Omnipotent Data

Chapter 454

"Hyperholomorphic Theory and Clifford Analysis on Kaehler Manifolds"

This was 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 research object of Cheng Nuo's graduation thesis - Kaehler manifold, is a complex manifold with a Riemannian metric that is invariant under the action of a typical complex structure.

The typical complex structures of Kaehler manifolds are parallel under the corresponding Riemannian connections. Therefore, the Kaehler manifold is a special kind of Riemannian manifold, which has a richer geometric structure 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 means of differential geometry.

In general, Kaehler manifold is a research object that covers almost all branches of geometry.

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

…………

From the outside world, news about Cheng Nuo's proof of Jacobi's conjecture was still spreading.

The 21-year-old conjecture prover has almost attracted the attention of major mathematics universities in the world.

The group of 21-year-old guys at their school just graduated from undergraduate.

And Cheng Nuo, at the same age, had already proved the Jacobi conjecture, one of the most important mathematical conjectures in geometry.

This makes the major universities feel ashamed.

They thought Cheng Nuo, a young man who had been silent for half a year, would finally make a big move and publicize it in a high-profile manner.

It turned out... not at all.

Except for the news that Cheng Nuo had returned to MIT, almost a month had passed, and Cheng Nuo seemed to have disappeared from the world, and it was difficult to find his trace.

"call--!"

MIT Library, a location near a window.

The warm sunshine happened to shine on Cheng Nuo, he stretched his waist, and looked at the results of his one-month hard work with satisfaction.

[Massachusetts Institute of Technology

Master Thesis

Hyperholomorphic Theory and Clifford Analysis on Kaehler Manifolds

Name: Cheng Nuo

Major: Basic Mathematics

Instructor: Fresnel Doyle

Abstract: There are many differences between the theory of multiple complex variables and the theory of single complex variables in essence. For example, there is the famous Hartogs phenomenon in multiple complex variables, but not in single complex variables; No longer established in...]

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

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

Professor Fresnel: "Well, let me make an arrangement, and I will inform you of the graduation defense time 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, there will be a graduation defense in the auditorium on the first floor of the School of Mathematics. Don't be late."

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

…………

Regarding the graduation defense, Cheng Nuo didn't need to make too much preparation.

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

If a ruthless person who can even prove Jacobi's conjecture can't even pass the graduation defense, the outsiders may have some conspiracy theories about MIT.

Wednesday, a very ordinary day.

Cheng Nuo changed into a suit and arrived at the auditorium on time before the defense began.

This graduation defense was specially prepared for Cheng Nuo alone.

It's October, not June graduation season.

Therefore, the teachers of the four defense teams all served Cheng Nuo alone.

This is not precedent.

But this kind of guy who forced the school to graduate,

On average, there are no more than two or three in ten years.

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

Although they just went through the process, the four of them did not intend to let the process go easily.

Especially those three professors in the geometry field, they are constantly frantically testing the strength of this newcomer who is known as the strongest in the geometry field.

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

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

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

"In the complex Clifford algebra, besides the complex algebra using the rule of chance mentioned in your dissertation, is there any other way to make the complex algebra generated by the complex differential form and the complex algebra generated by the operator dz be subsumed into for the same algebra?"

"This..." Cheng Nuo stroked his chin and thought for a few seconds, "There is this."

"You can use the formula, e^2=-1=one e0, k∈{1,...,2n}, ekeq+eqek=0, k≠q,..."

…………

Originally planned for a half-hour questioning session, Cheng Nuo and the three professors directly asked and answered each other for nearly an hour.

Cheng Nuo's mouth was dry as he spoke, and he hardly stopped talking.

Fortunately, the three professors who found it really impossible to ask Cheng Nuo, stopped making things difficult for Cheng Nuo, and ended this session.

ten minutes later……

Professor Fresnel sent the stamped graduation certificate and degree certificate to Cheng Nuo. "Student Cheng Nuo, on behalf of the Massachusetts Institute of Technology, I officially confer on you a Doctor of Science degree!"

Doctor of Science!

This is the highest degree in the science majors of the Massachusetts Institute of Technology, and it is out of reach for thousands of students who have struggled for several years.

And Cheng Nuo, after studying at MIT for a year, easily obtained a Ph.D.

It's a PhD, not a MS.

Cheng Nuo was a little surprised.

He skipped the doctorate stage directly and got a doctorate.

Professor Fresnel took the medal of Doctor of Science, put it on Cheng Nuo's neck, patted the still dazed shoulder, "You deserve it."

"Not to mention your previous achievements, just your graduation thesis, in terms of academic level, has already exceeded the requirements for doctoral graduation!"

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

Although "American Mathematical Symbols" is not as prestigious as "Annual Mathematics" in the American mathematics community, it is no problem to rank second, and it is also one of the top journals.

The next day, Cheng Nuo wore his academic gown and took a graduation photo of himself in front of the library.

Throw the doctor's hat high into the sky, and watch its free fall fall rapidly.

Cheng Nuo suddenly realized that his school days were over!

………………

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