Chapter 111 Thesis Completed
In Beijing, Qiao Yu put down the phone and excitedly turned his attention to the formulas on the computer, and began to re-examine the geometric background of the parameters and constants in the formulas.
Qiao Xi is right. There are many parameters and complex formulas. He now needs to find the commonality of these parameters, so what is the commonality behind the current conditions? No, not just common ground, but essential common ground!
Otherwise it is not enough to link these parameters together.
So naturally, Qiao Yu put forward a hypothesis: Whether it is modular form, -advanced geometry or quantized homology category, their parameters can be uniformly represented by a single geometric quantity.
The most critical part of this hypothesis is to find a unified geometric quantity that can capture the parameters that reflect the complexity of the curve in different geometric tools.
The next step is the most troublesome and critical step.
Qiao Yu began to analyze the core parameters of each geometric tool one by one, then listed its core parts, and then found the common ground of all these parameters.
To put it simply, whether these parameters are all controlled by a common constraint parameter, of course, this is only the first step.
After finding the common constraints, you have to find the connection between these parameters and the common constraints. This is another extremely complex proposition, but how can I put it, it fully meets Professor Zhang’s requirements and the proof process is Complexity leads to simplification.
And it can also make this formula a truly universal formula. When solving the upper bound problem of rational number points on curves, everyone does not need to think about anything else, just use his Qiao Yu-Qiao Xi theorem.
Immersed in the proof of the theorem, the sky darkened before I knew it.
It wasn't until there was a knock on the door that Qiao Yu woke up from his tedious work.
Qiao Yu looked up and glanced out the window, then stretched on the spot, and then went to open the door.
Senior Brother Chen was standing outside the door. When he saw Qiao Yu standing in front of the door, he immediately raised the lunch box he had just packed in the cafeteria and said, "When I went to eat just now, I saw you in the room. There was no movement, so I didn’t shout out for fear of disturbing you. I thought you must not have eaten yet, so I brought you a piece of food.”
"Thank you, Senior Brother Chen!" Qiao Yu grinned and gave Senior Brother a sincere smile, then took the lunch box and turned around and walked into the room.
After spending an entire afternoon’s brain cells, Qiao Yu felt really hungry.
This lunch box is very timely.
Chen Zhuoyang followed and walked in, mumbling: "Don't forget to sleep and eat all the time when you are studying. You have to eat no matter how busy you are. No matter what you do, your body is the most important."
"I know, Senior Brother Chen. Today is a special situation!" Qiao Yu explained with a smile, then opened the lunch box and ate hungrily.
Although I didn’t do much exercise in the afternoon, I spent too much mental energy and felt very hungry.
Even more hungry than playing basketball all afternoon.
Chen Zhuoyang looked at the content on Qiao Yu's computer curiously. Good guy, there were those complicated formulas and all kinds of messy custom symbols again, which made the senior fellow sigh inwardly.
It can’t be compared, it can’t be compared.
“Are you still studying your topic?” Chen Zhuoyang pointed at the computer and asked casually.
Qiao Yu looked up at the monitor, swallowed the food in his mouth, and then said: "Yeah, it's a pity that the results haven't been produced yet."
In the past, he would have said a few words, But now that he has just found a clue, and after realizing the difficulty of this problem, Qiao Yu has become much more cautious.
He didn’t want to boast before he made results.
Chen Zhuoyang said with self-pity: "Don't be impatient. How can the results be so easy? My boss introduced me to a research group before, which mainly focused on the quantization of geometric structures and modulus spaces on high-dimensional algebraic varieties. The main goal is to publish a paper that explores the relationship between modular forms and Kahler manifolds..."
"Um? Why are you sighing?" Qiao Yu was curious. asked.
"Forget it, it took more than a year to work on, but in the end, a team from Harvard did the same work and published several papers, which were better than ours. Then the project was hastily ended. In the end, the paper was casually published in a second-district water journal. The key point is But I have only done three games."
Chen Zhuoyang said melancholy.
