God's Crown

"An!" The voice behind was a little old, and An Yan turned around curiously to see who was calling him.When he looked around, he saw an old man walking towards him with a smile.

An Yan froze for a moment, who is this?He thought about it carefully for a while, and he didn't seem to think whether he knew the person in front of him.But since this person knows him, he will introduce himself later.The old man was accompanied by a young man, who should be his student or something.

It is actually a common thing to bring students to participate in such academic conferences.

After all, everyone has students and everyone has youth.It’s okay to bring students here to learn more, the old man walked up to An Yan and said, “We’ve met before.”

"Eh..." An Yan looked at the old man carefully, and for a moment he didn't know where he met the old man.Could it be at the previous academic report meeting?Seems like the only possibility.Besides, how could he be so vague about the old man's appearance in his memory.

"Who are you?" An Yan asked the old man very respectfully.

"Deligne." The old man said with a smile, "We are really destined."

"It turned out to be Dr. Deligne. Hello, it's a pleasure to meet you." An Yan stretched out his hand and shook Professor Deligne.

"I saw you many times at the academic report meeting before, and your academic report will be very exciting."

"It is a great honor for me to have your affirmation." An Yan said politely, "Who is this?"

"This is my PhD student, Lance."

"Hello, Mr. An Yan." Lance stretched out his hand and smiled at An Yan.

An Yan naturally responded with a smile and shook hands with Lance.

"This is Gou Liqun from the Department of Physics, Peking University. He is here to attend the academic conference instead of his professor."

"Hello." Professor Deligne was obviously not interested in Gou Liqun and Professor Li Bo. After greeting Gou Liqun and Li Bo very politely, he chatted with An Yan.

"Ann, my Anglerian space, I'm currently researching, and there are still some things I haven't been able to understand. I read your paper on Anglerian space, and it has incredible performance in both harmonic analysis and the Langlands program. "Professor Deligne said as he walked, "So..."

The two walked and chatted.

Gou Liqun and Lance glanced at each other, both showing a wry smile.

The world of the bosses is really too difficult to understand, and they can't even speak a word at all.For the first two, Deligne himself is a big boss of the Philippine Award, and An Yan is also a formidable young man.According to Professor Deligne, An Yan will be a very good mathematician in the future, especially in geometric topology and number theory.

The pleasant chat between the two is based on Professor Deligne's belief that An Yan can do something in the future, or it can be said that An Yan is qualified to chat with Professor Deligne.

Don't look at Lance as a student of Professor Deligne, but don't even think about chatting with the tutor on an equal footing, it's impossible.

Who is his professor with, that is the famous Professor Deligne, how could it be possible to chat with him on an equal footing.Moreover, as a student, it is impossible for him to chat with the professor on an equal footing.

As a Fields Medal winner, a famous mathematician.How picky his professor's eyes are.Lance was very clear, as if he was the doctoral student from Beijing University who was following An Yan.The professor is absolutely not interested in saying a word with him, even if it is a word, the professor would find it very troublesome, let alone other things.But it was different for An Yan. The professor seemed to want to talk to An Yan very much. On the way to the auditorium of Princeton University, he talked about many academic things along the way.

Professor Deligne regards An Yan as a person who can talk to him on an equal footing, and An Yan has no stage fright.The conversation with Professor Deligne was very fluent. On the way to the auditorium, Professor Deligne became more and more appreciative of An Yan.

Professor Deligne said with a smile, "Ann, you really surprised me."

"Why?" An Yan was a little confused, they were going to the auditorium of Princeton University soon.Standing outside the door of the auditorium, An Yan asked Professor Deligne suspiciously, "Professor, I don't quite understand what you said. Why did I surprise you?"

"Ann, I rarely see young people who are so accomplished in mathematics at such a young age." Professor Deligne thought for a while, and then frowned and said, "No, I haven't even seen it before. At such a young age. Especially without the guidance of a professor of mathematics, he has such outstanding mathematical attainments... This is really surprising. I believe that it will not take too long, Fields The prize will come your turn."

