Reaching out to take the "homework" handed over by Chen Zhou, Professor Atin did not look through it directly.

This research summary, in the hand, is heavy.

To say the least, it would have to be dozens of pages.

If you read it all, it would take hours to say anything.

Therefore, Professor Atin did not intend to delay Chen Zhou's time.

After he finished reading it, he could 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 research depth of Chen Zhou, so as to arrange future research topics for Chen Zhou.

Putting the "homework" on the desk, Professor Artin gently patted it twice with his hand, and then said, "I'll look at the homework later, and I'll ask you a question first." ”

Chen Zhou looked at Professor Ating: "Professor, may you ask." ”

Professor Artin: "Tell me what you think about non-commutative algebra and non-commutative algebraic geometry. ”

When Chen Zhou heard this, he pondered 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 correspondence in non-commutative geometry. ”

"For example, the K theory of rings is similar to the K theory of C* algebra, the Dram cohomology theory of smooth manifolds is similar to the cyclic cohomology theory of C* algebra, and so on......"

"In addition, the K-group of the AF algebra, the Morita equivalence of the ring and the C* algebra, the cyclic cohomology and the Conne length are all used in the non-commutative torus surface......"

Unlike the first time, in the face of Professor Ting's question, Chen Zhou chose to answer this time.

Moreover, Professor Ting's question this time is completely different from the first question, and it is also milder than the first question.

Noncommutative algebra includes noncommutative rings.

Just as commutative algebra is an algebraic tool for algebraic geometry.

Non-commutative algebra, that is, a tool for non-commutative algebraic geometry.

Rather than commutative algebraic geometry, it refers to the study of geometry by treating invariants as space itself.

Therefore, the question asked by Professor Atin today is the opposite of what he asked for the first time, and it is also the opposite of the homework that Chen Zhou handed in today.

This is also the reason why Chen Zhou feels that it is completely different from the first problem.

As for why it is milder than the first problem, it is because both non-commutative algebra and non-commutative algebraic geometry have undergone a long period of development.

In addition, Chen Zhou also has certain insights into the interaction and mutual influence of non-commutative geometry and classical geometry.

Regardless of the geometric properties on the exchange object, the algebraic properties on the non-exchange object lead to the algebraic properties on the non-exchange object.

Or an algebraic property on a non-commutative object, which can foreshadow the geometric property on an interchangeable object.

Chen Zhou has done a little research.

This research did not start after coming to MIT.

Of course, in front of Professor Artin, Chen Zhou still had the feeling that the class was getting an axe.

However, this feeling just reminded Chen Zhou.

He still has many shortcomings.

In addition, in front of Professor Artin, it is not a bad thing to expose his own shortcomings.

Chen Zhou also believes that through communication with Professor Artin, he can get some help.

After all, this is an important part of learning research and the importance of mentors.

Therefore, when Chen Zhou narrated, his tone was extremely stable.

After Chen Zhou finished speaking, Professor Atin nodded slowly, and then praised: "Yes, it seems that there is some truth in not coming to me for such a long time." ”

Hearing this, Chen Zhou was stunned for a moment, but soon said with a smile: "Professor, then don't blame me for taking up your time all the time in the future?"

Professor Atin smiled: "No, how can any teacher be afraid of students asking questions? Unless you ask questions, I can't answer them." ”

After a pause, Professor Atin pointed to the research summary handed over by Chen Zhou and said, "This, after I finish reading it, I will give you a feedback email." Also, I'll give you a suitable sub-project to do. ”

Chen Zhou hesitated for a moment, but still said, "Okay, professor." ”

Professor Atin also noticed Chen Zhou's hesitation, but he didn't think much about it.

Chen Zhou then left Professor Atting's office.

The reason for his hesitation just now was not that he was unwilling to do the sub-project given by Professor Artin.

It's just that, relatively speaking, there is a topic that is more attractive to him.

This was a mathematical problem he discovered while studying and researching the pile of materials he had taken from Professor Artin.

Closing the office door, Chen Zhou shook his head slightly.

Forget it, the current time, I really can't squeeze out a drop.

Wait until the sub-project is completed, or the brother guess is solved, and then let's talk about it.

Retracting his thoughts, Chen Zhou raised his hand and looked at his watch, it was still early.

You can go back to the dormitory and go out to eat again, or order takeout......

"Chen Zhou?"

A crisp female voice interrupted Chen Zhou's progress.

Chen Zhou followed the prestige, showed a smile, and greeted politely: "Hello, classmate Nott." ”

Noether was still dressed in a white dress, with thick blonde hair draped over his shoulders.

On his fair face, there was a faint smile.

I have to say that this girl is a typical Western beauty.

Knott walked up to Chen Zhou and asked, "Are you here to find Professor Artin?"

Chen Zhou nodded: "Just came out of Professor Atin's office. ”

Knott suddenly smiled and said, "I also came out of the tutor's office just now, it seems that today is really too coincidental." ”

"Well, it's a coincidence. Chen Zhou replied lightly.

Seeing this, Noether didn't care, and instead asked, "I heard that you are working on the Goldbach conjecture?"

Chen Zhou glanced at Nott and did not speak.

Knott immediately explained: "Don't get me wrong, I just asked casually, and I didn't mean to inquire." ”

Chen Zhou was noncommittal, he didn't care if the other party had the intention of inquiring.

"There has been no substantial progress yet. Chen Zhou replied casually.

"Oh, that's right......," said Noether after a moment's thought, "but I'm sure you'll soon be able to achieve something, just as you solved Crammel's theorem and Jepov's theorem." ”

Chen Zhou replied politely: "Accept your auspicious words." ”

"You're welcome, I would also like to see you make history again. Knott said with a smile.

Chen Zhou didn't speak, and walked side by side with Nott.

After a pause, Knott asked curiously, "Did you come to Professor Artin to study the Goldbach conjecture?"

Chen Zhou shook his head: "No, it's a problem of algebraic geometry." ”

"Oh?" Nott suddenly looked interested, "You're also studying algebraic geometry?"

When Chen Zhou heard this question, he laughed softly: "My tutor is a student of algebraic geometry. ”

Noether was stunned for a moment, and then slapped his head with his hand, cleverly hiding his embarrassment.

"Because of your excellent research in the field of number theory, I have forgotten that Professor Artin is a master in the field of algebraic geometry. ”

Chen Zhou, who heard this, smiled softly and did not say anything.

Chen Zhou finally discovered that this senior sister Knott was a little different.

After a pause, Knott invited, "I still have some questions, I would like to ask, if it is convenient, let's have lunch together at noon?"

Chen Zhou looked at Nott's delicate face and refused directly: "No, there is still some time before noon, I still have to go back to the dormitory." If there is any problem, I can help, you can ask now. ”

Hearing this, Noether smiled: "It's about algebraic geometry." ”