Scholar's Advanced Technological System - Teasing Personality

He got back to his hotel and checked his email. He received an email from the Philadelphia branch of Star Sky Technology.
    

The content of the email was very concise. It contained a list, and on the list, there were Chinese companies that had signed patent licensing agreements with Star Sky Technology. Among them were giant lithium material companies, and also investment companies and universities.
    

It came as no surprise that Zhongshan New Materials, the company that Professor Li had shares in, was also on the list.
    

If Lu Zhou had to carry out these negotiations by himself, he would be busy for the next two months.
    

[I have sent a copy of the relevant documents to your office at Princeton Institute for Advanced Study. If you think there are no problems, please sign the documents and return it to Philadelphia.
    

Best regards, White Sheridan.]
    

Lu Zhou replied to the email.
    

[I will return to Princeton in the near future. I will sign the documents as soon as possible.]
    

Lu Zhou clicked “Send” and threw his phone on the bed. He then got up and went to take a shower.
    

After his shower, he lay in bed and was about to take an afternoon nap. However, his nap was interrupted by a notification.
    

[Professor, when will you come back?]
    

The email was from Vera.
    

Lu Zhou remembered that he had been away for a long time and felt a little apologetic.
    

Although he planned to let his students take on the Collatz conjecture by themselves, he also agreed to give them advice and methods. He hadn’t been back for an entire month, and he had left the little girl alone.
    

Lu Zhou typed a few words on his screen and replied to the email.
    

[Soon, in a few days.]
    

Lu Zhou had already arranged for all of the necessary research work, so there was no reason for him to stay at the research institute. He could easily communicate from Princeton using the Internet.
    

Vera lay in bed and looked at the email on the screen. She finally sighed in relief.
    

Over the past few days, she had been worrying about Lu Zhou quitting his job as a Princeton professor to go back to China to teach.
    

But now, it seemed that her worries were superfluous.
    

The anxiety in Vera’s heart disappeared, and she gradually smiled.
    

A long time ago, when she was Ukraine, her peers viewed her as a strange child. No one could understand her strange math symbols.
    

The time she spent at Princeton was the best time of her life.
    

At Princeton, she could focus on any mathematics problem she wanted. She could devote her full attention to deep mathematical proofs.
    

She felt like time flew by when she was discussing mathematics problems with Lu Zhou. She had never felt this way before.
    

Not only that, but she had never received genuine care from a professor before. There weren’t any Berkeley professors that cared about her family difficulties or offered her a teaching assistant job.
    

Hardy always complained that Professor Lu was too demanding and gave him too much academic pressure. However, Vera had never experienced this kind of concern, so she quite enjoyed it.
    

On the other hand, she had mixed emotions.
    

Suddenly, another email notification popped up on her screen.
    

[How is the conjecture going? Is there any progress?]
    

Vera shook her head and got rid of her strange thoughts. She typed a reply on her screen.
    

[Not yet, but I recently discovered a new idea when I was reading a paper by Professor S. Eliahou. I have told Qin Yue and Hardy about this idea. This idea may become the key to solving the problem between the set of normal points z0 and transcend the whole function g(x).]
    

The Collatz conjecture was equivalent to the function equation h(z^3)=h(z^6)+{h(z^2)+λh(λz^2)+λ^2h(λ^2z^2)}/3z] (where λ=e^{2πi/3}) and the analytic function solution in the unit disc {z:|z|

This conclusion was proved by Professor Benguez and Professor Minardus in 1994. The follow-up study on the Collatz conjecture had been based on this foundation.
    

In Lu Zhou’s research framework that he developed for his students, he let g(z) be the transcendental function, z0 be a point in the complex plane, and Φ(g) be the set of normal points of g(z).
    

If someone could prove that the function column {g(z)}∞k=1 existed and that sub-column locally converged to ∞ or some analytic function in a neighborhood of the point z0, then the normal point where z0 is g(z) could be obtained.
    

In theory, these problems could be solved using the Group Structure Method. Its difficulty wasn’t much higher than Polignac’s conjecture.
    

Lu Zhou raised his eyebrows and looked interested.
    

[What idea?]
    

[It’s about…]
    

Vera stopped typing.
    

Perhaps it was because of her teasing personality, but she quietly deleted the sentence and wrote a new line.
    

[I want to tell you after you get back.]
    

When Lu Zhou read this message on the other side of the planet, he smiled and shook his head.
    

This chick is leaving me hanging.
    

However, she has been bad at expressing her thoughts, so I guess this is a small improvement.
    

After all, being extroverted means that you have to present yourself whether it is an academic point of view or a personal point of view. She has always been afraid of this.
    

Lu Zhou might consider introducing the Ivy Club to her.
    

The food there was delicious, but it had a high barrier of entry. Only well-known scholars or scholars that could debate with others could get in.
    

Right now, only Hardy earned the right to eat there. Lu Zhou took out US$5,000 from the Collatz conjecture fund to pay for his yearly membership fee.
    

Qin Yue was still working on his social skills.
    

As for Vera, she was still a long way from debating with the other scholars.
    

Lu Zhou wrote an email and hit “Reply”.
    

[Then tell me when I come back. I look forward to coming back to Princeton.]
    

Vera read this email and sighed. She was disappointed that Lu Zhou didn’t respond to her teasing.
    

She thought that Lu Zhou would react strongly to her flirtations.
    

But now it seemed that she had thought too much about it.
    

Vera sat on her bed and sighed before she buried her face in her knees.
    

After a long time, she crawled under the blanket and went to sleep.