Xueba's life simulator

Chapter 187 The Collision of Ideas

After Zhang Wei heard Zhou Ming say that he also had some understanding of automorphic forms, he happily talked to Zhou Ming about the issues he was currently studying on automorphic forms.

However, after talking for a while on the topic of automorphism, Zhang Wei shifted the topic to another field of his research, arithmetic geometry.

In fact, it is not accurate to say that it has been transferred, because the topic studied by Zhang Wei is originally the joint application of automorphic forms and arithmetic geometry, and here the two are considered a whole.

"I am going to study the quadratic extension of the possible branches to start with the F of the function Σ of F'/F over a finite field of counting features and a finite set of positions..."

Zhang Wei began to tell Zhou Ming what he was researching, and Zhou Ming listened very carefully.

After Zhang Wei finished speaking, Zhou Ming said to him: "According to what you said, I think you can try to prove the L-function of the product of normalized central derivatives... F'/F and 0≤a≤r, it's okay. Proving the number of self-intersection sets of linear combinations of Heegner-Drinfeld cycles."

After hearing Zhou Ming's suggestion, Zhang Wei rested his chin on one hand and crossed his chest on the other, and began to think about Zhou Ming's suggestion.

At this time, on the awarding platform, the awarding of other awards is also in full swing.

While Zhang Wei was thinking about what Zhou Ming just said in his free time, Li Si, who had been listening to Zhou Ming and Zhang Wei's discussion, also said to Zhou Ming: "Professor Zhou, I also have a problem and I want to discuss it with you. I don't know if I have this honor."

Li Si, who won the Morningside Mathematics Gold Medal with Zhou Ming today, is very polite and humble. Although the three of them are standing on the same stage today, Li Si also knows the gap between him and Zhou Ming.

Zhou Ming also said to him very naturally: "It's no problem to discuss, it's too polite for you to say it's an honor."

"I study string theory, and my main research directions are Landau-Ginzburg model and BCOV theory. I wonder if Professor Zhou knows anything about these two aspects?"

Although the hosts had already mentioned their respective research fields when presenting awards on the podium, before discussing specific issues with Zhou Ming, Li Si explained his research direction to Zhou Ming and asked Zhou Ming Does he know anything about it.

After all, Li Si wasn't sure if Zhou Ming had heard the host's introduction to them clearly at that time. What's more, even if Zhou Ming had heard it before, if Zhou Ming didn't know much about it, then he would start talking to Zhou Ming about it. , Zhou Ming couldn't talk to each other, wouldn't that embarrass Zhou Ming?
String theory is a branch of theoretical physics, and his field of research also belongs to mathematical physics, which is a mathematical theory and mathematical method aimed at studying physical problems, not pure mathematics, and Zhou Ming has not shown much physical mathematics before. aspects of the results.

He's here to ask for advice, not to torture people.

Speaking of string theory, if Li Si had asked Zhou Ming last year, Zhou Ming would have to say sorry to him, because he didn't know much about it.

However, now Zhou Ming has learned a lot about the Landau-Ginzburg model and BCOV theory mentioned by Li Si through the books and documents he read before.

Therefore, Zhou Ming said to Li Si: "I know a little about the Landau-Ginzburg model and BCOV theory, but I don't know much about it, so there may be something wrong.

If I say something wrong in a while, you must correct me. "

When Zhou Ming said to Zhang Wei just now, he said that he had some understanding. What he said to Li Si now is similar to Xi Europe just now. Therefore, in Li Si's view, Zhou Ming's lack of understanding cannot be regarded as the general population. I don't understand deeply.

In Li Si's view, Zhou Ming's lack of understanding refers to the inability to make breakthroughs in this field.

Just now, when Zhou Ming and Zhang Wei talked about automorphic forms and arithmetic geometry, it seemed that they only knew a little bit?And basically it was Zhou Ming who explained Zhang Wei's confusion, and what Zhang Wei said did not surprise Zhou Ming at all.

Therefore, after Zhou Ming finished speaking, Li Si directly told Zhou Ming about the Landau-Ginzburg model and the BCOV theory.

The Landau-Ginzburg model mentioned by Li Si is usually abbreviated as the LG model. It is an important model in the study of topological quantum field theory and an important object in the research of the mirror symmetry conjecture. Its corresponding classical geometric objects are symplectic manifolds and complex manifolds. Various theories on it, such as Gromov-Witten theory, complex structure deformation theory, Hodge structure, periodic mapping, periodic domain, etc.

The BCOV theory is related to the mirror symmetry just mentioned above.

Mirror symmetry is a cutting-edge branch emerging in the direction of modern mathematical physics in the past 30 to 20 years. It originated from the string duality in physics in the 90s.

Through the duality in string theory, Candelas and his collaborators successfully predicted the number of any-order rational curves on a typical Calabi-Yau three-dimensional manifold—“five hypersurfaces”.

This research result has greatly attracted the interest of the mathematics community in string theory, and mirror symmetry as a modern branch of mathematics has also emerged from it.