Qiao Yu probably understands Senior Brother Chen’s pain. Following the top tutor, the tutor also gave resources, but I failed to grasp it...
Of course, this is not entirely to blame on Brother Chen, after all, a research group can be counted as a whole.
But in other words, if Senior Brother Chen joins in and is able to turn the tide, the ending may be rewritten.
"Oh, Senior Brother Chen, what was your main job at that time?" Not knowing how to comfort him, Qiao Yu simply asked.
“Classification of modular forms of algebraic curves, research on the relationship with K stability. Hey, let’s not talk about this anymore. In fact, I want to tell you that the first draft of my thesis is almost completed. When will you go to Huaqing? , I can take advantage of you to come over next time and tie up the final touches." Chen Zhuoyang slowly revealed his true purpose.
Still too thin-skinned.
Qiao Yu felt that if it were him, he had done so many things before, and he would definitely not talk so much nonsense at this time. Only then did the real purpose come out.
However, he still thought about it and said: "Hey, Brother Chen, what are you talking about? For such an important matter, I can go to Huaqing just for you! But Grandpa Master said that day that he I’m quite busy this week and may not be free until next week. If you want Grandpa Shi to take a look at it in person, just give it to me before next Wednesday.”
This time point actually has nothing to do with when Mr. Yuan has time. It is simply that Qiao Yu feels that if he is in the right direction, he should be able to almost complete the results before next Wednesday.
When the time comes, it will be more convenient whether he helps his senior brother read the paper first, or he actually takes it to Huaqing and lets his senior brother help him palm the eyes.
Before he was sure that this direction was correct, he was not in the mood to care about other things.
Chen Zhuoyang said happily: "Next Wednesday? No problem! By the way, I don't ask Mr. Yuan to help me correct my paper. You just need to ask Mr. Yuan to help me see where there are problems and give me some comments. Just give me your specific opinions.”
Qiao Yu nodded and said affirmatively: “OK! Just remember to give me the paper before Wednesday.”
"Thank you so much, junior brother. I'll go back and work on my thesis first."
"Well, it's okay, you can go and do your work!"
"Hey..." watching Chen Zhuoyang off After leaving, Qiao Yu sighed and suddenly found that he had more and more things going on.
Study, read, coax the tutor and the tutor's tutor, do the project, write the paper, participate in the selection, and then go to IMO to get medals, while beating the peers of the same age... Now I have to prepare for my senior brother's Ph.D. Dissertation worries.
How much does he have to do by himself? This is probably the legendary saying that those who are capable work harder! Well, it seems that he must take on the task of revitalizing the Chinese mathematics community! After all, he is now sixteen years old and is no longer the fifteen-year-old brat he once was!
Thinking of this, the stuffed Qiao Yu became excited again. He sat down in front of the computer upright, working, working... In order to revitalize Huaxia Mathematics, and to show his tutor, senior master, and senior brother a little bit of Qiao's color, He had to work out Qiao's upper bound theorem no matter what!
……
Mathematical research often has a very interesting characteristic, and it is a situation that countless mathematicians have encountered, that is, during the research process, it is likely to get stuck somewhere. A step, or a certain issue, cannot make any progress for a long time.
Yes, it is stuck there alive.
Sometimes I have an epiphany. This hurdle has been overcome, and I feel suddenly enlightened. The road ahead is smooth.
But it is a pity that for most mathematicians in the world, this obstacle may last a lifetime, so the project ends without any problem, and the previous work and data are stored there, dreaming that one day, they will suddenly have an epiphany and let these Research will see the light of day one day in the future, but it is more likely that it will never happen again.
Qiao Yu is actually the same, it's just that his talent is a little higher than countless ordinary mathematicians.
When he realized the need to find commonalities in parameters under Qiao Xi's prompts, this problem seemed to be no longer a problem for him.
All the previous reasoning and proof processes have been done. It can be simplified by finding commonalities. The commonalities are hidden in the less obvious connections behind those parameters. As long as the work is detailed enough, Qiao Yu feels that this is absolutely That's the right direction!
