Experts

Zhou Yu'an presented their preliminary research results in Partial Differential Equations and Algebraic Geometry: "Let M be an n-dimensional complete Riemann manifold. Combining the Riemann curvature tensor and the Ricci curvature tensor, we construct this set of equations..."

The PPT displays this set of formulas: Γ=1/2g^kl{gil/xj+gil/xi-gij/xjl}...^2gij/t^2=-Rgij

"From the perspective of Partial Differential Equations, this is a highly nonlinear hyperbolic equation. Finding its exact solution would be enough, and perhaps it could be used to write a high-quality paper in one of the Top Four Journals."

"Yes, we have found some exact solutions to it. Thank you for your efforts, Small Joker." Zhou Yu'an looked at his younger brother, Small Joker, with affirmation and encouragement in his eyes.

Small Joker has been working in the Center Mathematics Department for a year, so he's considered a newcomer. He's only 25 years old this year, but he has already earned a PhD in mathematics, making him a top performer among newcomers.

This demonstrates the formidable strength of the Center Mathematics Department. Small Joker, a newcomer, produced research results worthy of publication in four major mathematics journals; all these precise solutions were derived by him.

Small Joker humbly expressed his gratitude to the center for providing such a great platform, and to Director Shen and Section Chief Zhou for their meticulous guidance. He explained that he had only performed the most basic operations, solving equations. The equations were actually constructed by Section Chief Zhou and Professor Xu.

The young man is quite likable. Small Joker's data presentation is impressive, he speaks pleasantly, and he's not at all aloof. Small Joker proactively takes on miscellaneous tasks such as photocopying, printing, setting up the meeting room, and preparing tea.

Academic leaders such as Shen Qi, Xu Yang, and Ou Ye praised Small Joker, noting that young people who are capable and willing to do the dirty work often attract special attention from leaders.

Zhou Yu'an continued his presentation, "But what we're doing is a project on the Mathematical Grand Unification, not just Partial Differential Equations. So, after finding the exact solution, we're trying to construct a new model using Algebraic Geometry."

"To give an analogy, the Mathematical Grand Unification is like a car. Its components are the various branches of mathematics: Algebraic Geometry is the side panels, Partial Differential Equations are the roof, number theory is the wheels, topology is the seats, and so on."

"The manufacturing standards for components vary widely, and mathematicians in different branches of the field study different things."

"And for a complete car, we want it to have only one standard."

"In Professor Xu's and my view, if we complete the 'welding' of Partial Differential Equations and Algebraic Geometry, then the 'body' structure of Mathematical Grand Unification will be locked in."

"Next, please welcome Professor Xu to present his research findings on 'A New Algebraic Geometric Model Based on the Definitive Solution of Hyperbolic Geometry Algebraic Geometry'." After Zhou Yu'an finished speaking, he handed the page turner to Xu Yang.

Xu Yang said, "Yu'an's analogy is apt but has some flaws, but overall it's okay. The Mathematical Grand Unification isn't simply about welding various parts together to form a complete car—it's an ideal. Forcibly assembling various parts together might lead to incompatibility, potentially causing the car to fail to start. Assembling a car inevitably involves new technical skills to ensure it can start smoothly. Of course, our first task is to assemble this 'car'."

"Hmm." Shen Qi nodded and said, "The combination of Yu'an and Professor Xu's ideas is basically the essence of the Mathematical Grand Unification. What is the Mathematical Grand Unification? Two key words: all theories converge on one, and feasibility. We are not mere porters or assemblers; our role is that of strategic coordinators and tactical designers. Professor Xu, please continue."

Xu Yang presented an extremely complex mathematical model. How complex? More than half of the mathematicians present could not understand it.

This is normal; the vast majority of mathematicians determine their main research area during their doctoral studies.

Some specialize in Algebraic Geometry, some focus on number theory, and some demonstrate exceptional talent in the field of Partial Differential Equations.

There are scholars who specialize in one area and minor in another; they are not few in number.

Mathematicians who are proficient in more than three branches of mathematics are relatively rare.

Xu Yang Algebraic Geometry, and he is also quite proficient in Differential Geometry and Partial Differential Equations. He can be considered an outstanding mathematician.

However, Xu Yang is not as proficient as Zhou Yu'an in Differential Geometry and Partial Differential Equations, and Zhou Yu'an cannot reach the same depth in Algebraic Geometry Xu Yang.

Ou Ye can easily outperform Xu Yang and Zhou Yu'an in number theory, but she is also outperformed by Xu Yang and Zhou Yu'an in Algebraic Geometry, Differential Geometry, and Partial Differential Equations.

At this moment, Xu Yang brought out the most profound knowledge in the field of Algebraic Geometry.

Ou Ye was completely outmatched; she couldn't understand it and could only remain silent.

"Let me explain this model," Xu Yang said, taking a sip of tea. "My colleagues at the center are remarkable. They constructed a system of equations for Hyperbolic Geometry flow and derived an exact solution. Based on the research of Section Chief Zhou and his team, my students and I built this hyperbolic model."

Shen Qi couldn't help but say, "Professor Xu, you've redefined Mori contraction? It's a wonderful concept. I've also seen something new. Old Xu is indeed a master; this technique is amazing. Skill breeds boldness."

A master is a master; Shen Qi saw through the essence at a glance. Xu Yang nodded to Shen Qi and said, "Old Shen, since you've seen through the essence, I won't waste any more time. I'll skip the process of establishing this curved model and just talk about the conclusions and difficulties. Does everyone agree?"

No objections, no objections.

That's just how math is; some things you just don't understand, and even if an expert explains them to you for a week, you might still not get it.

Instead of pretending to know what you don't, it's better to listen to experts explain their conclusions.

The conclusions given by experts are often highly generalized. For an expert like Ou Ye who is not in the field of Algebraic Geometry, she only needs to know the conclusions of the Algebraic Geometry section of this project.

Xu Yang continued, "Mori contraction is a theory invented by Shigefumi Mori. Mori began studying the Langlands Program very early on, and he won the Fields Medal in 1990. Mori's ambition was also to achieve the Mathematical Grand Unification, and many of his ideas are still very inspiring."

"Our model references the core elements of Mori contraction and adds some original content. Our preliminary conclusion is that, even if a generalized curvature minimal model exists, it is not smooth but rather a singular cluster with canonical singularities."

"At this point, does anything come to mind? Yes, that's right. As we worked on it, we discovered that our new model was somehow connected to the Hodge conjecture! Who proved the Hodge conjecture?" Xu Yang suddenly got excited as he spoke.

Everyone was also very excited. "Shen Qi!"