An Yan smiled, but did not speak.Not to mention him, even Xu Chengyang who was born in mathematics, Hui Zhiwei and other bigwigs have not won the honor of the Fields Medal, let alone him, a graduate student in the Department of Physics.

Speaking of the big guy Hui Zhiwei, he remembered it.This big guy is just this month, isn't he already serving as an associate professor in their Department of Mathematics at Stanford University?Maybe at some point, he might be able to ask this great god some questions.The inauguration ceremony of this great god is just this month, and he originally planned to attend it.But because of participating in the academic conference of Princeton University, that is, his Dipanto approximation has not been able to do well.Unfortunately, I was not able to attend the inauguration ceremony of this great god.

"You're over the award. As far as I know, my predecessors, whether it's Xu Chengyang or Hui Zhiwei, are all geniuses. I'm nothing in front of them."

"Well, you said that you have met both of them. They are indeed very good students. I heard that Hui is an associate professor in your Department of Mathematics at Stanford University?"

"Yes."

"That's really good." Professor Deligne smiled, and patted An Yan's shoulder, "Let's go, the math meeting is about to start."

"By the way, what day will your academic report be held?"

"It should be on the third day." An Yan thought for a while.

"So what is the topic you have prepared this time?" Professor Deligne said with a smile, "Of course I also know that for some reason, we only sent you an email in October. By the time you see it, it should have been Is it November?"

"Not really, I saw it after sending me the email." An Yan said, "I was preparing a project on the approach of Dipantus. Thankfully, it was finally completed before the academic report."

"It is conceivable that your academic reports must be very frequent." Professor Deligne said with a chuckle, "I am looking forward to your academic reports."

"Thank you, Professor."

The two smiled at each other and entered the auditorium.Gou Liqun and Lance behind them could only obediently follow them into the auditorium.

The auditorium was very solemnly furnished. After entering the auditorium, An Yan and Professor Deligne looked at each other and nodded slightly before parting ways.When he came to his seat, Gou Liqun next to him whispered, "What did you talk to Professor Deligne just now?"

"Some things about Euclidean space and Euler parameters." An Yan said with a smile, "Don't you guys who do fluid mechanics know about Euler angles?"

"It's a little far away, so I didn't hear clearly." Gou Liqun lowered his head in shame.What a joke Euler's formulas and theorems are widely used in mechanics.The two were talking about Euler's formula, but he didn't hear clearly.It's probably because I didn't notice it before, and I didn't hear clearly about my own affairs.

An Yan said to Gou Liqun, "Okay, it's about to start, don't talk."

After finishing speaking, An Yan raised his head and looked towards the front of the auditorium.Gou Liqun didn't talk anymore, and quietly looked towards the front of the auditorium.

In the solemn auditorium, there are countless top mathematicians from all over the world.All eyes were on the front of the auditorium, and the old man walked to the stage of the auditorium and said, "Today, we gather here to look forward to what will happen in the mathematics world in the coming year, and to review the What contributions have we made to the mathematics community in the past year. And, my personal favorite is the academic conversation and discussion..."

Gou Liqun asked An Yan cautiously, "Who is that on stage? He looks quite powerful."

"The one on the stage?" An Yan raised his eyebrows, "Dr. Langlands, don't you know?"

"Uh, he doesn't seem to be a professor at Princeton University, does he?"

"But he's a professor at the Institute for Advanced Study in Princeton."

"..." Gou Liqun looked at Professor Langlands talking on the stage, feeling a little dizzy.Probably because he didn't sleep well, he really wants to sleep now.After listening to Professor Langlands' speech, it took a while.He fell asleep in a chair.When he woke up, An Yan was pushing his shoulder and said, "Hey, are you still sleeping?"