This is indeed the case.
For three days, Qiao Yu almost stayed at home except for eating. He didn't even read a book. He devoted himself wholeheartedly to this work, and then he really discovered the existence of commonalities.
The higher the module form level, the more complex the curve, so the k-curve complexity.
The prime number p controls the local geometric behavior of the curve in the -adic field. Different prime numbers correspond to different geometric constraints. The prime number p is also related to the complexity of the curve, so p is the local geometric complexity.
The parameter q in quantized homology reflects the influence of quantized geometric objects on the global complexity of the curve. This is a further quantification of the geometric complexity of the curve, so q is the global geometric complexity.
In other words, although different geometric parameters come from different sources, they all reflect the complexity of curves from different perspectives.
What's this? This is the defining condition for parameter unification.
So on Friday night, Qiao Yu designed a unified geometric constraint parameter θ, and put forward a second hypothesis: the geometric constraint parameter θ is the modular form level, -adic number field prime number and quantization Some weighted combination of homology parameters that together reflect the global complexity of the curve.
Based on this assumption, it is obvious that a basic structure can be obtained: θ=f(g, k, p, q).
Of course, at this point, it is obviously not enough.
Because the weight of each parameter is different, to make the structure mathematically reasonable, a combination method that can perfectly reflect the weight of each parameter is needed.
The next step is the calculation and verification work, which is complicated but not difficult.
In just one night, he concluded that the growth of k increases logarithmically with the genus g, so: kglog(g); the complexity of local geometry changes exponentially as the genus increases. , so pe^g/2; in quantized homology, the relationship between parameter q and genus g directly calculates an approximate value: qg^3/2.
The formula comes out naturally: θ=f(g,k,p,q)=glog(k)+g^2log(p)+gq
Express the three parameters After bringing it in directly, it is: θ=glog(glog(g))+g^2log(e^g/2)+gg^3/2
At this step, there is only one deficiency grid g left. important parameters.
Next is the simplest simplification work: θ=g(log(g)+log(log(g)))+g3/2+g^5/2
Busy in front of the computer day and night for three days After that, Qiao Yu in February 2025 On the 21st of September, at 11:37 pm on Friday, I finally typed out the final formula for the rational point estimation of the curve on the computer: N(X)≤C(θ)=θ^g
θ is The geometric constraint parameter he designed, g is the genus.
This formula... is really beautiful!
After admiring it for a while, Qiao Yu immediately began to verify it. After all, the formula is useless because it must be useful.
What he has to do is to find out whether it is accurate based on his own formula.
Qiao Yu chose the classic elliptic curve y^2=x^3+x
According to the known conditions of BSD conjecture, it can be seen that the genus of the curve is 1, which can be directly introduced into the formula and then simplified to get The result is: θ=5, well, 5 to the power of 1 is still 5.
The conclusion is obviously correct.
Because this is the classic Hermitian curve. The rational number points on the curve have been calculated more than ten years ago.
Next came the special cases of the Model curve, the Fermat curve, and various cases of the Kubert curve... Qiao Yu tried them all.
For example, the Model curve: y^2=x^3+k, k is an integer. He verified k=-1, k=2 and other known finite rational points, and the results were all correct.
Then Qiao Yu opened Professor Robert Green's paper and used his own formula to make comparative calculations with the formula derived by Robert Green. On certain points, his formula was mostly the same as Robert Green's. The results are the same, but there are some uncertainties. There are still some differences between the two sides' calculations, but they are not significant.
Well, I’m too lazy to care about who is right and who is wrong.
At least at this point, he can start writing a paper. This step is the easiest for him.
Because he had already written down the process of deriving the formula for more than half a month before, and because he had long considered completing a paper, Qiao Yuben had prepared the entire derivation process in detail. The next step was to use professional language to describe those The derivation process is integrated.
It is nothing more than lemmas and theorems, and the proof part can basically be copied and pasted directly.
