"OK, I figured it out. ”

Shen Qi wrote on the blackboard:

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

......

"It's ...... An enhanced version of algebraic group modulus?" Ralph stood up suddenly, his eyes fixed on the blackboard.

"Yes, but not all. Shen Qi continued his deduction, and considering the modulo category, he did a linear mapping process to obtain a finite-dimensional orderedized algebra.

"I think there is a condition here that satisfies the law of reciprocity in the category of infinitesimal group representations, and ultimately gives the result of the irreducible representation of the superior Frobinius kernel. Let m≠n(modp), then St1 is the projective u(g)-mode, and therefore T(μ) is the projected u(g)-mode. Well, it's more of a lemma, and I need to prove it. Shen Qi turned back to Ralph and said, his eyes flashing with the wisdom of controlling everything.

"That'...... Please start your proof, Professor Shen. Ralph was shocked by Shen Qi's powerful aura.

"Wait a minute. Shen Qi walked to the bookcase and took out a literature to inquire.

Ralph: "......"

"Lie algebra, complex functions, group theory, their compendiums are engraved in my soul, but I can't remember all the details, so sometimes I need to look up some information. Shen Qi said, he smiled at Ralph: "You were thinking just now, it turns out that Shen Qi is also an ordinary person, he is not an omnipotent god. Yes, that's right, I'm not a god, I'm just more focused on my career than ordinary people, focus can be professional, and professional depth determines the height of my career. ”

"Professor Shen, what you said is so good. "Ralph was in awe, and secretly frightened, how can you gain insight into my inner workings?

After querying several conclusions in the Holmes-Shigeo Nakano method, Shen Qi made relevant proofs of the lemma on the blackboard.

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

Shen Qi knocked on the blackboard: "In the process of proofing, I used the Holmes-Shigeo Nakano method, the Bruoer model and Humphreys's theorem, all of which are existing theories, and I have not proposed any innovative inventions. Innovation is a very difficult thing, most of the time we do comprehensive application and theoretical remodeling, in a sense, comprehensive application is also a kind of innovation. ”

"Yes. Ralph nodded heavily, and he showed a cheerful expression: "The most important thing is the use of Weyl groups, where the point effect is still defined as ωv=ω(v+ρ)-ρ, so we get the dimension of its weight space is 1, that is, Q1(λ) is the projection coverage of the limitless g-modulus L1(λ)." ”

"Good. Shen Qi began to wipe the blackboard.

"Wait a minute, Professor Shen!" Ralph quickly pulled out his phone and wanted to take a picture.

"Don't shoot Ralph, there's no need. Shen Qi continued to wipe the blackboard, and quickly finished wiping the mathematical symbols of the blackboard: "It seems that you have not fully understood the comprehensive application I am talking about, its essence lies in the built-in logic rather than the external form, and the logic cannot be photographed." ”

"I ......," Ralph was ashamed.

Ralph is a classmate, down-to-earth and not playing false, but he is slightly lacking in understanding.

Yu Lei can speak well, and he seems to be a little impetuous, but his understanding is stronger than Ralph's, and his thinking is divergent.

After a long period of contact, Shen Qi became more and more familiar with the personality characteristics and academic strengths and weaknesses of the two students, extremely rigorous people may lack rich imagination, and people with unbridled thinking often cannot prove their conjectures or predictions put forward on a flash of inspiration.

No one is perfect, and teaching students according to 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'll give you some new hints, starting from another way, relying on commutative hyperalgebra, comprehensively using matrix elements, Frobenius morphism, baby Wilma mode, to complete the proof of the lemma just now." ”

"Pay attention to the order of the math tools I mentioned, if you were the first to use the baby Wilma model, you would be wasting your time. I may be a bit demanding of you, but I think it's necessary because you're a graduate student in mathematics at Princeton, and you studied at Princeton as an undergraduate. Shen Qi expressed his ardent hope to Ralph that as a math tutor, the most important thing is to "guide", not "irrigate".

Condition 3 for promotion to Mathematics Level 14 requires Shen Qi to supervise a student, the student has made great progress under Shen Qi's guidance, and the day the student publishes papers in the four major journals of mathematics is the end date of Shen Qi's condition 3 task.

Shen Qi will naturally make a move when he should make a move, but if he helps Ralph do everything, it will not be considered guidance, and the task cannot be completed.

It's so stressful...... Ralph was sweating.

In today's fast-paced society, who doesn't feel a little 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 mode of a typical Lie ultra algebra, the baby Wilma mold has a single u(g)-head, my question is, in your conception and deduction order, how to get that any irreducible u(g)-submodel is a homomorphism of a certain baby Wilma mode?"

"This is not difficult, so and so, and so and so ......" Shen Qi instructed in person.

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

"This is not difficult, this is so, this is so......" Shen Qi kept enough patience to guide Ralph.

"So Professor Shen ......"

"So Professor Shen ......"

"Ralph, you can only ask a maximum of three questions in a day, today's Q&A time is over, and then it's fun time, let's go, go relax. ”

Shen Qi called Yu Lei, and the three teachers and students ran around the Princeton campus, which was the relaxation method that Shen Qi taught the students.

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

"It's kind of a sprint compared to me. Ralph was lying on the lawn, panting like a cow.

"I'll talk about it later. Shen Qi said, "And today, there are still 10 kilometers left." ”

"You're too good at running, aren't you?" Ralph gripped the grass with both hands, refusing to get up, and he went into play dead mode.

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

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

"You're too weak. Shen Qi walked away and continued to run alone.

"Professor Shen is an amazing physical and energetic person, and in addition to mathematics, he is also good at physics and long-distance running. Ralph was 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 very good. ”

"Keep it a secret from me?"

"It's just not good. ”

"Don't say 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, the southernmost point, and turned west towards the faculty dormitory.

The energy is indeed abundant, even excessive, Shen Qi needs to release excess energy and physical strength, and he has resumed running exercise recently.

Shen Qi returned to the Princeton staff dormitory, Ou Ye learned to make soup, and lived a plain and warm life.

In his ordinary and warm life, Shen Qi cares about the physics paper he voted for PRL, which is his passion.

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

The daily life of the old husband and wife needs some passion points to adjust the lubrication, and Ouye's passion point is that she has discovered the integer point mystery of a kind of elliptical curve.

Elliptic curves have always been a subject of great interest in number theory and related fields, when Wiles proved Fermat's theorem, in fact he proved Fermat's theorem in a roundabout form by proving a class of results about elliptic curves.

"Awesome my Ye, you're following the trajectory of Wiles' success. Shen Qi was very happy to see that Ou Ye had come up with something new by herself without relying on him at all.

When he was drinking soup tonight, Shen Qi learned that Ou Ye had made research results in the integer points of elliptic curves.

Ou Ye 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 give you too many professional opinions, I want to vomit when I see number theory now, all I can do is shout 666 for you." If you have any questions and find a tutor, Professor Linden Strauss will definitely give you more help. ”

"Well, what about you, did PRL include your physics papers?" asked Oye.

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

Shen Qi waited for several days, and finally came to the good news, PRL included his paper "Research on Defect Topology Based on Spherical Stable Homotopy Groups".