"Ah!" Rubbing his eyes, Gou Liqun hastily opened his eyes, watching the sparse people leaving the auditorium, he touched his stomach that started to growl and said, "Is this the end?"

"It's been two hours." An Yan sighed, "Did you not sleep well last night? I see you have been sleeping."

"It was a bit late to chat with my girlfriend last night." Gou Liqun said with some embarrassment, "Is the society meeting almost over?"

"It's still early, you just came to a meeting and left? There will be a symposium and an academic report meeting. I remember that there are a few other professors from Peking University? Although they are all from the Department of Mathematics, but If you leave early, see if Professor Li Bo will peel off a layer of your skin."

Thinking about his boss, Gou Liqun gave a jolt and said, "Can we not mention the boss?"

"Let's go, let's eat first. After eating, I will take you to a symposium.

"

"Huh? What symposium?"

"You'll know about the symposium on nonlinear partial differential equations once you've been there. How come there are so many words..." An Yan glared at Gou Liqun, if he didn't know Gou Liqun, and he was also considered a friend.He really didn't want to go to the symposium with a big mess.

"Um, who invited this symposium?" It was also the first time for An Yan to come to Princeton University. Logically speaking, this kind of symposium is a place for academic exchanges between bigwigs you know.It is impossible for An Yan to know. It is said to be a symposium, but it is actually a place where big bosses find a place to drink tea, chat and exchange academic knowledge.There is a pleasant feeling that he must not be qualified to participate.

So here comes the question, how did An Yan know about this symposium?

"Professor Weiteng approached me just now." An Yan shrugged his shoulders and said, "This afternoon's symposium should be in the reception room. He told me that if you are interested, you can attend. There is nothing special today Academic report meeting, so I am going to participate in this symposium. Besides—" He looked at Gou Liqun and said, "Nonlinear partial differential equations should be widely used in your fluid mechanics, don't you want to participate? "

"I thought about it, but didn't the boss of Weiteng let you go? He didn't let me either." Gou Liqun thought of a group of big bosses sitting on soft chairs in the reception room, drinking coffee and snacks, chatting about non-linear bias Differential equations, probably—this is the symposium he most wants to attend.

An Yan is right. Nonlinear partial differential equations are indeed very important in fluid mechanics.It's so important that even if he doesn't want to learn this thing at all, he still has to unlock it.

Participating in this kind of boss-level symposium might give him a lot of inspiration and ideas.

"But let me say in advance that there may be many things to be said in this symposium. It doesn't have to be only nonlinear partial differential equations. I also want to find some inspiration from these big guys. I don't know if I can Found..." After An Yan finished speaking, she turned and left the auditorium, and Gou Liqun hurriedly followed.

He said dog-leggedly, "Boss, can you ask me to go with you for this symposium?"

"Well, after dinner, let's go together." An Yan nodded slightly.

When Gou Liqun was sleeping just now, Professor Wei Teng told him about it.An Yan glanced at Gou Liqun, who was still soundly asleep, and asked Dr. Wei Teng if he could take someone with him.

Dr. Weiteng didn't care, and told An Yan to bring someone to participate, so he took someone.

An Yan mainly thought that he and Gou Liqun came to Princeton University together, and it was very inappropriate to throw people away and go to this symposium by himself on the first day.Moreover, Gou Liqun is a student of the Department of Physics anyway, so the discussion of this group of bigwigs is of great use to Gou Liqun.

He thought it would be a lot better to take Gou Liqun to this academic conference.

I just don't know if Gou Liqun is willing to participate in this symposium, and he didn't tell Gou Liqun about it until he woke up Gou Liqun.

Judging from Gou Liqun's reaction, it should be that he also wants to participate in this symposium.

After leaving the auditorium, the two came to the restaurant of Princeton University according to the place Rich had pointed out to them last night.At this time, everyone sat together in twos and threes.Especially the group of mathematicians who came from afar and professors from Princeton University sat and chatted together.