The main thing is the subsequent proof process about the unified geometric constraint parameter θ, which needs to be written now.
Fortunately, Qiao Yu had a whole weekend to complete this paper.
In fact, of course there is no need to be in such a hurry. At Qiao Yu's age, there is no need to seize the day. It doesn't matter if the paper is completed a few days earlier or a few days later.
He doesn’t need a professional title anyway, and he doesn’t have the pressure of 3+3. Taking a step back, even if someone in the world of mathematics does the same research as him and publishes it first, the impact on him will not be big. Think about another subject.
After all, there is no pressure to publish a paper as a student.
It’s just that Qiao Yu’s idea is very simple.
He didn't study or read papers this week, so naturally he couldn't write down any reading experience on the weekend, and naturally couldn't hand it over to his tutor and grandpa Shi on Monday.
Of course, if he explains clearly, he believes that both Director Tian and Grandpa Shi across from him will believe him.
But how can a pale explanation be as convincing as throwing the paper directly into the mailbox of the tutor and grandpa Shi?
Send the paper to your email first, and then explain on WeChat: "I'm sorry, tutor/master, I didn't study as planned last week, so I can't send you my reading experience this week. The reason is last week I spent all my time perfecting my thesis, The paper has been sent to your mailbox.”
Qiao Yu doesn’t know what others think, but he has understood a truth since the fifth grade of elementary school. Actions are far more convincing and have results than words. Actions with results are far more convincing than actions without results.
Trust is either built through fruitful actions, or it is consumed through repeated words or fruitless actions.
Why can he have a stable cash flow since the sixth grade? Isn't it because he spent more than half a year in fifth grade to establish a good reputation and full trust among primary school students, and accumulated a fixed customer group of primary school students.
As long as he helped write the homework and signed for it, the teacher could not find out at all; whenever he agreed to take the exam for him and get high scores, he never failed.
In order to do this, he even gave up on his grades from the beginning. He wrote his homework blindly and got a C every time. But I could only get a low score.
And I never skip class or make trouble. He listens carefully during class performances and is busy doing homework for others during self-study... just to give the teacher the impression that this child is quite diligent and obedient, but his grades cannot improve.
The purpose is that even if a classmate secretly reports it to the teacher, the teacher will not believe that he is still capable of helping others with their homework and exams...
Now it is just a matter of going to school. Just use that set in reverse.
In fact, Qiao Yu has always been like this. He is thoughtful, has clear goals, and is extremely capable of action. Coupled with a decent IQ, he can naturally do things with twice the result with half the effort.
So Qiao Yu completed the writing of the paper on Sunday afternoon, and then it was time for the second inspection and revision of the paper.
After reading the papers of Lao Xue's master's students, Qiao Yu understood how ridiculous some detailed errors in the papers were in the eyes of the reviewers.
So Qiao Yu’s requirements for the paper are also to strive for excellence. At least no obvious improper wording, ambiguity caused by grammatical errors, and logical loopholes are allowed. The content of the literature review and the citation format must be unified. , meticulous.
Still busy until late at night, Qiao Yu completely sorted out the paper twice and made some minor revisions. After finally making him feel satisfied, he titled the paper "Based on Near-Complete Spaces, Modular Forms and The paper "Derivation of Rational Point Upper Bounds for Algebraic Curves in p-adic Geometry" was sent to two big guys, Tian Yanzhen and Yuan Zhengxin.
Based on the young man's desire to show off, Qiao Yu originally planned to send a copy to Professor Zhang Shuwen of Princeton.
But after thinking about it, he gave up. Although he was quite confident, it was the first time he had done a paper on such a big proposition, and it was completed entirely by himself. He was not sure about his final result. Whether the results can be recognized.
It would be better to let his mentor and grandpa master help him palm his eyes first.
If there is any big problem, he will still have the opportunity to modify it. If Professor Zhang were to find any serious faults, he would be taught a lesson by an outsider.
