My IQ has been increasing year by year.

Where has Chapter 280 progressed?

The atmosphere in the Harvard Science Center seminar room relaxed.

The defensive campaign based on the Poincaré conjecture has been developed to its final stage.

The manuscript, consisting of more than three hundred pages, sat securely in the center of the table.

Professor Zhou and Li Jianming quietly checked the venue arrangements and security details for tomorrow's meeting.

Cao Huaidong stretched, leaned back in his chair, and pinched the bridge of his nose.

Yau Shing-Tung picked up the cup in front of him and took a sip of water.

Put the cup back on the table.

His gaze naturally fell on the draft paper that Chen Zhuo had spread out beside him.

There were several lines of calculations written densely there, along with a few sketched manifold cross-section diagrams.

"I saw you taking notes here just now, what were you thinking about?"

Qiu Chengtong turned his head and looked at Chen Zhuo, his tone as if he were chatting casually with an acquaintance from the same group.

Chen Zhuo stopped twirling the pen in his hand.

He pushed the draft paper outwards slightly and smiled.

"I got distracted for a moment while listening to you guys talk about the singularity problem of Ricci flow."

Chen Zhuo shook his head.

"I'll also calculate some of my own things while I'm at it."

"After cutting open the entire scratch portion of the Hodge conjecture, where are we now?" Shing-Tung Yau asked.

Zhu Xiping also put down the red pen in his hand, raised his head and looked over. Cao Huaidong lowered his hand from between his eyebrows and his gaze fell on Chen Zhuo.

Chen Zhuo gently clasped his hands together and placed them on the edge of the table.

"It's stuck."

Chen Zhuo's voice was calm and undisguised.

"It's stuck on the boundary between analytic topology and algebraic closed chains."

Li Jianming took a blank sheet of paper and handed it to Chen Zhuo.

Chen Zhuo took it, but didn't rush to write. He just lightly touched the paper with the tip of the pen.

"Hodge classes are defined by differential forms on manifolds," Chen Zhuo continued.

"It relies on a continuous analytic structure, but the algebraic loop we are looking for is strictly constrained by polynomial equations and has extremely strong algebraic rigidity. The underlying logic of the two languages ​​is incompatible here. I want to translate the analytic language into the algebraic language, but there is a missing bridge in the middle."

Upon hearing this, Cao Huaidong leaned forward slightly.

"Once the geometric parameters of a manifold undergo continuous deformation, the variation of the Hodge structure will cause the original Hodge class to disappear."

Cao Huaidong followed Chen Zhuo's logic.

"In other words, the VHS theory did not always exist."

"right."

Chen Zhuo nodded.

"It only reappears on certain specific Hodge trajectories, and my current entry point is the Hodge trajectory."

Cao Huaidong tapped his fingers on the table without speaking, his mind racing to assess the feasibility of this logic.

What about the case of a divider with a codimensional of one?

Zhu Xiping asked from the side.

Is the classic Jacobian variety theory sufficient?

"Enough."

Chen Zhuo answered very decisively.

He drew a horizontal line on the paper.

"When p equals 1, the theory is complete, but I want to cut into higher dimensions."

Chen Zhuo drew another intersecting line below the horizontal line.

"For high-dimensional loops with p greater than 1, I've been trying to introduce intermediate Jacobian varieties recently."

Upon hearing this word, Zhu Xiping immediately frowned.

"Intermediate Jacobian cluster?"

Zhu Xiping stared at Chen Zhuo.

"In algebraic geometry, it usually degenerates into a complex Tolus, in which algebraic information is directly lost. How can you use a tool without algebraic information to find algebraic cycles?"

This is a fatal logical dead end.

The room was silent for a few seconds.

Qiu Chengtong looked at Chen Zhuo, waiting for him to continue.

Chen Zhuo still wore that gentle expression. He did not refute Zhu Xiping's words, but instead followed up on the questions raised by the other party.

"The algebraic information has indeed been lost."

Chen Zhuo took a pen and drew a circle on the two intersecting lines he had just drawn.

"So I tried to construct normal functions on this complex Torrus."

He stopped the pen tip in the center of the circle.

"I treat the normal function as a wandering detector. When the manifold parameters change on the Hodge trajectory, I use this detector to capture the topological traces mapped from the algebraic cycle."

Zhu Xiping's brows relaxed slightly, but the contemplation in his eyes deepened.

Cao Huaidong took the paper in front of Chen Zhuo and glanced at the lines on it.

"The thought process is going smoothly," Cao Huaidong said.

"But mathematically, how do you pinpoint this pattern?"

"This is the dead end we've reached."

Chen Zhuo looked at Cao Huaidong, his tone remaining largely unchanged.

"The problem now is how to rigorously prove mathematically that the location where a normal function produces a singularity must correspond to the birth of some algebraic cycle."

This is a huge barrier.

The detector found the singularity, but it wasn't the algebraic cycle they were looking for; a crucial equal sign was missing.

Yau Shing-Tung's hand holding the cup froze in mid-air.

He didn't drink the water, but slowly put the cup back on the table.

"What are your thoughts?" Shing-Tung Yau asked.

Chen Zhuo capped the pen.

"I've been looking into coefficient issues lately."

Chen Zhuo raised his head, looked at the three professors opposite him, and offered his perspective.

"The Hodge conjecture holds true for rational coefficients Q, but if we shrink it to integer coefficients Z, counterexamples emerge."

Li Jianming, who had been listening quietly, couldn't help but interject when he heard this.

"The sensitivity of algebraic loops to number fields?"

"Extremely sensitive." Chen Zhuo nodded.

He placed the pen in his hand on the table.

"This shows that the generation mechanism of algebraic cycles has extremely strict requirements on the discrete properties of numbers."

Chen Zhuo spoke very slowly, emphasizing each word clearly.

"Continuous analytical methods will inevitably fail here because they cannot capture the discrete nature of the problem."

None of the professors spoke.

They are all people who have ventured into the deep waters of geometry and algebra.

Chen Zhuo's perspective, which moves from continuous dimensionality reduction to discrete dimensionality reduction, and then back from geometric topology to the most basic arithmetic coefficients, is very complex and bold.

"So I've recently come up with a new idea."

Chen Zhuo picked up the pen again and fiddled with it in his hand for a moment.

"I plan to disassemble the tools I used to process discrete grid points and reconstruct them."

He looked at the draft paper in front of him.

"I'm going to try to use it to approximate the singularity of the normal function. I plan to try it myself while I'm in Boston."

After Chen Zhuo finished speaking, he did not continue to explain the specific construction method.

Silence fell over the seminar room once again.

The sounds of arguing in the corridor remained shut out through that heavy door.

Cao Huaidong stared blankly at the coffee cup on the table.

Zhu Xiping held a red pen in his hand, the tip of which hovered in mid-air. Qiu Chengtong leaned back in his leather chair, his gaze fixed on the light on the ceiling.

There is no need for polite praise or meaningless encouragement.

When a mathematical approach that is both intuitive and aesthetically pleasing is presented, their first reaction is to follow that path and frantically deduce its end in their minds.

Chen Zhuo withdrew his gaze, lowered his head, and opened the draft notebook in front of him.

The pen fell on the paper, writing down half a line of complex partial differential equations.