After An Yan took some food, she sat in the corner and took a sip of coffee first.Then he was about to eat, when Gou Liqun led Wang Yunqi to the dining table.An Yan looked at Wang Yunqi and nodded slightly, "How did you meet him?"

"I usually eat at this time." Wang Yunqi said, "I saw him as soon as I arrived at the cafeteria." As he spoke, Wang Yunqi glanced at Gou Liqun, and said with his mouth curled up, "I see this guy coming this way." Let's go, I think he should have dinner with you."

"What?" An Yan asked with a smile, "What problems did you encounter in An's space?"

"There is no problem now." Wang Yunqi frowned and said, "After I finish eating, I have to go to the library to continue reading."

"Didn't you go to the auditorium today?"

"Is there any difference from Huaguo's opening ceremony?" Wang Yunqi said flatly, "It's better to go to the auditorium and do a few more math problems, but I still want to listen to your academic report. "

An Yan smiled, he didn't know what to say about Wang Yunqi.I always feel that this guy seems to want to compete with him, but he dare not say so.what is this?Secret rivalry?Thinking about it, he shook his head, why think so much.Regardless of what this guy wants to do, what does it have to do with him.

"Then after you finish eating, go on reading."

"By the way, when will your new Mason conjecture be finished?"

"When did you complete your twin prime conjecture?"

"About a year or so."

"Then I'm still early." Wang Yunqi said calmly, "I'm not as good as your understanding of number theory, not to mention that I've only started working on this subject for half a year, I think, before the middle of next year. , I shouldn’t be able to do it. Although, your conjecture of twin primes is much more difficult than mine.”

"You don't have to underestimate yourself so much. When I was your age, I was worse than you."

Wang Yunqi raised his head, looked at An Yan dumbfounded and said, "May I ask, are you Guigeng this year?"

"After this year, I'll be 21 years old." An Yan scratched his head and said, "What about you? You just went to college, so you're only seventeen or eighteen years old now? You look like you've just turned 16."

"Well, I'm 17 years old this year." Wang Yunqi said absently, "But compared with you, there is still a big gap."

Emmmmm......

Although, but... why do you always like to compare with me?Am I a unit of measure?An Yan especially didn't understand Wang Yunqi's mentality, he always felt that he was like a unit of measurement, being compared by him.If it was changed to before, he would definitely not be able to bear it.But now, nothing is unbearable.As long as it doesn't touch the core interests, he doesn't want to care so much.

Maybe his second term of middle school is over?

"Why is there such a big gap?" Gou Liqun next to him interjected.In his opinion, no matter whether it is An Yan or Wang Yunqi, they are definitely gods of learning, and this is the future boss.What bike do you want?

One of the two is 21 years old and the other is 17 years old. It can almost be said that the age of academic research has not yet begun.They have more time for academic research than most academic researchers.

Generally, when you graduate with a Ph.D., you really start to conduct academic research.The general Ph.D. graduates have reached their thirties.But for the two of them, they were able to start academic research when they were in college, several years earlier than others, even more than ten years.

Besides, can a guy who can start academic research during college be some mediocrity?

There is a certain gap between them and the average Ph. D., and this gap will only increase with the time they study.It is impossible to have the possibility of shrinking.

This is also the reason why Gou Liqun was shocked, because there is still a gap?Is the world where you learn from gods so scary?I used to think that as a doctor of Beijing University, he was already considered the top batch in China.He is not a graduate student of Peking University, but was admitted to Peking University from another university.

After becoming a graduate student, he discovered that real geniuses have long been conducting academic research in top universities around the world.For example - the two big men in front of me.He used to think that he was a top student, but in the eyes of these two, he was probably the representative of the phalanx of scumbags.

Is this the world of learning gods?Is this why the god of learning is so powerful?It just makes people tremble!

