Who Was More Enchanting?
"Yu Lei, overall, your academic performance during this period has been satisfactory."
Shen Qi acknowledged Yu Lei's recent efforts; in this project in collaboration with Victoria University, Yu Lei had exhausted all his intelligence and mathematical talent.
In fact, Shen Qi did not provide Yu Lei with much detailed guidance on this topic of Function Theory; he only provided a framework and indicated the direction.
Yu Lei does have a foundation in mathematics, after all, he was once a member of the Olympic Math national team, which is one of the top 6 in China, and he received his training in the Mathematics Department of Shuimu University.
Yu Lei was on a business trip to Canada, he incurred some romantic entanglements. The reason the local powerful Guy family didn't break Yu Lei's leg was threefold: first, to give face to Shen Qi; second, because offending Princeton was risky; and third, Yu Lei had indeed made certain contributions to the project.
At this point, Shen Qi needed to provide Yu Lei with more detailed guidance to help Yu Lei develop quickly. He pointed out a flaw in the data. "Yu Lei, you cannot easily assert here that F1 does not have a subsequence at the point z=0. You lack a flawless and rigorous argument. I am not completely negating your current argument, but I hope you can do better."
"I'm all ears." Yu Lei immediately became serious and focused, entering a state of complete academic concentration.
Shen Qi casually picked up a piece of white paper and wrote as he spoke, "If there exists a subsequence of F1 such that {Fn} is normal at point 0, then there must be a positive number M1 such that |Fn(z)|≥M1 for all z∈△δ... I did a simple deduction, and here g is a very large meromorphic function."
Shen Qi turned the white paper 180 degrees so that Yu Lei could see the formula on it.
Yu Lei's eyes lit up; he had discovered something even more exciting than a pretty girl. "Your simple derivation of gn(ζ) = Fn(zn + ρnζ)/ρn, which bypasses Monteil's theorem and deviates from the Julia direction, is even more captivating."
French mathematician Julliard, building on the theories of his compatriot Montaire, proposed the Julia direction. For transintegral or transmeromorphic functions, the Julia direction is a half-ray J = {z|arg z = θ0} originating from the origin in the complex plane C, which has the following properties. This is an important theoretical basis in Function Theory.
Shen Qi scribbled a couple of lines on the draft paper and came up with a new idea: if we don't rely on the Julia direction, is it possible to obtain a normal family of holomorphic functions?
"This is Shen Qi direction that he just casually came up with..." Yu Lei had been following Shen Qi for nearly a year and finally learned some real skills from him. "The Shen School is indeed profound and extensive. Little Brother Qi can throw out some valuable insights so easily, and they are incredibly impressive!"
"Hmm, you're getting into it, very good, keep it up." Shen Qi was satisfied with Yu Lei's reaction. He asked, "Mathematics or girls, which is more charming?"
"Is there even a question?" Yu Lei answered matter-of-factly, giving his answer without hesitation, "Of course, the girl is more charming!"
Shen Qi: "So I wasted my breath?"
Yu Lei: "Mathematics cannot be described as 'charming,' it's like a drug, a poison! I can remain sober in front of girls, but I find it hard to quit my addiction to mathematics."
"You've spoken so sincerely, you've moved me," Shen Qi said with a smile. He then shared his understanding of Function Theory with Yu Lei, as well as his views on the future research directions for this topic.
Under Shen Qi's guidance, Yu Lei benefited greatly and became more confident in his academic pursuits.
On another front, Shen Qi's other student Ralph, made steady progress.
Ralph was a calm and steady man who had never caused Shen Qi any trouble. He didn't drink, smoke, get his hair permed, or flirt with women; such an honest and upright young American man was a rare find.
Shen Qi often advised Yu Lei spend less time chasing girls and more time reading books.
Shen Qi's attitude towards Ralph, who only studies and doesn't pursue women, was completely different. "Ralph, you need a girl. You can try dating a girlfriend."
It depends on the person. Not maintaining normal interactions with the opposite sex for a long time is not necessarily a good thing.
Ralph said, "I actually had a brief relationship with a girlfriend, but we broke up in less than a week."
Shen Qi asked, "Why?"
"Because of my religious beliefs, I refuse premarital sex." Ralph, a religious and patriotic young American, quickly shifted the topic to Lie Algebra, which was part of his research project. "Professor Shen, regarding the results on the Irreducible Representation Frobenius Kernel representation of supergroups, the Yale members in the team have their own opinions, and we have some disagreements, so the project progress has been temporarily suspended."
"Details, I need more details." It's Shen Qi's responsibility to solve problems for students.
Ralph handed Shen Qi two documents, one representing his ideas and the other from Yale, on the project "Research on Linear Lie Algebra and Their Supergroups," which was jointly promoted by Princeton and Yale.
Shen Qi flipped through the documents, his brow furrowing slightly. He said, "Ralph, this is a bit tricky. Have some coffee and give me some time to analyze it."
"Okay." Ralph saw Shen Qi with this expression for the first time and couldn't help feeling a little nervous.
It seems he is only human, not an omnipotent god... Ralph sat on the sofa drinking coffee, looking at the portraits of the four great mathematicians Gauss, Euler, Newton, and Archimedes hanging on the wall, and thought to himself, they are not gods either, they are people who are close to gods.
Shen Qi walked to the blackboard, pondered for a moment, and then began to work out the problem with the chalk.
The classical theory of reduced Lie Algebra states that every irreducible modulus projection cover has a Z-filter.
Following Lie, prominent algebraists included Brauer, Humphreys, Holmes, and Nakano Shigeo, who successively refined Lie Algebra and Lie theory.
Last year, Australian mathematician Williamson, who shared the Fields Medal with Shen Qi, made new contributions in this field.
The most famous and authoritative algebra master in contemporary China is Academician Xi Ruihua, who has achieved world-class status in the subfield of algebraic groups and quantum groups.
The joint Princeton and Yale project, "Research on Linear Lie Algebra and Their Supergroups," is certainly not a superficial or perfunctory work; its academic value is extremely high.
Shen Qi discovered through the materials submitted by Ralph that Ralph was being pressured relentlessly by Yale, Ralph was stuck in a dead end regarding the superior results of the Irreducible Representation of the Frobenius Kernel.
Ralph struggles with the Reciprocity Law of the Brauer type, but he lacks Humphreys's rigorous, almost obsessive, logical reasoning ability, Holmes and Nakano Shigeo imagination and creativity, and Williamson and Academician Schiele's all-seeing perception.
The Lie Algebra project has progressed beyond the scope of academic argumentation previously defined by Shen Qi. Ralph is out of his depth and his mentor, Shen Qi, must personally step in to point Ralph in a new direction.