Systematization and the Hodge Conjecture

Two weeks later, the new semester begins.

The Richardson Concert Hall in the Nassau Hall, was packed with distinguished guests.

This is Princeton's most important venue for performances and lectures. Guests who have spoken here include Bill Clinton, Hillary Clinton, Bill Gates, and Condoleezza Rice.

Today it's Shen Qi's turn, and his presentation is titled "Systematization and Hodge Conjecture".

The hundreds of guests included senior officials from IMU, mathematics professors from internationally renowned universities, mathematics experts from authoritative research institutions, editors-in-chief of famous mathematics journals, executives from large academic publishing groups, and media representatives.

All faculty and research staff from the Princeton Mathematics Department and the Department of Mathematics at Princeton Institute for Advanced Study attended the meeting, along with a representative from Princeton University.

Director Feierman wasn't exaggerating; the scene was spectacular and top-notch.

Invitations to Shen Qi's keynote speech were extremely difficult to obtain. The large team of "Systematization and Hodge Conjecture" consisted of 20 people, and the remaining 19 were eager to hear Shen Qi's speech in person. In the end, only six people came: Lu Guozhen, Director Wu, Yu Lei, Ralph, and one researcher each brought by Lu Guozhen and Director Wu.

Before the speaker, Shen Qi, even took the stage, the guests in the hall were already whispering and discussing amongst themselves.

"Have you seen the paper that Shen Qi pre-recorded on arVix two weeks ago?"

"After reading it several times, I believe he proved the Hodge conjecture in a masterful way."

"But I still have doubts. It's said that the pre-recorded version on arVix is a condensed version."

"The mystery is about to be solved! Look, Shen Qi is coming on stage!"

Shen Qi onto the stage, and the entire audience burst into applause. Shen Qi waved in response, and the applause gradually subsided, leaving the hall quiet.

"Ladies and gentlemen, good morning. I am Shen Qi, Professor of the Princeton Mathematics Department. I will be giving a presentation on 'Systematization and Hodge Conjecture.' The presentation is expected to last all day. Thank you for coming to listen." Shen Qi began his keynote speech with these polite opening remarks.

"Before the formal presentation, please allow me to introduce my team. Our team has twenty members, which is an extremely impressive lineup for a fundamental mathematics project."

"I am honored to have been selected as the team leader. I would like to thank Mr. Lu Guozhen, Mr. Wu Yuyong, and their team members for their contributions to this project. The three academic institutions of Princeton, Yenching University, and Morning Star Mathematics Center have worked together very well in this project and have achieved significant breakthroughs."

In the audience, Lu Guozhen and Director Wu, who were sitting together, were extremely excited. This was probably the most exciting moment of their lives.

Shen Qi used a page-turning pen to control the PPT slides on the large screen. "More than half of the world's mathematicians are seeking breakthroughs in Algebraic Geometry. Choosing a topic is very important. We have chosen one of the most difficult problems in Algebraic Geometry — the Hodge conjecture."

"The work to directly prove the Hodge conjecture has been ongoing for decades, and it is only in recent years that the University of Bonn and the École Normale Supérieure have made substantial research results."

Professor Schultz from the University of Bonn was also present; he was expressionless and as cold as ice.

Professor Viduka of the ENS Paris patted Schultz's thigh and whispered, "Peter, negative emotions are the devil. Learn from me; I'm very open-minded. My only purpose in coming here today is to learn from Shen Qi's experience as a fan."

"I shouldn't have come," Schultz said, then closed his eyes.

On stage, Shen Qi spoke with ease and confidence, "Last September, I went back to China. That day, when I was chatting with Mr. Lu and Mr. Wu, I suddenly felt that something was wrong. I said, 'Hey guys, why can't we build a system to prove that the Hodge conjecture is a correct proposition in a systematic way?'"

"Mr. Lu and Mr. Wu strongly agreed with my point of view, so we jointly launched the 'Systematization and Hodge Conjecture' project, which has now been running for exactly one year."

Down in the audience, Old Wu pondered deeply, "Was there such a day last September? I remember Professor Shen did come to our center, but he didn't mention anything about systematization. He just said to me, 'Old Wu, let's solve the Hodge conjecture.'"

"Old Wu, you're still too young," Old Lu said with a smile.

Old Wu: "Old Lu, you're only a year older than me. We're both almost sixty. What's the point of talking about being young or not?"

Old Lu put a finger to his lips as a shushing gesture. After Shen Qi finished explaining the project background, he began to elaborate on the key academic points related to the project.

On stage Shen Qi, following the standard academic paper format, first presented the core abstract before introducing the main text. "Our overall approach is to first establish a system, tentatively called the 'Shen-Lu-Wu System,' or SLW system for short."

"The significance of the SLW system lies in its ability to explain problems in fields such as Algebraic Geometry, topology, and Mathematical Analysis using the concept of 'local Grand Unification '."

"The Hodge conjecture can be explained using SLW. Topological problems can be explained using SLW, such as the already proven Poincaré conjecture. Mathematical Analysis problems can also be explained using SLW."

Shen Qi raised his arms and shouted, "Yes, yes, anything is fine!"

Wow!

The entire audience was stunned.

The two striking key points, "local Grand Unification" and "it's possible, it's possible, it's all possible," did not appear in the abridged version of Shen Qi's paper published on arVix.

Two months ago, Lao Lu and Old Wu went to the United States and returned to China after handing over the documents. They did not get to see the full text of "Systematization and Hodge Conjecture" personally compiled by Shen Qi.

Only four people have seen the final version of Shen Qi's thesis in full: Feierman, Faltings, Deligne, and Ralph.

"Grand Unification!"

"Both can be explained!"

The entire audience erupted in cheers, and the situation began to spiral out of control.

Old Lu and Old Wu jumped up, both surprised and delighted, but more surprised than delighted. "Shen Qi, how did you make things so big? This is beyond our capabilities!"

The two researchers, Lao Lu and Old Wu, who brought along to experience the atmosphere, were stunned.

"This... this is unified?" The researcher from Yanda University was dumbfounded. He was a key member of the AN section, which was under the responsibility of Lu Guozhen.

"We can never figure out Boss Shen's way of thinking..." The researcher at Morning Star Mathematics Center was an elite in the TP sector. He never dared to imagine that the project he participated in would accidentally become Grand Unification. He originally thought it was just about proving Hodge conjecture.

Schultz jumped to his feet, looking incredulous. It turned out that Shen Qi hadn't considered him an opponent at all. Shen Qi wasn't interested in individual cases; Shen Qi ambition was Grand Unification! He would just deal with the Hodge conjecture incidentally during the process of Grand Unification.

Seeing that the situation was about to get out of control, Shen Qi quickly explained, "Local, local! Local Grand Unification, not the absolute, complete Grand Unification you're imagining! Everyone, please sit down, please return to your seats!"