Volume 1: Student Life Chapter 440: Encounter by Chance
Professor Ating took the "homework" handed to him by Chen Zhou, but did not look at it directly.
This research summary feels heavy in my hand.
At least it should be several dozen pages.
It would take at least several hours to finish watching the whole thing.
Therefore, Professor Ating did not intend to waste Chen Zhou's time.
Just wait until he finishes reading it, and then communicate with Chen Zhou.
In addition, the reason why Chen Zhou was asked to write such a research summary.
The main purpose is to understand the specific depth of Chen Zhou's research so as to arrange future research topics for Chen Zhou.
Putting the "homework" on the desk, Professor Atin patted it twice with his hands and said, "I'll look at the homework later. Let me ask you a question first."
Chen Zhou looked at Professor Ating and said, "Professor, please ask."
Professor Artin: "Tell me about your current views on non-commutative algebra and non-commutative algebraic geometry."
Chen Zhou was silent for a while before he said slowly, "From a mathematical point of view, the transition from commutative algebra to non-commutative algebra is similar to the transition from classical mechanics to quantum mechanics in physics..."
"Now, with the vigorous development of the field of non-commutative geometry, many classical mathematical theories have found appropriate correspondences in non-commutative geometry."
"For example, the K-theory of rings is similar to the K-theory of C* algebras, the de Rham homology theory of smooth manifolds is similar to the cyclic cohomology theory of C* algebras, and so on..."
"In addition, the K group of AF algebra, the Morita equivalence of rings and C* algebras, cyclic cohomology and Cones' long exact series all have certain applications on non-commutative torus surfaces..."
What was different from the first time was that this time, when faced with Professor Ating’s question, Chen Zhou chose to answer.
Moreover, the questions Professor Ating asked this time were completely different from the first ones, and were also milder than the first ones.
Non-commutative algebra includes non-commutative rings.
Just like commutative algebra is an algebraic tool for algebraic geometry.
Non-commutative algebra, that is, the tools of non-commutative algebraic geometry.
Non-commutative algebraic geometry refers to treating the invariants as space itself and then studying geometry.
Therefore, the question Professor Ating asked today was the opposite of the one he asked the first time and the one that Chen Zhou submitted today.
This is also the reason why Chen Zhou feels that the problem is completely different from the first time.
As for why it is milder than the first problem, it is because non-commutative algebra and non-commutative algebraic geometry have both gone through a long period of development.
In addition, Chen Zhou also has certain insights into the interaction and mutual influence between non-commutative geometry and classical geometry.
Whatever is a geometric property on commutative objects, leads to an algebraic property on non-commutative objects.
Or the algebraic properties on non-commutative objects can predict the geometric properties on commutative objects.
Chen Zhou has done some research on this.
This research did not start after I came to MIT.
Of course, in front of Professor Ating, Chen Zhou still felt like he was showing off his skills.
However, this feeling just reminded Chen Zhou.
He still has many shortcomings.
In addition, it is not a bad thing to expose one's own shortcomings in front of Professor Atin.
Chen Zhou also believes that he can get some help through communication with Professor Ating.
After all, this is an important part of learning research and the importance of a mentor.
Therefore, Chen Zhou's tone was extremely steady when he was narrating.
When Chen Zhou finished speaking, Professor Ating nodded slowly, and then praised: "Not bad, it seems that there is some reason why you didn't come to see me for such a long time."
Hearing this, Chen Zhou was stunned for a moment, but soon smiled and said, "Professor, then don't blame me for taking up your time in the future?"
Professor Ating smiled and said, "No, what teacher is afraid of students asking questions? Unless you ask a question that I can't answer."
After a pause, Professor Ating pointed to the research summary submitted by Chen Zhou and said, "After I read it, I will send you a feedback email. In addition, I will give you a suitable sub-topic to work on."
Chen Zhou hesitated for a moment, but still said, "Okay, Professor."
Professor Ating also noticed Chen Zhou's hesitation, but didn't think much about it.
Afterwards, Chen Zhou left Professor Ating's office.
The reason for his hesitation just now was not that he was unwilling to do the sub-topic given by Professor Ating.
But, relatively speaking, there is a topic that attracts him more.
This was a mathematical problem he discovered when he was studying the materials he got from Professor .
Closing the office door, Chen Zhou shook his head slightly.
Forget it. There really isn’t enough time left now.
Let’s talk about it after I finish the sub-topic or solve the problem.
Chen Zhou collected his thoughts and looked at his watch. It was still early.
You can go back to the dormitory to work hard, then go out to eat, or order takeout...
"Student Chen Zhou?"
A clear female voice interrupted Chen Zhou's progress.
Chen Zhou looked in the direction of the voice, smiled slightly, and greeted politely: "Hello, classmate Nott."
Nott was still wearing a white dress, with thick blonde hair falling on her shoulders.
There was a faint smile on her fair face.
I have to say that this girl is a typical Western beauty.
Nott walked up to Chen Zhou and asked, "Are you here to see Professor Ating?"
Chen Zhou nodded: "I just came out of Professor Ating's office."
Nott immediately smiled and said, "I just came out of my tutor's office . It seems like today is such a coincidence."
"Well, it's quite a coincidence." Chen Zhou replied indifferently.
Noether didn't care about this and asked, "I heard you are studying the Goldbach conjecture? Have you made any progress?"
Chen Zhou glanced at Nott and said nothing.
Nott immediately explained: "Don't get me wrong, I just asked casually, I didn't mean to pry."
Chen Zhou did not comment. He did not care whether the other party intended to pry into the matter or not .
"There has been no substantial progress for the time being." Chen Zhou replied casually.
"Oh, I see..." Noether thought for a moment and said, "However, I believe you will soon achieve certain results, just like you solved Cramer's theorem and Jebov's theorem."
Chen Zhou politely replied, "Thank you for your good words."
"You're welcome. I also hope to see you make history again." Nott said with a smile.
Chen Zhou didn't say anything and walked side by side with Nott.
After a pause, Noether asked curiously, "Are you here to see Professor Artin because you are studying the Goldbach conjecture?"
Chen Zhou shook his head: "No, it's a problem of algebraic geometry."
"Oh?" Nott immediately showed an interested look, "You are also studying algebraic geometry?"
When Chen Zhou heard this question, he chuckled and said, "My mentor studies algebraic geometry."
Nott was stunned for a moment, then he slapped his head with his hand, cleverly concealing his embarrassment.
"Because of your outstanding research in number theory, I had forgotten that Professor Artin is a master in algebraic geometry."
Hearing this, Chen Zhou smiled softly and didn't say anything.
Chen Zhou finally discovered that this senior sister Nott was a little different.
After a pause, Nott invited, "I still have some questions that I want to ask you. If it's convenient, can we have lunch together at noon?"
Chen Zhou looked at Nott's delicate face and refused directly: "No, it's still some time before noon , and I have to go back to the dormitory."
"If you have any questions that I can help with, you can ask now."
Hearing this, Noether smiled and said, "It's about algebraic geometry."