Well, being taught by one's own tutor can also increase feelings, but being taught by outsiders can only be aggrieved when others are still doing it for his own good.
Not to mention that my tutor and my grandpa have a good relationship with Professor Zhang. If they approve this paper, Professor Zhang will definitely see it. It’s just a matter of time, so there’s no need to worry.
After sending the paper, Qiao Yu hurried out, ran to the second floor and took a comfortable bath, returned to the room, blew his hair casually, and then fell asleep.
My body is not tired this week, but my brain consumes too much and I tend to feel sleepy.
……
Huaqing University, Qiuzhai.
Yuan Zhengxin walked into the office at 7:50 as usual, then turned on the computer and logged in to WeChat. He planned to print out the reading experience Qiao Yu sent him and take a closer look.
The old man has become accustomed to the fact that Qiao Yu will send him a document on time every Monday around 7:30 in the morning about his thoughts and gains from reading and reading papers.
This distance education method is not a student, it is better than a student.
It is easy for people to fall for sweet words, especially the elderly.
Children always like to complain that their elderly people spend money indiscriminately, and their money is defrauded by outsiders on health care and financial management. However, they never examine whether they are too perfunctory with their parents, and whether their children's identities are as good as others take them to be. Careful and meticulous.
Excellent salesman, greeting the elderly regularly every day, paying special attention to the emotional needs of the elderly. As long as it does not cost money, he can satisfy the elderly in everything, and even come to the door to hammer the back and pinch the feet. He is more caring than his own son or daughter. Dear, you speak nicely. After a long time, it can really melt the heart of an iron man...
I am chatting about homely things when I have nothing to do: "Dad, you are sick, you need..."
The business will probably be completed. Well, people's defensive psychology always gradually disintegrates invisibly.
Not to mention that Qiao Yu has made some minor upgrades here. He doesn’t call him dad, he calls himself grandson...
"Grandpa, I didn't study this week, so I don't have any experience. But your grandson is not lazy. I completed the paper I have been studying for a long time this week and it has been sent to your mailbox. You must help I’ll take a closer look to see if there’s anything wrong! My goal is to be published in one of the top four journals in mathematics!”
This sentence is followed by a serious expression, which is very consistent with the persona of a grandson. Looks very naughty.
The old man smiled subconsciously, probably thinking: His grandson still wants to be published in the world's four top mathematics journals. Isn't publishing a section header enough for you?
Of course the mood is still very good.
After chatting with Lan Jie, the old gentleman had already downloaded Qiao Yu’s paper and read it.
I was very satisfied, especially after learning from Qiao Yu that the paper was almost written by me, my evaluation of Qiao Yu was naturally higher.
Originally, he planned to ask the corresponding author of the paper, Professor Xue Song of Yujiang University, to inquire about something, but when he learned that Xue Song had been transferred to Yanbei University, he stopped thinking.
Although he loved Qiao Yu to the core, it was still difficult to let go of some barriers.
After all, he is a teacher, and the other party hasn’t said much yet. Should he be asked to bow his head and admit his mistake to the traitor first?
But if it involves Qiao Yu...
Well, anyway, this kid recognizes him as his master and grandfather, and admits that he is from his lineage, and that's enough for the time being.
Soon, the paper was printed.
The old man heard Zhang Shuwen describe Qiao Yu’s thoughts, so he was not surprised by the title of this paper. However, after reading the introduction and table of contents, the old man directly turned to the last two pages to see the final result. , couldn't help but be stunned, and became a lot more serious.
Hey guys, this kid really made a universal estimation formula?
This also made the old gentleman look a little more serious and even a little more excited when he read this paper.
Don't mention it, if this result is correct, at least if no obvious flaws can be found for the time being, this result is really qualified to be included in the four top mathematics journals.
If Qiao Yu's method is correct, applied to numerical applications, it can effectively assist in judging the convergence of the iterative process, help analyze errors, and optimize the convergence speed of related algorithms. Especially when solving optimization problems, it can help set constraints to ensure that the solution is within the range of rational numbers, helping to simplify calculations.
