I just want to be a quiet scholar

Chapter 329 Teaching
"OK, I figured it out."

Shen Qi wrote on the blackboard:

Let Xr+(T)={λ=∑m+n, i=1λiεi∣0≤λi-...}
……

"This is... an enhanced version of the algebraic group model?" Ralph stood up abruptly, his eyes fixed on the blackboard.

"Yes, but not all." Shen Qi continued his deduction, taking into account the modular category, he did a linear mapping process, and obtained a finite-dimensional structured algebra.

"I think there is a condition here to satisfy the law of reciprocity in the category of infinitesimal group representations, and finally give the result of irreducible representations of supergroup Frobenius kernels. Let m≠n(modp), then St1 is a projection u(g)-module, so T(μ) is projected u(g)-module. Well, this is more like a lemma, and I need to prove this lemma." Shen Qi turned to Ralph and said, his eyes The wisdom that controls everything shines in it.

"Then... please start your proof, Professor Shen." Ralph was overwhelmed by Shen Qi's powerful aura.

"Wait a minute." Shen Qi walked to the bookcase, took out a document to check.

Ralph: "..."

"Lie algebra, complex variable function, group theory, their outlines are engraved in my soul, but I can't remember all the details, so sometimes I need to check the information." Shen Qi said, he told Lal Husband smiled: "You were thinking just now, so Shen Qi is also an ordinary person, he is not an omnipotent god. Yes, that's right, I am not a god, I just focus more on myself than ordinary people Career, focus can be professional, and professional depth determines the height of career.”

"Professor Shen, what you said is very good." Ralph was in awe, but also secretly startled, how could you gain insight into my inner activities?
After checking several conclusions in the Holmes-Shigeo Nakano method, Shen Qi proved the lemmas on the blackboard.

This process lasted more than ten minutes. Shen Qi wrote and Ralph watched. The two were very focused, one imparting knowledge and the other absorbing knowledge.

Shen Qi tapped on the blackboard: "During the proof process, I used the Holmes-Shigeo Nakano method, the Brauer model, and the Humphreys theorem, all of which are existing theories and have not proposed any innovations. Invention. Innovation is very difficult, and what we do most of the time is comprehensive application and theoretical reshaping. In a sense, comprehensive application is also a kind of innovation.”

"Yes." Ralph nodded heavily, and he showed a cheerful and enlightened expression: "The most important thing is the use of Weyl groups, and the function of the middle point is still defined as ωv=ω(v+ρ)-ρ, so We obtained that the dimension of the weight space is 1, that is, Q1(λ) is the projective cover of the restricted irreducible g-module L1(λ).”

"Very good." Shen Qi began to wipe the blackboard.

"Wait a minute, Professor Shen!" Ralph quickly took out his phone, wanting to take a picture.

"Don't shoot Ralph, it's not necessary." Shen Qi continued to wipe the blackboard, and quickly wiped out the mathematical symbols on the blackboard: "It seems that you haven't fully understood what I mean by comprehensive application. Its essence lies in the built-in logic Without an external form, logic cannot be photographed.”

"I..." Ralph felt ashamed.

This classmate, Ralph, is down-to-earth and not playful, but he lacks a little understanding.

Yu Lei is eloquent and looks a little impetuous, but his understanding is stronger than Ralph's, and his thinking is divergent.

After contacting for a long time, Shen Qi became more and more familiar with the personality traits and academic strengths and weaknesses of the two students. Extremely rigorous people may lack rich imagination, and people with wild thinking often cannot prove their conjectures or predictions made by sudden inspiration.

No one is perfect, and teaching students in accordance with their aptitude is a test for teachers.

Shen Qi said: "You can repeat my thinking logic, but please don't copy my proof process, Ralph, I will give you some new hints, starting from another way, relying on commutative super algebra, comprehensively using Matrix elements, Frobenius morphisms, and baby Wilma modules complete the proof of the lemma just now."

"Pay attention to the order of the mathematical tools I mentioned. If you use the baby Wilma model first, it will be a waste of time. I may be a bit demanding of you, and I think it is necessary because you are a graduate student in mathematics at Princeton , you also studied at Princeton as an undergraduate." Shen Qi expressed his earnest hope to Ralph, as a mathematics tutor, the most important thing is to "guidance" rather than "indoctrination".

The third condition for promotion to Mathematics Level 14 is that Shen Qi is required to mentor a student. The student has made great progress under Shen Qi's guidance. The day when the student publishes a paper in the four major mathematics journals is the day when Shen Qi's condition three task is completed.

