I Just Want to Be a Quiet Top Student

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

"Me too."

Ralph and Yu Lei expressed their opinions, determined to follow Shen Qi to study for a Ph.D.

"Well, I will design a doctoral topic with you."

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

"Yu Lei, Ralph, you completed the graduate courses in three semesters, and each published a high-quality thesis. Yu Lei's graduate thesis was related to complex variable functions, and Ralph studied Lie algebra or abstract Algebra. Your two doctoral topics will not be separated by me, and you will complete a project together, yes, complex variable function + abstract algebra, and you will join hands to enter the field of algebraic geometry." Shen Qi has set the framework, which is part of his plan.

"Finally, we have touched the hottest branch." Ralph was excited.

"I'm very excited. What we are doing this time is a project designed by our instructor." Yu Lei was full of fighting spirit.

Topology is an angel, abstract algebra is a devil, and complex variable functions are closest to reality.

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

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

The topic of algebraic geometry in the 21st century turns 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 that more than half of the world's mathematicians devote themselves to this research field that combines angels, demons and reality?

Because completing the grand unification of mathematics must rely on algebraic geometry, this is a truth that even graduate students in mathematics understand, Shen Qi certainly knows it.

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

The summer vacation for Princeton doctoral students is two weeks. After the summer vacation, Yu Lei, Ralph and Shen Qi designed a doctoral project together, marching towards algebraic geometry.

In September, when the new semester started, the three teachers and students finally set up the framework. Even if this subject of algebraic geometry was conquered, it would not be possible to complete the unification of mathematics, but it was the only way to go.

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

The other two of the four predicted points, Unimak and Nilkoskoye, are quiet and peaceful like a paradise, and they have not been hit by any natural disasters.

During the summer vacation, Shen Qi bought an astronomical telescope to watch the stars at night, using his spare time besides designing mathematics projects.

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

Whether it is classical physics or quantum physics, they are all connected with the universe in the end.

There are too many troubles caused by predicting earthquakes, and Shen Qi has not mentioned natural disasters such as earthquakes recently. I look up at the vast universe, and it will not make the people of the earth feel panic, right?

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

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

"On Complexity" attracted Edward Witten's attention. After he reviewed the thesis, he immediately arranged Shen Qi's doctoral defense.

Department of Physics, Institute for Advanced Study, Princeton.

Three old men sat together, and the youngest among them, Witten, was almost 70 years old.

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

Witten is quite special. Nearly ten years after he won the Dirac Medal, 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 life. He has already won the Fields Medal.

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

Witten made the opening remarks first: "Qi, the three of us old guys have read your paper "On Complexity". This defense will omit the respondent's statement, and we will directly ask questions."

"Okay, Professor Weiteng, Professor Karen, and Professor Mortis." Shen Qi nodded, ready to answer.

"Qi, you mentioned in your paper that most 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." Professor Karen was the first to ask the question.

Shen Qi returned: "Chaos is a random behavior, and it is very difficult to accurately find a high-dimensional chaotic solution. For example, in weather forecasting, although the movement of the atmosphere is determined by deterministic equations, since the initial conditions cannot be precisely controlled, the chaotic The existence of the solution is rooted in being very sensitive to the initial conditions, which makes it impossible to achieve long-term accurate weather forecasting. So we'd better focus on the low-dimensional chaotic system first, which is relatively easy to achieve precise control. In my paper, I discussed Some ideas do not seem to be the most perfect, and it may take me a long time to perfect."

Professor Mortis continued: "Qi, I am more concerned about the real space turbulence mentioned in your paper."

"Hmm." 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. The turbulent system model, I don’t know what practical use it has, and the application level is left to the applied scientists.”

"Odd, it seems that you are also afraid of trouble." Wei Teng laughed, and he continued to ask: "Your paper is very jumpy, and it discusses extremely profound principles of complexity. The whole world can understand your paper. There should not be many people in the paper. What I want to ask is the complex connection between chaos, turbulence and the universe, which you mentioned in your paper."

"The uniformity of the universe does not apply to every detail of the universe, such as the solar system, the Milky Way, and even galaxy clusters. In places far away from the matter of the universe, the space-time geometry is Minkowski space-time. I try to find the relationship between chaos, turbulence and general relativity. I did the same, and derived a weird equation...”

Shen Qi answered fluently. He and three top theoretical physicists discussed purely theoretical academic issues that few people in the world could understand.

The defense meeting lasted the whole afternoon, and at the end of the chat, Wei Teng, Karen, and Mortis were also a little confused. What kind of universe is the universe we live in?

"I have no more questions. I think Qi's Ph.D. defense in physics can be passed." Witten began to make a concluding speech.

"pass."

"pass."

Karen and Mortis expressed their opinions one after another.

"Thank you three professors." Shen Qi completed one of his goals this year, and he received a Ph.D. in physics from the Institute for Advanced Study in Princeton.

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