After the old man became serious, he called the assistant directly into the office: "Go and inform me that I will not attend the group meeting this morning. Then just give me a summary of the speeches made at the meeting. ”
“Okay, Professor”
……
At Yanbei University, Qiao Yu was doing morning exercises outside his dormitory and study room.
Working on some papers last week, I felt like I was welded to a stool every day. I felt like I hadn’t done any good exercise in a long time, so I just wanted to do some exercise.
He is only sixteen years old. If he maintains a certain amount of exercise, he can grow taller.
And for Qiao Yu, the new week is like being recharged for seven days, giving him the joy of squandering time.
This is probably the benefit of living a fulfilling life. Being lazy every now and then can bring you a full sense of happiness.
Unlike those who are used to fishing every day, after all, once a person is used to fishing, the happiness brought by fishing will become less and less. However, once one cannot fish anymore because of something, the harm caused will not be the same. There are tons...
When Chen Zhuoyang came to the front of the building with energetic steps early in the morning, what he saw was the scene of his junior brother doing jumping exercises at the door, and he suddenly felt like he had seen youth. .
"Good morning, Qiao Yu!"
"Good morning, senior brother Chen..." Qiao Yu gasped and replied.
With some emotion, it seems that he has not done anything like exercise since he went to college, so it is easy for people to miss the youthful days of high school.
Then I subconsciously remembered that the guy in front of me was only sixteen years old, still a freshman in high school.
"At least I have more beautiful memories of high school life than he does."
Chen Zhuoyang thought to himself in his heart, and then suddenly discovered that he had not contacted his classmates in high school for a long time. , there is a group of classmates, but unfortunately not many of them can talk all year round.
In addition, various class reunions have been almost demonized in recent years. It seems that no one has the intention to get together, and no one will organize such a thankless thing. I suddenly feel like high school again The memories of those three years seemed meaningless.
The only thing he misses is probably that his scores were consistently ranked among the top five in the class. Every time the teacher reported the scores for the exam, the envious eyes of the classmates around him, right?
Unfortunately, after I came to Yanbei University, I never had that feeling of being taken seriously by others again. Looking back now, Chen Zhuoyang feels that he should have woken up earlier. When he was studying for a master's degree, the classmates around him were already inhumanly strong, which was completely different from when he was an undergraduate.
Really, he feels that with only seven points of effort in undergraduate studies, his grade point can be stabilized in the top 3% of his grade. When a brother in the dormitory is still worried about completing his homework, he can quietly play games next to him. During the game, he can give guidance to the brother in the dormitory on his homework. This is his daily routine.
People who have never been a top student cannot understand that sense of superiority.
But after he was admitted to Yanbei to study for a master's degree, he already had to go all out to gain some status among the classmates led by his tutor.
As for playing games? What a joke!
After arriving at the research center to study for a Ph.D., except for the day when I was excited after passing the exam, I was constantly hit by the shock. His goal was also to achieve results at the doctoral level, and he was recommended to go abroad for exchange. Academicians handled his doctoral defense. After graduation, Yanbei University directly offered him a professor or researcher position in order to keep him...
Now it has become As long as I can graduate.
The change in mentality has been a lifelong pain for Chen Zhuoyang. It can only be said that the person who was once full of yearning for mathematical research is dead. Many times, Chen Zhuoyang has begun to suspect that he may not be as good as he imagined, because He watched helplessly as he gradually failed to keep up with the progress of his classmates.
But since Qiao Yu came, Chen Zhuoyang felt that it was no longer a question of whether he was good or not. He began to suspect that he might be slightly mentally retarded.
After all, the ignorant are fearless. If he hadn't been stupid enough, how could he have the courage to take the doctoral examination under Director Tian?
Fortunately, the embarrassing days are about to pass.
If he can pass the thesis and prepare for the defense in two or three months, he can graduate. He can say goodbye to this place full of talented people and never come back again...