Subsequently, four physicists Bershadsky, Cecotti, Ooguri, and Vafa gave an effective recursive algorithm for high genus potential functions - BCOV Feynman rule, and established a physical model of full genus mirror symmetry, which is the BCOV theory .

After Li Si told Zhou Ming about his related research in this area and some problems encountered in the research, Zhou Ming thought about it and said to him: "In fact, the research on supersymmetric quantum field theory has shown that the LG model can As a new geometric object for research, the geometric invariants constructed by it can reflect the invariants in classical geometry.

The research on the LG model deformation theory and Hodge theory can be based on the quantum singularity theory to discuss some geometric problems in the LG model...

You can also try to use the NMSP theory to see if you can realize the finite generation properties and finite initial conditions of the BCOV conjecture on the quintic hypersurface. If you can, you can also prove the Yamaguchi-Yau polynomial structure conjecture.

If you spend more energy on the calculation of overall mirror symmetry and high genus count invariance, I think you should be able to achieve some breakthrough results..."

As for the research Li Si mentioned, Zhou Ming made this guess after learning his identity.

After all, many of the things that Qiu Chengtong researches in the mathematics center are naturally in the field of Qiu Chengtong's research.

After hearing these suggestions from Zhou Ming, Li Si didn't know what to say for a while. Zhou Ming gave too many suggestions, and he didn't have time to digest them for a while.

Zhang Wei on the side didn't think about what Zhou Ming said to him earlier, but he didn't know when he started to focus on listening to Zhou Ming's suggestions to Li Si.

"Professor Zhou, are you interested in teaching at Columbia University? With your strength, you must be a tenured professor at Columbia University."

Zhang Wei told Zhou Ming that in his opinion, the domestic environment for studying mathematics is obviously not as good as that of the United States, otherwise there would not be so many young people going to the United States.

Seeing that he had not yet poached corners, Zhang Wei took the lead in poaching corners. Zhou Ming just smiled at this and said to him: "Professor Zhang, as the saying goes, don't treat people with admiration for three days. It's different now." In the past, the domestic scientific research environment is now changing day by day.

I have no interest in teaching in the United States, and I am not used to living there.

On the other hand, Professor Zhang, you grew up in Huaguo since you were a child. Compared with over there, you probably don’t have the habit of living in Huaguo in many places, right?Do you want to come back to Huaguo and come to our Huaguo University of Science and Technology?

I promise, there will be nothing less than what is given to you over there.

I can even guarantee that not only the treatment here is better than that over there, but you will also have a better environment to concentrate on studying mathematics here. "

Seeing that Zhou Ming not only did not agree to his proposal, but instead came to persuade him to go to HKUST, Zhang Wei was originally not prepared to accept Zhou Ming's invitation, but after Zhou Ming finally said that he promised salary and scientific research environment, he began to waver.

Zhang Wei plans to go to the Massachusetts Institute of Technology next year. You must know that the Department of Mathematics of the Massachusetts Institute of Technology is one of the top ten universities in the world for the Department of Mathematics.

Moreover, he didn't quite believe Zhou Ming's guarantee, how could the research environment at Huaguo University of Science and Technology be better than that in the United States.

"Professor Zhou, I have also heard about Luzhou City's 'Ten-Year Plan' for the Science and Technology City, which shows the determination of Luzhou City and even the entire Bai Province.

However, it is enough for HKUST to have you, so I will not go.

but……"

Zhang Wei refused to Zhou Ming, but in the end he added a special word but these two turning points.

"But I have also heard what Professor Zhou and Professor Qiu said before. If Professor Zhou can really teach a master of mathematics within ten years, then I will take the initiative to go to HKUST.

Or, if Professor Zhou can solve a worldwide problem again in the past few years, I am afraid that wherever Professor Zhou is, there will be a holy land of mathematics.

For Professor Zhou, I will also leave the United States and go to HKUST.

However, I am worried that it will not be whether I am willing to go to Huaguo University of Science and Technology, but whether Huaguo University of Science and Technology is willing to accept me. "

Zhou Ming didn't expect that Zhang Wei's last turning point was not a matter of treatment, but had something to do with him.

Therefore, Zhou Ming, who originally didn't have much hope, after hearing Zhang Wei's last words, said to him confidently: "Haha, it seems that it is not long before Professor Zhang comes to our USTC. "

At this time, Li Si on the side had digested some of Zhou Ming's proposal just now, and he said to Zhou Ming: "Professor Zhou just said that a unique calculation can be used to prove the high genus of the Calabi-Yau quintic hypersurface. A series of structural conjectures about mirror symmetry?
This kind of thinking seems to be researched by Tsinghua University, but what is the calculation method that Professor Zhou said? "

When Li Si said this, he quickly thought of some methods that Zhou Ming used to prove the twin prime number and Goldbach's conjecture, so he continued to say to Zhou Ming: "Professor Zhou said that you are proving the twin prime number conjecture and brother What methods did Debach use to conjecture?"

