"Professor Shen, I chose you as my doctoral supervisor. ”

"Me too. ”

Ralph and Yu Lei expressed their stance and followed Shen Qi to study for a doctorate.

"Well, I'll work with you on the PhD project. ”

Shen Qi has been playing in the earthquake world for a while, and it is time to take care of his two mathematics doctoral students, and a professor who can't bring out a PhD is not a good professor.

"Yu Lei, Ralph, you completed your graduate studies in three semesters and each published a high-quality paper, Yu Lei's graduate thesis is related to complex variable functions, and Ralph is studying Lie algebra or abstract algebra. Your PhD project will not be separated by me again, you will work together on a project, yes, complex variable functions + abstract algebra, you will join forces to enter the field of algebraic geometry. "Shen Qi has set the framework, and this is part of his plan.

"Finally, we touched on this hottest branch. Ralph was excited.

"I'm very excited that we are doing a project designed by our mentor himself. "Yu Lei is highly motivated.

Topology is angelic, abstract algebra is devil, and complex variable functions are closest to reality.

Riemann used complex variable functions to study the double rational transformations of curves in the 19th century, which is considered a major advance in algebraic geometry.

At the beginning of the 20th century, Poincaré skillfully used his expertise in topology to intervene in the study of algebraic geometry.

The theme of algebraic geometry in the 21st century shifts to manifolds or clusters defined by one or more equations, i.e., high-dimensional figures, where abstract algebra is a necessary tool.

Why is algebraic geometry so popular that more than half of the world's mathematicians devote themselves to this field of study that combines angels, demons and reality?

Because to complete the unification of mathematics, we must rely on algebraic geometry, which is a truth that even mathematics graduate students understand, and Shen Qi certainly has numbers in his heart.

Sooner or later, it is better to enter the field of algebraic geometry, it is better to start now.

The summer vacation of Princeton doctoral students is two weeks, and after the summer vacation, Yu Lei, Ralph and Shen Qi work together to design a doctoral project and march into algebraic geometry.

In September, the new semester began, and the three teachers and students finally built a framework, even if this algebraic geometry topic was overcome, it could not complete the unification of mathematics, but it was the only way.

The framework of the project was set up, and the specific research work was carried out by Lei and Ralph, and Shen Qi grasped the overall progress.

The other two of the four predictions, Unimac and Nilkoskoye, are quiet and peaceful, and they have not been hit by any natural disasters.

During the summer vacation, Shen Qi bought an astronomical telescope in his spare time outside of design mathematics topics to watch the stars at night.

Modern cosmology is based on Einstein's theory of general relativity, also commonly known as the Big Bang theory.

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

There are too many troubles caused by predicting earthquakes, and Shen Qi hasn't mentioned earthquakes or other natural disasters recently, I look up at the vast universe, and it won't make the people of the earth panic, right?

The universe gave Shen Qi some inspiration, and he extracted the purely mathematical and physical theory part from "The Study of New Earthquake Models" and wrote a new, purely theoretical paper "On Complexity".

As soon as the semester began in September, Shen Qi submitted "On Complexity" to Edward Witten as his doctoral thesis in physics.

"On Complexity" attracted the attention of Edward Witten, and after reviewing the dissertation, he immediately arranged for Shen Qi's doctoral graduation defense.

Department of Physics, Institute for Advanced Study in Princeton.

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

All three are recipients of the Dirac Medal, the highest honor in the field of theory and mathematical physics, and is not awarded to former Nobel, Fields and Wolf Medal winners.

Witten is special in that he won the Dirac Medal and nearly a decade later, he won the Fields Medal.

Shen Qi did not have the opportunity to receive the Dirac Medal, the highest honor in theoretical physics, in his lifetime, and he had already won the Fields Medal.

Shen Qi attaches great importance to today's defense, and the three respondents he faced are the most authoritative experts in the field of theoretical physics.

Witten made the opening remarks first: "Qi, your paper "On Complexity", we three old guys have read it, this defense omits the respondent's statement part, and we will ask questions directly." ”

"Okay, Professor Witten, Professor Cullen, Professor Mortis. Shen Qi nodded, ready to answer.

"Qi, you mentioned in your paper that most of the phenomena in nature should be described by infinite-dimensional spatial differential equations, and the difficulty is the chaotic solution, tell me about your chaotic solution. "The first to ask questions was Professor Karen.

Shen Qi replied: "Chaos is a random behavior, and it is very difficult to accurately find a high-dimensional chaotic solution, such as weather forecasting, although the movement of the atmosphere is determined by deterministic equations, but because the initial conditions cannot be precisely controlled, the existence of chaotic solutions is rooted in being very sensitive to the initial conditions, which makes long-term accurate weather forecasting impossible to achieve." Therefore, it is best to focus on low-dimensional chaotic systems first, which are relatively easy to achieve precise control. Some of the ideas I discussed in my paper don't seem to be perfect, and they will probably take me a long time to perfect. ”

Professor Mortis continued: "Strange, I am more concerned with the turbulence of real space that you mentioned in your paper. ”

"Uh-huh. Shen Qi smiled, and then replied: "Turbulence is indeed related to chaos, but for a system that exhibits turbulence, it is considered to be a manifestation of space-time chaos, I gave a model of a low-dimensional turbulent system in my paper, and I don't know what its practical use is, and the application level will be handled by the applicationist." ”

"Qi, it seems that you are also afraid of trouble. Witten laughed, and then he asked: "Your paper is very jumpy, and it deals with extremely esoteric complexity principles, and there should not be many people in the world who can read your paper." What I want to ask about is the complex connection between chaos, turbulence, and 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, far from the matter of the universe, the geometry of space-time is Minkowski space-time, and I tried to find a concrete connection between chaos, turbulence and general relativity, and I did so and deduced a weird equation ......"

Shen Qi answered fluently, and he and three top theoretical physicists discussed purely theoretical academic problems that few people in the world can understand.

The defense meeting lasted for a whole afternoon, and at the end of the conversation, the three big bulls of Witten, Karen, and Mortis were also a little entangled, what kind of universe is the universe we are in?

"I don't have a problem anymore, I think Qi's Ph.D. in physics graduation defense can pass. Witten began to make his closing remarks.

"Passed. ”

"Passed. ”

Cullen and Mortis have expressed their positions.

"Thank you, three professors. Shen Qi accomplished one of his goals this year by earning a Ph.D. in physics from the Institute for Advanced Study in Princeton.

……

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