In his heart As he walked past Qiao Yu with complicated thoughts, he suddenly heard a cell phone ringing.
Subconsciously he took out his cell phone from his pocket, but it turned out that it was not his, and then a youthful voice came from behind him.
"Hey, Director Tian, good morning!... Well, I've eaten and I'm exercising... Oh, now?... Well, okay, I'll be there right away."
Chen Zhuoyang turned around and asked: "Qiao Yu, the boss asked you to go to the office?"
"Yes." Qiao Yu nodded.
"Oh, do you know what I asked you to do?"
"I wrote a paper last week and sent it to my supervisor last night. Director Tian probably wants to give me some advice, right? Or If he finds any problems with the paper, he will tell me clearly and then rewrite it," Qiao Yu replied cheerfully.
“Oh, the paper is finished? Which one?”
"It's the issue discussed in the last seminar, about the accurate prediction of rational points on the upper boundary of the curve."
"Has it been completed using Schulz's method?"
"Yes, um, senior brother, I'm sorry. Director Tian asked me to come over quickly, so I'll leave first. Let's talk back." After saying that, Qiao Yu waved casually to Chen Zhuoyang, and then trotted towards Tian Yanzhen's office. Run to the building where you are.
Chen Zhuoyang looked seriously at Qiao Yu's quickly leaving back, and suddenly felt that it looked like his lost youth.
……
"Director Tian, what do you want from me?" Qiao Yu knocked on the door, but did not go in directly. Instead, he opened the door a crack and only stuck his head in, looking at Tian Yan sitting at his desk. Zhen asked.
Looking like something was wrong, he immediately ran away.
Tian Yanzhen raised his head and glanced at the funny Qiao Yu, and was so angry: "Come in, close the door!"
"Oh, okay, Director Tian." Qiao Yu was now old He walked into the office honestly and closed the door.
Tian Yanzhen glanced at Qiao Yu, who had empty hands, and said, "Pick a book and sit aside and read it. I will ask you any questions at any time."
After speaking, Tian Yanzhen patted the paper on his desk.
"Okay!" Qiao Yu readily agreed, then came to Tian Yanzhen's bookcase, turned around and asked again: "Director Tian, which book is the most expensive in your bookcase?"< br>
"Huh?" Tian Yanzhen turned to look at Qiao Yu again without knowing why.
"Anyway, I will definitely read it today. You will give it to me when I leave. It will be more cost-effective for me to choose a more expensive one. After all, I don't have many opportunities to come to your place to read." Qiao Yu explained seriously road.
One sentence made Tian Yan really angry again: "Okay, don't worry about these books of mine. If you want to read them, come and get them at any time. When you graduate, I will give them all to you."
Qiao Yu said excitedly: "Director Tian, I'm serious about it! I will come directly to move books on the day I graduate. You can't stop me."
Tian Yanzhen said casually: "No problem, you Even if you come here to move, it’s just a few books, of little value.”
Qiao Yu casually took out a “Classic Introduction to Modern Number Theory” from the bookcase and retorted: “Ordinary books are definitely of little value, but in this case. in your office The book is different. The value of the book is firstly the author, and secondly the person who collects it!
When I get the book, I will go to the auction. These are all books collected by the masters of Chinese mathematics. Then Why can’t the value be doubled hundreds or thousands of times?”
Tian Yanzhen was stunned for a moment, and then said with a straight face: “Why are there so many weird words? Sit down and read a book. I didn’t ask you, so don’t talk. ”
"Oh, okay, Director Tian." Qiao Yu immediately sat down and started to flip through the book.
Flattery should not be too frequent or too deliberate. It is enough to make the instructor happy once in a while, otherwise the threshold will be raised and it will be very troublesome in the future.
As for whether the teacher will accept this or not, that is a matter of opinion.
But from a human perspective, people all like to hear nice words, especially those from the most proud disciples. As long as he persists and conscientiously picks the most favorable times and occasionally flatters him, Qiao Yu believes that whether Director Tian has a straight face or not, he must be happy in his heart.
