Omnipotent Data

Chapter 454

"Superholomorphic Theory on Kaehler Manifolds and Clifford Analysis"

This is the name of Cheng Nuo's graduation thesis.

In the past six months, the geometry of complex manifolds has once again become one of the hot research directions.

The object of Cheng Nuo's graduation thesis, Kaehler manifold, is a complex manifold with a Riemann metric that is constant under the action of a typical complex structure.

The typical complex structure of Kaehler manifold is parallel again under the corresponding Riemann connection. Therefore, the Kaehler manifold is a special kind of Riemannian manifold, with richer geometric structures, and thus more colorful geometric properties.

Moreover, Kaehler manifolds can also be studied from the perspective of algebraic geometry. In addition, the geometric structure of Kaehler manifolds can be explained by differential geometry.

In general, the Kaehler manifold is a research object covering almost all branches of geometry.

This is also an important reason why Cheng Nuo determined the Kaehler manifold as the subject of his graduation thesis.

…………

Outside the world, news about Cheng Nuo's proof of Jacobi's conjecture continues to ferment.

The conjecture prover who is only 21 years old makes him almost attracted the attention of major mathematics universities in the world.

The 21-year-old guys in their school have just graduated from undergraduates.

And Cheng Nuo, at the same age, had already proved the Jacobian Conjecture, one of the several major mathematical conjectures in geometry.

This makes the major universities feel ashamed.

They thought that Cheng Nuo, the young man, had been silent for half a year, but now he finally made a big move that would make a high-profile announcement.

As a result...no.

Except for the news of Cheng Nuo's return to MIT, nearly a month has passed, and Cheng Nuo seems to have evaporated from the world, and it is difficult to find his trace.

"call--!"

MIT Library, a location near the window.

The warm sunshine happened to be shining on Cheng Nuo, he stretched his waist greatly, and watched with satisfaction the results of his month of hard work.

【Massachusetts Institute of Technology

Master Thesis

Superholomorphic theory and Clifford analysis on Kaehler manifold

Name: Cheng Nuo

Major: Basic Mathematics

Instructor: Fresnel-Doyle

Abstract: The theory of functions of multiple complex variables and the theory of single-complex variables are essentially different. For example, there is the famous Hartogs phenomenon in multiple complex variables, but not in single-complex variables; the famous basic theorem of Riemarm mapping is in multiple complex variables No longer established in...]

Cheng Nuo checked his graduation thesis from beginning to end again, simplified several deduction processes, and then sent the 32-page graduation thesis to Professor Fresnel.

Cheng Nuo: "Professor, I have finished writing my graduation thesis."

Professor Fresnel: "Well, let me make arrangements. I will inform you of the time for graduation defense later."

More than half an hour later, Professor Fresnel sent a message to Cheng Nuo.

Professor Fresnel, "Next Wednesday at ten o'clock in the morning, the lecture hall on the first floor of the School will conduct a graduation defense. Don't be late."

Cheng Nuo: "I know, I will be there on time."

…………

Regarding graduation defense, Cheng Nuo didn't need to do much preparation.

In fact, for MIT, Cheng Nuo's graduation defense is just a process.

If a ruthless man who even proved Jacobi's conjecture can't even pass the graduation defense, people from outside may have some conspiracy theory about MIT.

Wednesday, a very ordinary day.

Cheng Nuo put on a suit and arrived at the lecture hall on time before the start of the defense.

This graduation defense was specially prepared for Cheng Nuo alone.

It is October, not the graduation season in June.

Therefore, the four teachers in the defense group all serve Cheng Nuo.

This is not a precedent.

But this kind of guy who forced the school to graduate, on average, can't get two or three in ten years.

Of the four members of the defense group, the group leader is naturally Professor Fresnel. The other three are all professors of school geometry.

Although they only walked through the process, the four did not intend to relax the process promise.

Especially the three professors in the geometry world are constantly frantically testing the strength of the strongest newcomer in the geometry world.

During the questioning session, Cheng Nuo had no time to rest at all, and kept accepting questions from these three professors one after another.

"Student Cheng Nuo, in the eleventh page of the paper, in the superholomorphic D-problem on Kaehler manifolds, you use the matrix differential form to define the superholomorphic Cauchy-Riemann operator. What is the purpose?"

"First of all, the elements of the matrix include not only the differential form, but also the so-called contraction operator. Suppose there are two strictly increasing multivariates in {1..., n), which are r-multiples j=(j1, ......, jr) and......"

"In complex Clifford algebra, besides the complex algebra that uses the multiplication rule mentioned in your thesis, is there any other way to put the complex algebra generated by the complex differential form and the complex algebra generated by the operator dz into For the same algebra?"

"This..." Cheng Nuo touched his chin and thought for a few seconds, "This is there."

"The formula can be used, e^2=-1=一e0, k∈{1,...,2n}, ekeq+eqek=0, k≠q,..."

…………

In the half-hour question session originally planned, Cheng Nuo and the three professors directly asked each other and answered each other for nearly an hour.

Cheng Nuo said that his mouth was dry and he almost never stopped.

Fortunately, the three professors who found that it was impossible to ask Cheng Nuo ~www.readwn.com~ stopped making trouble for Cheng Nuo and ended this session.

ten minutes later……

Professor Fresnel delivered the graduation certificate and degree certificate that had been stamped in advance to Cheng Nuo. "Cheng Nuo, on behalf of the Massachusetts Institute of Technology, I officially grant you a PhD in Science!"

Doctor of Science!

This is the highest degree of MIT's science major, and it is out of reach of thousands of students who have struggled for years.

And Cheng Nuo, after studying at MIT for a year, easily got his doctorate.

Is a doctor of science, not a master of science.

Cheng Nuo was a little surprised.

He skipped the PhD stage and got his PhD.

Professor Fresnel took the Medal of Doctor of Science, put it on Cheng Nuo's neck, and patted the still-stupefied shoulder, "This is what you deserve."

"Without mentioning your previous achievements, your graduation thesis alone, in terms of academic level, has already exceeded the qualifications for PhD graduation!"

"I have contacted an editor in chief of "American Mathematical Notation" and your graduation thesis will be published in the next issue of the journal."

"US Mathematical Symbols", although the status in the US mathematics circle is not as good as the "Annual Journal of Mathematics", it is no problem to rank second, and it is also one of the top journals.

The next day, Cheng Nuo was wearing academic uniform and took a graduation photo of himself alone in front of the library.

Throwing the doctor's hat high into the sky, watching its free fall quickly fall.

Cheng Nuo suddenly realized that his school days were over!

………………

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