"Why?" Wang Yunqi said with a smile, "I've read some of his materials, and he started to study seriously after repeating his third year of high school. But in more than three years, he can grow into a prominent academician. Famous back, this is probably unprecedented."

"What about you?"

"I have liked reading since I was a child, so I can't compare him, and I can't compare." Wang Yunqi ate very fast, and walked away with the plate in a short while, "I went to the library to read."

"..." This guy really came and went in a hurry.

"What do you think of him?" An Yan asked Gou Liqun while eating.Wang Yunqi's back was no longer visible. Apart from the library and classrooms, this guy seemed to have no other place to go.It's really similar to him, even if he doesn't go to the library, he doesn't know where to go.

"How do you think about it?" Gou Liqun said dumbfoundedly, "This is the matter of your apprentices, don't ask me a scumbag, as a scumbag, I don't know anything, I don't understand anything."

An Yan thought for a while, but didn't speak.After eating, they chatted for a while before leaving the restaurant.Go to the living room of Princeton University. When they came to the living room, Lance was already waiting for them outside.

Seeing them walking towards the living room, Lance said with a sigh of relief, "My God, you finally arrived."

"Are you late?" An Yan still thought that he would come later, and those big bosses might not have come to the living room so early.From what Lance meant, it seemed that they were a little late.

"No, it's not too late." Lance sighed, "Most of the people have already come."

"Who will be in today's symposium?" An Yan looked at Lance curiously and said, "Professor Witten asked me to come. You are here, and your mentor, Professor Deligne, is also here?"

"of course."

"anything else?"

"Mr Langlands."

"Mr. Langlands is here too." An Yan nodded, "Is there no one else?"

"And from Ser Atia."

After Lance finished speaking, An Yan and Gou Liqun were shocked.What, Sir Artia is here?How...how could it be, that was Sir Michael Atiyah.

And Sir Artia is in England, how could he come to America?

"Are you sure there is Sir Artia?" An Yan gasped and asked Lance in an unbelievable voice. His current mood is beyond words.Sir Atiyah should come to attend a little academic conference in Princeton, it seems like a fantasy.

No matter how much they thought, they couldn't figure out why Sir Atiyah would come to this Princeton Mathematical Conference.

"It is indeed Sir Atiyah." Lance nodded very positively, "Although I don't know why Sir Atiyah appeared in Princeton, but he did come."

Lance himself was also very shocked. Looking at his expression, it seemed that he had not calmed down now.

Taking a deep breath, An Yan no longer wants to discuss who else is in this symposium.Whoever is here will lose all brilliance and be dimmed.

Who is Sir Michael Atiyah?That is one of the greatest mathematicians of the twentieth century, with outstanding achievements in topology, differential equations, mathematical physics, algebra and other fields.

Whoever will come here today, unless it is Herr Grothendieck, will be overshadowed and become a foil.An Yan's mentality is very good. I came to this symposium to serve as a foil to learn from the bosses, and to find inspiration by the way.

Didn't expect to meet Sir Michael Atiyah.This was a surprise he had never imagined.

"Is this the first reception room?" The visitor gently took off his felt hat and looked at Lance.He was wearing a dark windbreaker, and looked at An Yan and Gou Liqun expressionlessly.

"Mr. Faltings, this is the first reception room." Lance said politely, "Please!"

Faltings walked into the gate, turned his head to look at An Yan and said coldly, "Why, don't you go in?"

"Come in." An Yan nodded resolutely. Sir Atiyah was in the reception room, and Mr. Faltings was also here.This is really a rare gathering of bigwigs.

Walking into the reception room with Faltings, I found that there were quite a few people in the reception room.Apart from Professor Witten, Sir Atiyah was obviously sitting in the most prominent position.

Mr. Langlands followed, and Professors Deligne and Witten, and Mr. Burgan.After Faltings walked in, he found a seat close to Sir Atiyah and sat down.An Yan quietly sat in the corner, everyone was sitting around, even in the corner, everyone could still see An Yan.

