Research starts with PhD students

Chapter 34 We are not in the same world at all!
Looking at the title, I'm skeptical.

After reading the content, I quickly became addicted.

Friedrich read the paper with the mindset of finding problems. He did not think there was any algorithm that could solve the second-order nonlinear partial differential equation.

Solving nonlinear partial differential equations is a difficult problem in mathematics.

Many important nonlinear partial differential equations are still struggling to prove the smoothness of their solutions, including the Monge-Ampere equation, the NS equation, the nonlinear Schrödinger wave function equation, and so on.

Since the properties of this type of equations have not been proven, how is it possible to directly calculate the results using computer means?
Even if we limit ourselves to elliptic partial differential equations, it is impossible!

When he actually started reading the first "Methodology", Friedrich forgot the idea of ​​finding problems. He found that the initial "Substitution Transformation Method" was very clever and could make the system of equations containing partial differential equations easy to understand.

For a single partial differential equation, the transformation method will make the equation more complicated, but from the perspective of computer algorithms, the analysis will be simpler.

"That part is fine, it's a very good study."

Friedrich made a comment and then looked at the parameter evaluation system in the second part, which is to simulate the calculation of the human brain with the parameters of the equation and get the result of substituting the numerical values.

He finished reading it quickly.

He did not give a high evaluation of this part. "If it involves applications, this part will determine the accuracy of the final calculation, but it is actually replaceable."

"The results obtained are not very accurate."

Friedrich shook his head and began to read the third part, which was the most core part - the determination of asymptotic solutions.

This part is also the most complicated, requiring examination of the logical issues involved, and is also related to the initial transformation method.

“If there was a problem, it should have been in this section.”

Friedrich felt that he had found the core point and began to try to understand the content, but after a long time, he felt that he was almost confused by the logic.

"Boom, boom."

There was a knock on the office door.

Assistant Marta came over with a cup of black tea and said with concern, "Mr. Yost, you have been working for three hours straight."

“It’s time to take a break.”

Marta said as she placed the tea on the table.

Friedrich pressed his forehead hard and sighed, "Maybe I'm getting old. I can't even understand a doctoral student's thesis."

He took a sip of the tea, then picked up the phone and dialed a number.

"Du~~~"

The call is connected.

A teasing voice came from the other side, "Old Yost, why did you think of calling me? Did you dream about God? Don't worry, I will definitely attend your funeral on time!"

"Even if you die, I won't die!"

Friedrich's face turned black with anger. He gritted his teeth and said, "Maxim, I don't have time to talk to you. I have a logic problem. I sent it to your email."

"Okay, okay, you're still so boring..."

Opposite him is the famous former Soviet mathematician, current president of Rutgers University, winner of the Kraft Medal, the Shaw Prize, and the Fields Medal, the famous Maxim Kontsevich.

……

Sudong City.

Zhang Shuo and Luo Yongjun jointly organized a celebration banquet for the project. Those who attended the banquet included Gao Xiaohong, Liu Chengjie, and two other professors who participated in the project.

One is Ye Shuyuan and the other is Tang Yongcheng, who is also a doctoral supervisor professor in the School of Mathematics.

Luo Yongjun shouted that he wanted a seafood feast, but in fact, he only ordered a king crab, and the rest were home-cooked dishes.

Although the dishes were not of such high quality, it was a free meal after all, and also a celebratory banquet for the project, so the atmosphere at the table was still very good.

Gao Xiaohong, Zhang Shuo and Liu Chengjie do not drink.

Luo Yongjun had a few drinks with the two professors, talked briefly about the project, and then changed the topic to talk about school matters.

Gao Xiaohong and Zhang Shuo sat next to each other. Gao Xiaohong started talking about graduation. “Have you considered writing a graduation thesis?”

Zhang Shuo pursed his lips in amusement, "Professor Zhao Chengbo also asked me this. Why are you all urging me to write my graduation thesis? I'm only in my first year of doctoral studies."

Gao Xiaohong smiled and said, "Because you are very young. You graduated with a PhD in mathematics at the age of 25. That's amazing!"

“Many doctoral students just started school at the age of 25.”

"Moreover, you have indeed reached the conditions to prepare a graduation thesis. You should have already written a paper in a top journal of mathematics and computer science. The only thing left is the graduation thesis."

Ye Shuyuan suddenly said, "Yes, Zhang Shuo, I think you can prepare your thesis now."

"In your case, you can stay in school directly after graduation."

"Staying on campus is different from being an external employee. Once the required years are up, you can be promoted to associate professor."

Others nodded.

Postdoctoral fellows signed by universities now all get promotion-or-leave contracts, and their contracts will not be renewed if they fail to meet scientific research requirements within the contract period.

It is different for PhD students who stay in school.

PhD students who stay on campus usually start as assistant professors and can be promoted as long as they produce normal results within the contract period.

This is also the unspoken rule of colleges and universities.