The teacher didn’t let him talk anyway, so he didn’t argue and just read quietly.
It’s just that I haven’t been quiet for a few minutes...
“Are you sure that k/p/q are really independent in this paragraph? Is there enough data to support it?”
“Well, I will It has been deduced and the parameters of multiple known curves have been introduced for fitting. It seems to be no problem at the moment."
"You don't have to fit it manually? Going to supercomputing for numerical simulation? There are enough data samples in the LMFDB curve database to conduct numerical verification and batch analysis through supercomputing, which will be more convincing. ” Huh? Go to a supercomputer?" Qiao Yu was confused. He just wanted to publish a paper, so he wanted to rent a supercomputer?
"Oh, you don't have an account for the school's supercomputer, right? In this case, you can use my account first. Okay, you continue reading and I will continue reading."
After saying that, Qiao Yu saw Tian Yanzhen picked up the pen and made a note on the printed paper, and then continued to read.
The rest of the process was lackluster.
“Are you sure that the relationship between modular form level k and genus g can be universally applicable, especially in situations where high genus curves or moduli spaces are non-trivial?”
“Not just k, This part is actually a place where multiple tools meet. Professor Zhang said that the proof process can be complicated. The entire logic of this piece is based on the multi-level complexity of algebraic geometry. Here I used the theorem of the weak BSD conjecture..."
That's about it, one question and one answer.
Tian Yanzhen raised questions, and then Qiao Yu tried his best to explain in detail his thoughts besides the paper...
Unknowingly, all morning It was over, and it wasn't until Qiao Yu felt his stomach growl that he finished reading the paper.
"Last question, did you complete this paper by yourself?" Tian Yanzhen looked at Qiao Yu seriously and asked.
Then without waiting for Qiao Yu to answer, he took the initiative to explain: "I am not doubting you, but submitting such a paper after supercomputer verification will be a very serious matter.
< br>
If you have discussed it with others in various ways, and the other party has indeed given you some effective suggestions or directly participated in the research on the topic, it may cause controversy if the author only signs your name after the paper is published. In this case, you'd better communicate clearly with the other party, such as whether you need to add the other party's name. "
There is no need to think about it. Qiao Yu replied directly: "Well, indeed, I have only communicated with Qiao Xi about this paper. If it can be published, I originally planned to publish it. The second author adds her name. "
"Qiao Xi? Tian Yanzhen was stunned for a moment, and then immediately said: "Your mother?" ”
“Yes, my mother, the most important part is the simplification of results. I really couldn’t think of how to effectively unify those parameters, so I called my mother. My mother told me that mathematics It is to look for possible hidden logical connections between different conditions.
I was inspired by this sentence to achieve the final result. That... is that my mother currently has no workplace. She has been staying at home to take care of me, so adding her as the second author is not a big problem if the workplace column is left empty, right?
When I look at other papers, it seems that the authors are followed by their affiliations. If there is no affiliation, will there be any problems? "
Tian Yanzhen closed his eyes and thought for a while, sighed deeply and said: "It is not a problem that she does not have an employer, and she is not the first author. As long as she indicates IndependentResearcher or directly writes Yanbei International Mathematics Any research center will do.
I mean you have not discussed this paper with anyone else in the mathematical community, including... Mr. Yuan, right? "
"Yes, Teacher Tian. Grandpa Shi only received this paper from me last night, so there will definitely be no controversy in this regard. You can rest assured! " Qiao Yu replied with great certainty.
As soon as he finished speaking, his cell phone rang again. Qiao Yu took out his cell phone and looked at it. His expression was slightly embarrassed, but he still said: "Hey, Grandpa Shi’s phone number. ”
"Then why are you hesitating? Take it."
Director Tian sat there and said lightly.
Thanks joasse for the reward and encouragement!
PS: The 26th day of the 10,000-word update has been completed!
(End of this chapter)