I Just Want to Be a Quiet Top Student

"If you consider graduate courses, these seven branches contain more than 80 subdivided courses in total, and there are 11 subdivided courses under just one functional analysis."

"Of course, undergraduates in the Department of Mathematics only need to study the most basic functional analysis theories, such as linear operator theory and variational method, and advanced courses such as Banach space and topological linear space are the learning tasks for graduate students." Witten Speaking of which, he is an expert in functional analysis, and physical problems cannot be separated from the mathematical processing methods of functional analysis.

"So strange, when you entered the Princeton Graduate School, which branch did you choose as your main research direction?" Witten asked.

"My main field of study is mathematical physics. Dear Professor Witten, you were the supervisor I applied for at first." Shen Qi revealed a secret.

"Charles, why don't I know about this kind of thing?" Witten looked at Director Fefferman suspiciously.

"Hey, Edward, please, don't look at me like that! When you were the dean of the department a few years ago, you said that you will not bring any graduate students in the future." Director Fefferman won the Feifei Award at the age of 29, and he Such a smart person will not take the blame, and the blame is justified, timely and accurate.

"Oh, is that so, maybe I forgot." Wei Teng looked at Shen Qi, expressing regret that he would never have the chance to be Shen Qi's tutor again in this life, because Shen Qi will participate in the doctoral graduation defense in a few months .

"The daily affairs of the Department of Mathematics, such as admissions, are handled by Carl. Edward, you have been the dean of the department, and you know the admissions process. Carl is completely following your previous instructions, and you can't blame him." Director Fefferman explained.

"I see." Witten nodded, he was on an equal footing with Fefferman in the Department of Mathematics.

The director of the Department of Mathematics of Pudong University changes every three years, and the big cows take turns. The position of director does not have additional income or subsidies, and it is purely in the nature of serving the people.

The recently retired F+W+A superstar John Milnor was the head of the department, and Andrew Wiles, who has returned to the UK, was the head of the department. Witten was the head of the previous department, and this time it is Pfeiffer’s turn Man.

The top leaders at all levels in Princeton mainly focus on academics. Taking the Department of Mathematics of Pudong University as an example, the old director Witten and the current director Fefferman don’t care much about daily administration, except for the appointment and dismissal of personnel and the approval of academic funds, which involve people and money. Important matters and other miscellaneous daily chores in the department are handed over to the chief secretary.

The chief secretary of the Department of Mathematics is Karl. He has been working as the secretary for eighteen years and has served six department heads. In a sense, Karl is the chief executive of the Department of Mathematics.

Shen Qi has met Karl, this old man is equivalent to the general manager, and Karl has the final say on many matters other than academics.

Because of the relatively independent system of politics and academics, Shen Qi did not complain that Professor Wei Teng did not accept him as a student: "Let the past go, the most important thing is to live in the present."

"Come back to business, Qi, your main research direction is mathematical physics, but you have made even greater achievements in number theory, functional analysis, and abstract algebra. The four papers you have published recently are related to these three branches, and two of them have been published In two of the four major mathematics journals." Director Fefferman said.

Shen Qi said: "I am ashamed to say that after I studied at Princeton, I did not achieve any results in the main direction. The same is true for my first auxiliary major in algebraic geometry. Number theory is my second auxiliary major. Group theory or Yes, abstract algebra is my third auxiliary major. 'Muller-Shen theorem' belongs to improvisation, and the non-Euclidean geometry tutorial class is a teaching assistant task arranged by the department. I did not include functional analysis and geometry into formal research before scope."

"Qi's comprehensive and professional academic characteristics should no longer follow the standard setting of main attack and auxiliary. My opinion is that after passing the doctoral defense, let Qi do one to two semesters As a lecturer, it doesn’t matter which course he teaches, it’s a transitional period anyway.” Wei Teng put forward his views.

Shen Qi agreed: "Choose one of number theory, abstract algebra, and functional analysis, or choose two of the three. In fact, I really want to open a new course. I will call it "History of Number Theory" for the time being, but the biggest problem is There is no teaching material for this course, because my teaching material is still being compiled, as for the progress... About 1% is completed, um, the rough outline is finished."

"I don't think there is a problem. The most suitable position for Qi should be a position that focuses on academic research. If you master it well, you may be able to create a new branch of mathematics or even a school. Professors or associate professors need to apply again as lecturers. The two papers in the Journal of the American Mathematical Society are even qualified to apply for professors or associate professors, of course, the premise is that you must first get a PhD and become an official lecturer at Princeton." Fefferman took a sip of coffee, looked at Xiang Shenqi: "For extremely outstanding young talents, Princeton sometimes relaxes its standards."

But no matter how relaxed Princeton's standards are, there is a bottom line.

It is the bottom line of Princeton that the Ph.D. is issued after at least one year of Ph.

Fefferman and Witten seem to have helped Shen Qi plan his career path for the next few years. Shen Qi has no objection. He has to stay in Princeton for a while, at least until the day Ouye gets his doctorate .

As for Shen Qi's doctoral defense, it was actually a procedure. With two papers in the four major journals, he could at least be hired as an associate professor at Pudong University. A mere doctoral defense is not a trivial matter.

During the time of chatting over coffee, the two bosses decided on Shen Qi's future lecturer position. If all goes well, Shen Qi will officially take up the post this fall.

While chatting, Shen Qi talked about his "Shen's Proximity Theorem": "Shen's Proximity Theorem in Banach space, I submitted this paper to "Mathematical Inventions" on Christmas Eve, It is currently under review, and this is my latest paper, I know the rules, it doesn’t count if it’s passed by the journal, but it’s counted if it’s passed by Princeton.”

Witten asked: "What is the main conclusion of the 'Shen's Proximity Theorem' in Banach spaces?"

Shen Qi wrote on the blackboard:

H={x*∈X*:x*(x0)=x*(x0)=1}

...

So z*α(x0)=1→z*α(x0)=1→z*∈H, x*co^ω*(B(X*)/B(x0*))

Shen Qi explained: "It is obtained from this that each ω* closed convex set of X* is a Chebyshev set that is approximately compact. I will temporarily name this conclusion 'Shen's approximation theorem', and the final name needs to be obtained IMU's approval. I can only write the core outline on the blackboard, and I can submit the full text of the paper to Professor Witten and Director Fefferman for review at any time."

"This strange proof is correct." Experts took a look, and Witten, who is good at functional analysis and space theory, recognized "Shen's Proximity Theorem".

"Is it "Invention of Mathematics", this is so interesting, Qi, you will have the third paper in the four major journals, and all this, you have done it in less than two years. Qi, your age this year is ?” Director Fefferman asked.

Shen Qi: "22 years old."

Director Fefferman nodded in praise: "It's amazing."

Shen Qi and Wei Teng drank coffee without talking, they both knew that the most remarkable one was Director Fefferman.

At the age of 22, Fefferman had been promoted to a full professor at the University of Chicago. At the age of 22, Witten was a doctoral student in the Princeton Department of Physics. At the age of 22, Shen Qi was a doctoral student in the Princeton Department of Mathematics.

Fefferman is a gifted child, while Wei Teng and Shen Qi are late bloomers.

During the coffee time on Wednesday, pretending to be B time, the big winner at the end was Director Fefferman.

Before the end of coffee time, Fefferman asked: "By the way, Qi, there will be an international academic conference and award ceremony at NASA in a while, and I wonder if you have heard of the Science Breakthrough Award and New Horizons?"

"I've heard of it." Shen Qi was a little surprised. Could it be that another prize came?