Externally hired professors are externally hired after all. They may leave after reaching the peak of their career, or choose to study abroad, or they may be poached by other universities.

PhD students who graduate from our school are our own people and always carry the school’s label, so their treatment is naturally relatively better.

Several professors chattered and urged Zhang Shuo to finish his thesis quickly.

Luo Yongjun was more anxious for Zhang Shuo to graduate than anyone else. "Hurry up and prepare your thesis. When you graduate, we will be colleagues."

"We can work on a project together." Luo Yongjun still took Sun Xingli's joke to heart.

Now that I can't find a direction for my research, I actually need Zhang Shuo to help me think about it? It feels weird. He really is like a student being guided by a mentor.

If Zhang Shuo graduates, they will be colleagues, and it is normal for colleagues to help each other with research.

Let’s do research together!
Zhang Shuo could only agree, "I'll think about it when I have time."

……

The celebration banquet is over.

Zhang Shuo and Liu Chengjie returned to the dormitory together.

The two of them entered Zhang Shuo's dormitory together. As soon as they entered the door, they heard Huang Kai couldn't wait to talk about how his mentor had found a clear direction.

"Teacher Ye gave me a nonlinear wave equation and asked me to study it carefully, either to solve the problem or to study the properties of the equation."

"This way I'll know what to do next!"

Huang Kai spoke excitedly, as if he had already achieved results and published an SCI paper.

This direction is very popular.

This is the case for many master's and doctoral students majoring in partial differential equations. The instructor will give the students a complex equation to study.

Finally, perhaps I could publish a paper titled "Study of the Existence and Properties of Solutions of a Certain Type of Partial Differential Equations."

Or it could be "Numerical Analysis of Solutions of a Certain Class of Nonlinear Partial Differential Equations".

Or, "A Special Solution of a Certain Class of Nonlinear Partial Differential Equations".

In short, they are very similar.

The "certain type" may be a fractional-order equation, an equation with a special operator, or a nonlinear equation of higher difficulty with certain application characteristics.

This type of research is insignificant, but if it is elevated to the study of the smoothness of equations, the difficulty will increase dozens or hundreds of times.

Liu Chengjie suddenly asked, "Huang Kai, what is your mentor's last name?"

"leaf."

"what is it call?"

"Ye Shuyuan, what's wrong?"

Liu Chengjie immediately smiled and said, "We also had dinner with your mentor today, a project celebration dinner," he said with a smug look on his face.

Huang Kai said disdainfully, "What does it have to do with you? That's Zhang Shuo's project."

He then looked at Zhang Shuo and sighed, "It feels like you and I are not on the same level. I worked so hard to curry favor with the instructor just to get him to give me more guidance, but you..."

"Ugh!"

Liu Chengjie also added, "Professor Ye also toasted Zhang Shuo and told him to take him with him if he has any big projects in the future..."

His tone no longer had the smugness in it, and instead he sighed along with Huang Kai.

Zhang Shuo shook his head indifferently, "They are all ordinary students. I was just a little luckier. I had a good idea when I went to the Institute of High Energy Physics, and then I got a project."

"we are the same."

This sentence seems to have some effect.

Huang Kai immediately put his arm around Zhang Shuo's shoulders excitedly, "Yes, we are good friends living in the same dormitory!"

He suddenly noticed a new email notification on his computer.

Zhang Shuo clicked on it and took a quick look, and found that it was a notice written entirely in English, with the first line labeled "Journal-Of-High-Energy-Physics".

"Is this an email from an academic journal? What is JOHEP?"

Huang Kai asked, pointing at the email.

"JHEP! No O! Journal of High Energy Physics, CERN's academic journal of physics."

Liu Chengjie knew more information. He asked Zhang Shuo, "JHEP sent you an email. Did they confirm the publication date?"

Zhang Shuo nodded, "It says it's the third of next month."

"congratulation!"

Liu Chengjie's words were full of envy, "I can publish in a top journal in my first year of PhD. I will be satisfied if I can publish an ordinary SCI journal next year."

Huang Kai continued to sigh, "We are good friends in the same dormitory, but we are still not in the same world!"

"Ugh!"

"Ah~~"

Zhang Shuo not only received an email from JHEP confirming the publication date, but also received an email from the editorial department of Advances in Mathematics.

He saw the email the next morning.

The editorial department of New Advances in Mathematics confirmed that his paper had passed the initial review.

At the same time, he sent a message saying that the special reviewer Mr. Friedrich Jost wanted to talk to him about the paper, and attached a private email address.

Zhang Shuo sent an email with doubt, "Hello, Mr. Yost. I am Zhang Shuo from Soochow University, the author of the general algorithm for elliptic partial differential equations."

"I am honored that my paper has been reviewed by you!"

"The editorial department of New Advances in Mathematics told me that you wanted to discuss the paper with me?"

Zhang Shuo's message was very polite.

In fact, he had no idea who Friedrich Jost was.

(End of this chapter)