"That's right.

Regarding the symmetry conjecture, in mathematics, after Givental, Lian Wenhao, Liu Kefeng, and Qiu Chengtong independently proved the mirror symmetry conjecture of genus 1996 in 1997 and 0, it was not until 2007 that A.Zinger was able to overcome the genus 1 mirror image formula.

The higher genus mirror symmetry conjecture has always been one of the most difficult challenges in the field, and has stagnated in the years since.

The best way to calculate the genus-1 potential function may be to transform the Witten-type invariant into a twist invariant.

Following this idea, you can say that you try to generalize Zinger's genus 1 mirror image theorem from the local to the whole.

If it can come to fruition, this will be the first major breakthrough in the mirror symmetry of the high-defense whole in many years..."

Zhou Ming continued to explain Li Si's doubts.

While Zhou Ming and Li Si were talking, the silver medals of the Morningside Mathematics Awards were all given out, and the mathematicians who won the silver medals also walked off the awarding platform, and some of them turned towards Zhou Ming. As they walked over, they gathered around and listened to Zhou Ming.

It is a bit sad to say that although this conference is called the World Congress of Chinese Mathematicians, and the Morningside Mathematics Prize is awarded to Chinese, most of the winners are Chinese working overseas.

If Zhou Ming hadn't won the gold award, the two winners would have been divided equally between domestic and foreign countries.

As for the silver awards, most of them are Chinese who grew up in China and then went to work overseas. As for whether they will change their nationality, Zhou Ming is not clear about this.

"Zhang Wei, are you here too?" Among the few people walking towards Zhou Ming, a man with short hair asked Zhang Wei.

"Yun Zhiwei, are you here too? Are you also here to see Professor Zhou?" Yun Zhiwei asked Zhang Wei formally, and Zhang Wei saw that Yun Zhiwei, who was not sitting here, was walking from the podium After getting down, he also walked towards Zhou Ming, and asked him as well.

Although Yun Zhiwei is one year younger than Zhang Wei, both of them were recommended to the School of Mathematical Sciences of Peking University in 2000, which is considered to be the same class.

It's just that Zhang Wei went to Columbia University to study in 2004 four years later, and Yun Zhiwei entered the Department of Mathematics of Princeton University in the same year.

The reason why Yun Zhiwei asked this question was not that he didn't know that Zhang Wei had also won the award, but that he didn't expect Zhang Wei to hook up with Zhou Ming.

"I've been hearing people say Professor Zhou's name over the past year, and it never stops in my ears. This time I finally met Professor Zhou when I returned to China, so I definitely want to meet and chat with Professor Zhou."

This Yun Zhiwei said to Zhang Wei very frankly.

"Then your trip was not in vain. I also came to ask Professor Zhou for some questions. You didn't see what Professor Zhou told me and Li Si just now. No wonder he can solve so many problems at such a young age. Professor Zhou is really amazing.

By the way, what's your problem? "

Before Zhou Ming could speak, the two alumni chatted first.

"My current research field is not still those, mainly geometric representation theory." After Yun Zhiwei said this to Zhang Wei, he began to chat with Zhou Ming again.

"...I don't know much about computers, but my wife is an assistant professor of computer science at the University of Southern California, and she knows a lot about it..."

……

Zhou Ming chatted with these 30-year-old mathematics professors until the end of the morning award ceremony. Although their knowledge and experience are not as extensive as those of the old mathematicians, they are not as good as those old mathematicians in their 80s and 80s. When you are young, your brain is much more active than that of an old man in his [-]s and [-]s, and he has more thoughts in his mind.

In the process of their communication, Zhou Ming also gained something.

Li Zhizhi is right. Sometimes, it is really necessary to get in touch with other people in this field to let ideas collide.

"Although there are still some seminars in the afternoon, the three themes of the afternoon seminars are the golden age of fundamental physics, quantitative biology and biomedicine, and the irrational effects of big data.

These have nothing to do with us, we will leave soon.

Today, we had a long talk with Professor Zhou, which left us unfinished. I really want to talk for three days and three nights, and I will talk to Professor Zhou again when I have a chance.

If Professor Zhou goes to the United States in the future, he must also come to us. "

"Don't worry, there will be opportunities in the future. Besides, you can also come back. The country is now in a period of rapid development, and the environment will get better and better.

In a few years, China will fully catch up with the United States. If you come back then, I’m afraid you won’t be able to keep up with the times, haha. "

"Professor Zhou, we will also consider these. Since Zhang Wei made a promise, I will make the same promise as him."

When Yun Zhiwei, Zhang Wei and the others were about to leave here, these people looked like they were still unsatisfied. It was like reading a book in a bookstore and seeing the excitement, but the book was suddenly taken away. Naturally, it didn’t feel good. .

And Zhou Ming also said something to them to stay.

However, Zhou Ming reckoned that even if they really returned to China in two years, there would be someone among the younger generation in China who could catch up with them.

(End of this chapter)