Gather His Focus

"Professor Shen, I choose you as my doctoral supervisor."

"Me too."

Ralph and Yu Lei declared that they were determined to pursue their doctorates under Shen Qi.

"Alright, I will work with you to design the doctoral thesis."

Shen Qi has been dabbling in the field of earthquake studies for a while now; it's time for him to settle down and mentor his two math PhD students. A professor who can't mentor PhDs isn't a good professor.

"Yu Lei, Ralph, you both completed your graduate studies in three semesters and each published a high-quality paper. Yu Lei's graduate thesis is related to Complex Analysis, Yu Lei 'Ralph research focuses on Lie Algebra, or rather, Abstract Algebra. Your doctoral projects will no longer be separated by me; you will work together on a single project. Yes, Complex Analysis + Abstract Algebra. You will join forces to enter the field of Algebraic Geometry." Shen Qi had already set the framework; this was part of his plan.

"Finally, we've reached this most popular branch." Ralph was visibly excited.

"I'm so excited! This time, we're working on a project personally designed by our supervisor," Yu Lei, full of fighting spirit.

Topology is an angel, Abstract Algebra is a devil, and Complex Analysis are closest to reality.

Riemann's use of Complex Analysis to study the birational transformations of curves in the 19th century is considered a major advancement in Algebraic Geometry.

At the beginning of the 20th century, Poincare skillfully used his expertise in topology to engage in the study of Algebraic Geometry.

In the 21st century, the focus of Algebraic Geometry has shifted to manifolds or clusters defined by one or more equations, i. e., high-dimensional graphs, for which Abstract Algebra is a necessary tool.

Why is Algebraic Geometry so popular, drawing more than half of the world's mathematicians to this field of study that combines angels, devils, and reality?

Because achieving Mathematical Grand Unification requires relying on Algebraic Geometry, a fact that even Mathematical Research understand, Shen Qi was certainly aware of this.

I'll have to get into Algebraic Geometry sooner or later, so I might as well start now.

Princeton doctoral students have a two-week summer break. After the summer, Yu Lei, Ralph, and Shen Qi designed their doctoral thesis together, venturing into Algebraic Geometry.

By September, with the start of the new semester, the three teachers and students had finally established a framework. Even if this topic of Algebraic Geometry were solved, it would not achieve the Mathematical Grand Unification, but it was an inevitable step.

With the project framework in place, the specific research work was carried out by Yu Lei and Ralph, while Shen Qi oversaw the overall progress.

The other two of the four predicted locations, Unimak Island and Nirkoscoye Island, are peaceful and idyllic, untouched by any natural disasters.

During the summer vacation, in his spare time outside of designing math projects, Shen Qi bought a telescope to observe the stars at night.

Modern cosmology is built upon Einstein's theory of General Theory of Relativity and is often referred to as the Big Bang theory.

Whether it's classical physics or Quantum Physics, they are ultimately connected to the universe.

Predicting earthquakes causes too much trouble, and Shen Qi hasn't mentioned natural disasters like earthquakes lately. I look up at the vast universe; surely that won't cause panic among the people of Earth?

The universe gave Shen Qi some inspiration. He extracted the purely Mathematical Physics theory from "Research on a New Earthquake Model" and wrote a new, purely theoretical paper, "On Complexity".

At the start of the new semester in September, Shen Qi submitted "On Complexity" to Edward Witten as his doctoral dissertation in physics.

"On Complexity" caught the attention of Edward Witten, who, after reviewing the paper, immediately arranged for Shen Qi's doctoral dissertation defense.

Physics Division, Institute for Princeton Institute for Advanced Study.

The three elderly men sat together; the youngest of them Witten, was almost 70 years old.

All three are recipients of the Dirac Medal, the highest honor in theoretical and Mathematical Physics, which is not awarded to former Nobel Prize, Fields Medal, or Wolf Prize laureates.

Witten is somewhat unique; nearly ten years after receiving the Dirac Medal, he won the Fields Medal.

Shen Qi will never have the opportunity to receive the Dirac Medal, the highest honor in Theoretical Physics, but he has already received the Fields Medal.

Shen Qi attaches great importance to today's defense, as the three examiners he is facing are the most authoritative experts in the field of Theoretical Physics.

Witten began by saying, "Qi, we three old guys have all read your paper, 'On Complexity.' We'll skip the presentation part and go straight to the questions."

"Okay, Professor Witten, Professor Karen, Professor Mortis." Shen Qi nodded, preparing to respond.

"Qi, you mentioned in your paper that Sun Yat-sen University nature should be described by infinite-dimensional spatial Differential Equation, and the difficulty lies in Chaos Solution. Tell me about your Chaos Solution." Professor Karen was the first to ask the question.

Shen Qi replied, "Chaos is a random behavior, and it is extremely difficult to find precise Chaos Solution. For example, in weather forecasting, although atmospheric motion is determined by deterministic equations, the existence of Chaos Solution is rooted in their extreme sensitivity to initial conditions because the initial conditions cannot be precisely controlled. This makes long-term accurate weather forecasting impossible. Therefore, we should focus on low-dimensional chaotic systems first, as they are relatively easier to control precisely. I have discussed some ideas in my paper, which do not seem to be perfect yet, and it may take me a long time to refine them."

Professor Mortis continued, "Qi, I'm more concerned about the Real Space Turbulence you mentioned in your paper."

"Hmm." Shen Qi smiled and then replied, "Turbulence is indeed related to chaos, but for a system exhibiting turbulence, it is considered a manifestation of spacetime chaos. I presented a low-dimensional turbulent system model in my paper, but I don't know what its practical applications are. Let applied scientists handle the application-level issues."

"Qi, it seems you also dislike trouble," Witten chuckled. He then asked, "Your paper is quite abrupt, discussing extremely profound principles of complexity. There probably aren't many people in the world who can understand it. What I want to ask is about the connection between chaos, turbulence, and the complexity of the universe, which you mentioned in your paper."

"The homogeneity of the universe does not apply to every detail of the universe, such as the Solar System, the Milky Way, or even galaxy clusters. In places far from cosmic matter, spacetime geometry is Minkowski Spacetime. I tried to find a concrete connection between chaos, turbulence, and General Theory of Relativity, and I did so, deriving a strange equation..."

Shen Qi answered fluently, discussing purely theoretical academic issues with three top Theoretical Physics that few people in the world could understand.

The defense lasted the entire afternoon. Towards the end, even the three leading experts, Witten, Karen, and Mortis, were somewhat perplexed: what kind of universe do we live in?

"I have no further questions. I believe Qi's Ph. D. dissertation defense in physics will be successful," Witten began his concluding remarks.

"Pass."

"Pass."

Karen and Mortis both expressed their opinions.

"Thank you, professors." Shen Qi had achieved one of his goals for the year: he earned his Ph. D. in physics from the Princeton Institute for Advanced Study.

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