand.”

Guan Yi froze for a moment.

He did indeed have a question.

But it wasn’t about what Li Dong had just been discussing on stage.

It was about his own research topic.

His research was on the convergence of curvature flow.

Specifically, the problem of the long-time existence of the Ricci flow on high-dimensional compact manifolds.

The paper he had published in the Duke Mathematical Journal solved a key estimate for the decay rate of the curvature tensor in the three-dimensional case.

But he had been stuck on the case of four dimensions and higher for nearly half a year.

The sticking point was that the Weyl curvature tensor did not decay fast enough on high-dimensional manifolds.

In three dimensions, the Weyl tensor is always zero, so it wasn’t an issue. But in four dimensions and above, this term started causing trouble, and he couldn’t find a good method to control its long-time behavior.

But just as Li Dong was lecturing on the limit behavior of the zero pair correlation function, an idea suddenly flashed through Guan Yi’s mind...

The method Li Dong used to control the remainder term O(log⁻¹T), that technique of suppressing high-order oscillating terms layer by layer with weighted averages...

What if it could be transplanted into the energy estimates of the Ricci flow to control the decay of the Weyl tensor...?

The idea had only existed in his mind for about ten seconds, hazy and indistinct.

He was just about to grasp it.

But just as Li Dong said, ”that concludes today’s public lecture,” the inspiration suddenly vanished!

Then he heard Li Dong say, ”if there are no questions, I’ll be going.”

He didn’t know what came over him; he just stood up.

”Teacher Li Dong, what I want to ask is... in a slightly different field from what you were just talking about. Is that okay?”

Sitting in the front row, Xu Hongwei frowned.

He didn’t know what was going through Guan Yi’s mind at that moment.

He just saw his student, who was arrogant to the core, stand up before someone younger than him to ask a question from a ”different field.”

Xu Hongwei’s first reaction was...

’This kid is unconvinced. He’s trying to make things difficult for him on his own turf.’

He was just about to stand up and smooth things over when Li Dong already smiled.