This is also a well-known problem that Professor Hamilton encountered in the course of his research on Richy Flow.

The Ricci flow is an equation named after the Italian mathematician Gregorio Ricci. It can be used to complete a series of topological transformations, commonly known as topological surgery. Constructing the geometry to turn irregular manifolds into regular manifolds plays an important role in solving arbitrary three-digit irregular manifolds. It is also a key method to solve the three-dimensional Poincaré conjecture. After learning that Professor Hamilton was studying Richstream, Professor Yau realized the importance of Richflow, and even asked several of his students to study Richstream with Hamilton.

When using the Ricci flow for spatial transformation, later on, there will always be points where there is no control over the direction. These points are called singularities. How to grasp their movements is the key to proving the three-dimensional Poincaré conjecture. After drawing on the work of Yau and Li Weiguang on nonlinear differential equations, in 1993, Hamilton published an important paper on understanding the singularity.

However, it is not more than ten years later, so Professor Hamilton has not yet found a solution to the singularity of the Richie Stream, so when he was researching, although he found the problem, he never found a solution.

"That's the way it is, at the moment when I'm studying the Richie Stream, there is always a problem with the singularity, I don't know how to explain the singularity, I've realized their importance. But these singularities are like a naughty child, and they will always get out of your control. Jun, do you have any good ideas? ”

Junxin put down the cup in his hand, picked up the paper and pen next to him and began to write, draw, and draw. Professor Hamilton soon discovered that this was exactly the correlation equation for the Richy flow that he had just mentioned. I couldn't help but feel a burst of surprise. What surprised him was that he had been studying Richie Flow for almost two years, and he had only mastered some of these equations and formulas, but he just talked to Junxin about it, and Junxin was able to write out these Richie Flow equations exactly as he could. And what surprised him the most was that the formulas he wrote were all crucial formulas, and those who could write such formulas were generally people who had a very deep understanding of Richstream. He had never heard of Junxin learning Richie, but he just listened to Yau Chengtong's suggestion and came to Junxin to talk about his problems.

The good news is that since Junxin can quickly write the core formula of Richflow, it proves that he also has a certain understanding of Richflow.

"Professor, your problem is that the Richy Flow formula cannot control the direction of the singularity after the spatial transformation. I don't have any good advice, but I think Professor Yau will have a good approach. ”

"Won't it?" Hamilton asked suspiciously, "It's still Qiu's suggestion to come to you if he has a way, why do you want me to come to you?" ”

"Hehe, I'm not saying that Professor Qiu realized that some of his results could be used to solve the singularity problem of Richie Flow, but some of his research could indeed be used to solve this problem in depth."

Junxin's words were a bit of a twist, but Hamilton understood. Professor Yau's most notable research is naturally the study of the Calabi-Yau manifold, but this does not mean that Yau's research is only based on the Calabi conjecture. He also has a lot of research, but sometimes it doesn't necessarily attract attention, and apparently what Junxin is talking about is one of them.

"What are you talking about?" Professor Hamilton asked.

In 1972, Yau and Li Weiguang collaborated to develop a set of theories for studying geometric structures using nonlinear differential equations. The Calabi conjecture was made on this basis. I think this recipe is a good reference. ”

"Be specific." Hamilton was starting to get a little excited.

"Okay, Professor." Junxin smiled and began to talk about the application of the theory of nonlinear differential equations in the study of geometric structure in the Richie flow, as well as some of his own understandings and ideas. By the way, some of the ideas in Professor Hamilton's 1993 paper on the singularity of Richy Flow were stated.

Professor Hamilton was shocked, and when Junxin finished speaking, he patted Junxin on the shoulder with excitement, but he couldn't say a word.

"It's going to be a wonderful article!" Suddenly, someone behind me said, "I seem to see the day when Poincaré's conjecture will be solved, it is very exciting!" ”

Junxin looked back, I don't know when, the meeting of the bigwigs has ended, and I don't know when I came to Junxin's back. The United States is the world's research center for geometry, especially in differential geometry, Riemannian geometry and topology, and there are many experts in this field of nature, and they understand what Junxin just said much faster than when Junxin explained Moder's conjecture. And the one who opened his mouth to comment was Professor Yau Chengtong, the founder of the methodological theory that Junxin just talked about.

"Playboy, how's it going? My recommendation is right, right? Professor Yau squeezed his eyes at Professor Hamilton and said. Their friendship was so close that ******* name was a joking nickname given to Hamilton by Yau.

"Very beautiful. I already feel the prospect of solving this problem and I think I'll be able to finish him soon. Jun, you and I will complete the thesis together! ”

Junxin was a little surprised, Hamilton meant to give him the first author, but it was nothing to think about, although this is not common in the scientific community, but it is often seen in the mathematical community.

"You're welcome, Professor Hamilton." After thinking about it, Junxin still refused and said, "I just proposed a solution, which is also an idea." You may have noticed it quickly. If you don't want to, just mention my name. "Junxin means that it is good to be tied for the first author.

"Jun, I feel that the proof of Poincaré's conjecture may fall on you." Professor Qiu said with emotion.

"You've won a prize!" Jun Xin was able to calm down when he encountered this kind of praise before, "I will continue to work hard, but I feel that Richie Flow may be interesting, well, I plan to add a Richie Flow study to the next stage of research." ”

"Okay, let's not talk about that, Professor Qiu, what meeting did you just have? It feels like it's important. ”

"Hehe, this is kept secret for the time being!" Professor Qiu didn't bother to continue to praise or anything, "But tomorrow we will have an external press conference, and you will know when the time comes, and it will be meaningless to say it now." ”

"Oh?" Junxin said that it was getting more and more interesting.