Shen Qi would naturally take action when it was time to do so, but if everything was done for Ralph, it would not be considered a guide, and the task could not be completed.

It was stressful... Ralph was sweating profusely.

In today's rapidly developing society, who is not under pressure?

There is pressure to be motivated.

Ralph Lai refused to leave Shen Qi's office. He broke the casserole and asked: "Then, Professor Shen, when studying the finite-dimensional modules of typical Lie super algebras, the baby Wilma module has a single u(g)-head. , my question is, in your conception and deduction sequence, how to get any irreducible u(g)-submodule is the homomorphic image of a certain baby Wilma module?"

"It's not difficult, it's like this, it's like this..." Shen Qi gave the opportunity face to face.

"So that's it, I understand." Ralph recorded the important information in a small notebook, and asked again: "Then, Professor Shen, the use of matrix elements is a basic algebraic tool, I don't think it's that simple, please tell me ..."

"It's not difficult, like this, like this..." Shen Qi remained patient enough to guide Ralph.

"Then Professor Shen..."

"Then Professor Shen..."

"Ralph, you can only ask a maximum of three questions in one day. Today's Q&A time is over, and the next one is entertainment time. Let's go and relax."

Shen Qi called Yu Lei, and the three teachers and students ran on the Princeton campus. This is the way Shen Qi taught the students to relax.

"Ralph, you're so bad, you'll be exhausted after running 10 kilometers!" Yu Lei yelled.

"There's a kind of sprinting with me." Ralph lay on the lawn panting like a cow.

"We'll talk about it after the sprint." Shen Qi said, "Today, there are still 10 kilometers left."

"You're too good at running, aren't you?" Ralph grabbed the grass tightly with both hands, refusing to get up, and he entered the mode of pretending to be dead.

"Yu Lei, let's continue for another 10 kilometers." Shen Qi summoned Yu Lei.

Yu Lei immediately fell on the lawn: "Actually, my advantage is also sprinting."

"You are too weak." Shen Qi walked away, continuing to run alone.

"Professor Shen has amazing physical strength and is full of energy. Apart from mathematics, he is also good at physics and long-distance running." Ralph was really convinced.

"He won the long-distance running championship when he was studying in China. By the way, Ralph, how is the progress of your project with Yale?" Yu Lei asked with concern.

"not so good."

"Still keeping it a secret from me?"

"It's just not good."

"Forget it, I don't care anyway." Yu Lei looked at Shen Qi who was drifting away. He and Ralph were both Shen Qi's first batch of graduate students, and he didn't want to lose to Ralph academically.

Shen Qi ran all the way to Carnegie Lake at the southernmost point, and turned west to the faculty dormitory.

The energy is indeed abundant, even excess, Shen Qi needs to release the excess energy and stamina, recently he has resumed running and exercising.

Shen Qi returned to the staff dormitory in Princeton, Ouye learned how to cook soup, and lived an ordinary and warm life.

In his ordinary and warm life, Shen Qi was very concerned about the physics paper that was submitted to PRL, which was his passion.

Shen Qi's passion point is Ouye's passion point, and Ouye's passion point will also keep Shen Qi excited.

The daily life of old couples needs some passion points to adjust and lubricate. Ouye's passion point is that she discovered the mystery of integer points of a kind of elliptic curve.

Elliptic curves have always been an interesting topic in number theory and related fields. When Wiles proved Fermat's last theorem, he actually proved Fermat's last theorem in a roundabout way by proving a class of results about elliptic curves. .

"That's amazing my Ye, you are following Wiles' success trajectory." Shen Qi was very happy to see that Ouye created something new by herself without relying on him at all.

While drinking soup tonight, Shen Qi just learned that Ouye had made research results on the integer points of elliptic curves.

Ouye shook his head: "It's not a result at all, what I just thought of yesterday is just an idea."

Shen Qi: "Then let this idea become a correct proposition. I won't provide you with too many professional opinions. I feel sick when I see number theory now. All I can do is call 666 for you. If you have any questions, find a tutor. Professor Linden Strauss will definitely give you more help."

"Well, what about you, has your physics paper been accepted by PRL?" Ouye asked.

"I don't believe it, I'm also waiting for news."

Shen Qi waited, waited, waited, waited, waited for several days, and finally got a piece of good news. PRL included his paper "Research on Defect Topology Based on Spherical Stable Hotopy Groups".

(End of this chapter)