"Pang, the great bulls in the field of fluid mechanics should be very happy if they know that you are going to study the NS equation!"

Tao Zhexuan said with a smile.

The crowd laughed.

Today, in the academic world, Professor Pang is a golden signboard.

Wherever he is interested, there will certainly be rapid development in any field.

Needless to say, there are many conjectures in the field of mathematics.

In the field of carbon nanomaterials, electronic-grade purity carbon nanotubes, super-large graphene materials, ultra-high-strength flying blade materials, etc., have all proved Pang Xuelin's ability.

Not to mention the world-changing lithium-air battery.

The emergence of this kind of battery has directly changed the global energy pattern and industrial pattern.

Even the old American commander, who has always liked to talk about the river and not take the usual path, was forced to bow his head by this cross-era product.

And academia, not to mention.

At present, all major countries in the world have increased their investment in carbon nanomaterials and lithium-air batteries in an attempt to break China's monopoly position.

As a result, scholars in electrochemistry and carbon nanomaterials in various countries around the world are comfortable.

In the past few years, they have received as much research funding as the past ten years combined.

Even in China, due to the siphon effect caused by Pang Xuelin, domestic scientific research funds have converged to the Qiantang Laboratory, and the country's top scholars in electrochemistry and carbon nanomaterials have also gathered in a steady stream.

This is also the reason why Li Changqing and Cao Yuan's team will complete superconducting 128 in such a short time.

Now, Pang Xuelin has turned his attention to the NS equation, once a breakthrough is made, the future human breakthroughs in fluid mechanics, aerodynamics, plasma dynamics and other applications will be enough to make scholars in these fields eat a lot of money.

Pang Xuelin couldn't help crying and laughing: "I just made a temporary idea, but I didn't think about it so much." ”

The crowd chatted until ten o'clock in the evening, and then they dispersed.

Early the next morning, Pang Xuelin still came to Jiang University to sit on duty.

The work of the Qiantang laboratory has been on the right track, and this semester, Pang Xuelin began to have time to focus part of his energy on teaching.

Especially his students.

encountered such an unreliable boss, in the past few semesters, basically except for the beginning and end of the semester, most of the time can only contact Pang Xuelin by email.

Ai Ai and Meng Yao are okay, Ai Ai is more able to make trouble, and often contacts Pang Xuelin through WeChat from time to time.

In addition, this year, a paper studying the relationship between Ponzi geometry and algebraic topology was published in the Journal of the American Mathematical Society, and he was invited to give a 45-minute report by the International Congress of Mathematicians.

Ai Ai no longer needs Pang Xuelin to worry about it, this girl is now a rising star in the international mathematical community.

Her thesis at the level of the Big Four journals is fully qualified as her doctoral dissertation.

Meng Yao was abandoned by Pang Xuelin under Li Changqing, and was inexplicably pulled into the superconducting 128 project.

By the time the project is completed and published, Meng Yao will almost be able to complete his graduation thesis.

At that time, Pang Xuelin's identity as a student, coupled with the experience of the superconductivity 128 project, Meng Yao can get the title of associate professor or above in any school he goes.

However, Meng Yao didn't care about this, he had already made it clear to Pang Xuelin, and after graduation, he joined the Qiantang Laboratory and became an official researcher of the Qiantang Laboratory.

With his academic level, he is fully capable of being independent in the future.

The remaining three, a Frenchman David Harque, another German girl, Sophie Heyman, and the last one is Tomoko.

Zhizi is now working in the Golden Dragon Group, and he is busy every day, especially in the past month, Zhizi is stationed in the United States to negotiate with the United States on matters related to the Golden Dragon battery factory.

Pang Xuelin hasn't seen her since he returned from China's Sun World.

Even in the eyes of several other students of Pang Xuelin, Zhizi has long been regarded as Pang Xuelin's student.

As for David Halker and Sophie Heyman, their performance in the past year can only be regarded as mediocre, although they have successfully completed the tasks assigned by Pang Xuelin, but they have not achieved anything in the academic field like Ai Ai and Meng Yao.

However, it's not that they can't do it, it's that they haven't somehow acquired it in the last year, and they've become obsessed with differential geometry.

Moreover, he tried to use the ideas of Ponzi geometry to solve some problems in differential geometry.

It's a novel idea, but if you want to make a difference, you'll have to toss it for a few more years.

However, Pang Xuelin naturally wouldn't let them drag on like this, and today he called his disciples over just to talk about the next graduation.

"Ai Ai, Halke, Sophie, Meng Yao, you have been studying under me for two years, and this year is the third year, I have no idea of delaying your graduation, so in the next year, you have to focus on your graduation thesis."

In the office, Ai Ai, Halke, Sophie, and Meng Yao all stood at Pang Xuelin's desk.

"Teacher, can we choose the topic of the dissertation?"

Halk wondered.

Pang Xuelin smiled slightly, and said: "Ai Ai and Meng Yao can choose their own topics, I will not interfere with the research of the two of you, give you the greatest freedom, if you have any questions at that time, just come to me directly." As for Halk and Sophie......"

Pang Xuelin paused, took out two pieces of white paper full of words from the desk, handed them to the two of them, and said, "This is your topic for the next year, and you can solve this topic cooperatively or independently." As long as you can successfully complete this project within one year, I will allow you to graduate. ”

Halque took the note and read it.

Immediately afterward, Sophie's brow furrowed.

One of the core problems of global differential geometry is the study of the relationship between local and global invariants, and the relationship between curvature and topology.

Let's look at the surface S, which has a measure on it, and also has the Gaussian curvature K, and if the surface is compact and boundless, the Gaussian curvature K can be integrated on the entire surface.

A surface does not necessarily have only one measure, there can be another measure, after changing the measure, the corresponding Gaussian curvature K will also change, but the integral value has nothing to do with the measurement of the surface, but only related to the Euler schematic number χ(S) of the surface. This is the profound meaning of the Gauss-Bonnet formula.

For the high-dimensional Riemannian manifold M, the Gaussian curvature can be generalized as the cross-sectional curvature, which is determined by the Riemannian curvature tensor, and the integrand is a very complex algebraic formula composed of the curvature tensor, called the Gauss-Bonnet integrand, which is integral to the entire manifold and should be determined by the Euler schematic number χ(M) of the manifold.

Its connotation was proved to be obtained by Chern, which came to be known as the Gauss–Bonnet–Chen formula, which is a measure of the tight, boundless even-dimensional manifold......

……

David Harker looked at it for a long time, then raised his head and said to Pang Xuelin: "Professor Pang, do you want us to prove the Hopf conjecture?" ”

Sophie on the side couldn't help but look up and looked at Pang Xuelin curiously.