Professor Witten and Professor Deligne smiled at him, and Mr. Langlands looked at An Yan for a while and nodded.

Mr. Bulgan first looked at An Yan for a while, and then turned his head expressionlessly.Faltins, on the other hand, remained silent, and his gaze didn't seem to have a foothold.

An Yan is a little scared now, after all, facing so many big shots.It is absolutely a lie to say that he is not worried, he is already feeling a little uneasy in his heart.With so many bigwigs, even if Mr. Langlands did not win the Fields Medal, he is not short of the Fields Medal.

How many mathematicians have been supported by a Langlands program, the devil knows.

As for the remaining group of bigwigs, they are all Fields Medal winners.It can be said that he is sitting here with a nameless person like him.

"This is?" The first person to speak was Sir Atiyah, he looked at An Yan and said, "A young mathematician?"

"Sir Atiyah." Then Professor Witten spoke, "He is Ann, An Yan from Stanford University, the one who solved the twin prime numbers and determined Ann's conjecture."

"I see." Sir Atiyah spoke a little unclearly.

"Hello, Sir Atiyah." An Yan said with a slight bow, "It's a pleasure to meet you today."

Faltings sneered at this time, but others didn't care.It made An Yan look a bit embarrassed, Bulgan said at this time, "I have seen your An's space, it is very interesting. I plan to do some research on harmonic analysis."

"Thank you." An Yan took a deep breath. If he were to deal with these big guys, he would definitely collapse.

A group of Filipino bigwigs came to the symposium. He is here to be the recorder and witness.

An Yan thought so in her heart, but Gou Liqun was actually under more psychological pressure.He actually met so many famous bigwigs in his lifetime, this is simply... an unimaginable thing.

Can you imagine Faltings sitting not far from you?Sir Atiyah is looking straight at you, and Langlands is looking at you?

Surrounded by a group of bosses, Gou Liqun is very flustered now, he wants to leave here but after thinking about it, he can't.Are you kidding me, what kind of place is this, he comes and leaves whenever he wants?If it wasn't for An Yan, he wouldn't be able to enter this door at all.

Didn't you see that buddy outside the door is still guarding?

Although he has been watched and appraised by the bosses, the misery is worse than that buddy outside the door.With so many bigwigs, he couldn't even hear what the bigwigs were talking about.

"Is everyone here?" Faltings said coldly.

"It's ready." Professor Weiteng nodded slightly, "Then let's start now."

"First, let me talk about the Dipanto equation."

"Dipanto's equation?" Burgan frowned slightly, "Witten, don't tell me you solved the abc conjecture."

"How is it possible?" Professor Witten shook his head and said, "I looked at this academic report earlier, and it seems that Ann submitted a problem about the equation of Dipanto's approximation?"

"The Dipanto equation?" Faltins said, holding his coffee. "What an interesting proposition."

"Then let's get started."

Langlands didn't say anything, and didn't seem to care what topic was being discussed.In other words, it is possible to discuss any topic.

…………

Lance stood outside the gate and walked back and forth, looking at the door in front of him and sighing, not knowing what to say.

Those big guys were inside, but unfortunately I couldn't hear anything.If he could hear what the bosses said, maybe he could make some progress in mathematics.

He asked Professor Deligne why he couldn't enter the reception room to listen to this symposium.He remembered that Professor Deligne allowed him to listen to every symposium before.But this time, Professor Deligne rejected him and told him that he might not understand this symposium, and it would not be of any benefit to his development in mathematics.

Although he believed Professor Deligne's words, he still had some regrets.This time, so many bigwigs were holding a seminar in a reception room, but he had no qualifications to attend the lecture.This is simply - a more painful thing than killing him.

When Wen Maoshi passed by the living room, he saw Lance walking up and down outside the door.

He and Lance are both researchers in the New York laboratory, but now that Lance is completing his doctoral thesis in Princeton, Wen Maoshi is quite familiar with Lance.

He asked curiously, "Lance, what are you doing walking around outside the door?"

"Oh." Lance saw Wen Maoshi walking towards him, rubbed his eyebrows and said, "It's nothing, the professor is holding a seminar inside, and I'll stay outside."

"Oh? Professor Deligne won't let you sit in?"

"That's such a pity." Wen Maoshi said with a smile, "By the way, I have a question about Fourier series and I want to ask you."

"A question about Fourier series?" Lance was stunned for a moment, "Are you working on Angler's space?"

"That's right." Wen Maoshi nodded and replied honestly, "You also know that our New York laboratory has been targeting him. Why did you choose to give up?"

A smile was slightly outlined on the corner of Lance's mouth. He originally thought he was the worst one.But after seeing Wen Maoshi, he was sure that he was not the worst one.At least his professor Deligne still cared about him and gave him advice.As for the guy in front of him, he didn't seem to have any contact with his professor after graduating from his PhD.He wanted to deal with An Yan wholeheartedly, but he didn't know that he had already been sitting with the boss of the Philippine Awards and talking loudly.

The professor thought that his participation in this symposium would do him no good, but at the same time invited An Yan to attend.

What is the truth of this, in fact, a discerning person can figure it out once he thinks about it.An Yan has reached an incomparable level in mathematics.

As for Wen Maoshi, Lance is still confident that he is much better at mathematics than this Wen Maoshi in front of him.Even if he is not the opponent of An Yan, this Wen Maoshi is even less likely to be the opponent of An Yan.

But Lance didn't say much, just smiled and said, "It's nothing, I just have a doctoral dissertation to finish, so I won't join your research group. Wen, do you have anything to do?"

"I still remember what you said." Wen Maoshi said to Lance apologetically, "I still have something to do, so I'm leaving first."

Seeing Wen Maoshi leaving in a hurry, Lance showed an incomprehensible smile.This guy, does he really think that he can stand shoulder to shoulder with An Yan.That's really a big misunderstanding of An Yan and himself. He also had this kind of misunderstanding about himself and An Yan before.

But from now on, he no longer has this kind of misunderstanding.

…………

【y(w)=F(y(w))

That is, given an appropriate initial rational function y0(w)=N0(w)D0(w), the iterative function F( ) can be obtained...

Operational effectiveness refers to the real solution (ActualSolution) of the non-regular scaling equation y(w)=F(αy(σw)), that is, the iterative process (given the initial rational function y0(w))

……

而在极端频率条件1<∣∣w±1∣∣→∞1<|w±1|→∞时，方程(15)简化为一个准正则(quasi-regular)标度方程……

ζ is a constant, y±IQ(w) is called the analytical rough solution (Smyticrough solution) of equation (15), and its operation order μ±IQ=±12 has nothing to do with the scale parameter α and scale factor σ, which is a type I singularity One of the singular properties of scaling equations.

……①]

While explaining her own understanding, An Yan looked at the big bosses around, it seemed that the big bosses were not talking, and were listening to An Yan's words seriously.

Gou Liqun could understand a little bit when An Yan first started talking.But now he finally understood why Wang Yunqi said that he and An Yan could not be compared at all.

This is also very suitable for him. He didn't understand a word of what An Yan said.He could only stare at An Yan with wide-eyed eyes, and the bosses were all in a state of thinking.He is still in a daze alone, why does he want to come to this big boss's party with An Yan.

This is simply making yourself unhappy, it is really a headache.

"The above is the main content of my academic report." After An Yan finished speaking, she sat down.

"It's very exciting." Professor Deligne said with a smile, "I believe that if these contents are explained on the day of the report, it will definitely become the most exciting academic report at Princeton University this year, bar none."

Faltings narrowed his eyes and said slowly, "You are indeed very good, but as far as the mathematicians I have seen, you are not the best among the younger generation.