The top student must be diligent

Therefore, they will definitely only choose their own people to do this project.

But at this time, another question arises again. Can they complete the construction project as soon as possible?

In terms of infrastructure strength, no country in the world can surpass China.

Therefore, the Japanese reactor was completed so quickly at the beginning.

As for this JNEO organization...

It is difficult to evaluate.

Refer to the original ITER. The slow construction speed of ITER is largely due to the slow construction speed. After a long construction period, not much has been built.

And if the United States wants to start nuclear fusion experiments as soon as possible, it may have to spend a lot of money on this construction cost.

Therefore, facing the completely sarcastic response from the Ministry of Foreign Affairs, although many people in the US government are broken, there is no good way.

It is not World War II now, and their workers are not the workers in Los Alamos back then.

...

Time has come to the middle of April.

In Xiao Yi's office at the University of Science and Technology.

Xiao Yi is studying his own problems in his office as usual.

He didn't need to worry about what was happening internationally, and the plans of the United States had no impact on him at all.

In the past month, his research on the hail conjecture had reached a fairly deep level.

"The representation of the hail group in the complex vector space has now been completely figured out..."

Xiao Yi looked at the description of the representation of the hail group on the draft paper: [For each positive integer n, there is a vector space V_n of dimension n, and the role of the hail group on V_n is defined: If H_k is a generator, then it maps the kth basis vector in V_n to the 3k+1th (if k is odd) or k/2th (if k is even) basis vector, and the other basis vectors remain unchanged. 】

"Then, including the characterization of invariant vectors, has also been completed, and in the representation space V_n, I just found a special type of vector that can remain unchanged under the action of hail groups, and also proved that these invariant vectors correspond one-to-one to the periodic orbits of hail sequences. In particular, this special vector directly corresponds to the invariant vector of the 4-2-1 cycle, which exists and is unique in each representation space."

Thinking of this, Xiao Yi smiled slightly.

Just to this point, it has already led the mathematics community by a lot.

Because the research on this issue in the mathematics community is really not so advanced.

The most advanced results are probably the results of Terence Tao in 2019.

He used the method of logarithmic density to prove that in the sense of logarithmic density, almost all hail orbits will drop to any given function below the starting point, provided that this function diverges to infinity, no matter how slowly.

In a sense, his proof is equivalent to saying that almost all natural numbers conform to the Collatz conjecture.

However, this proof may be enough in physics, but for mathematics, almost all is never "all".

Just like in mathematics, infinity is not equal to all.

However, despite this, Tao's achievement is still considered one of the most important achievements in the field of Collatz conjecture.

And now, although Xiao Yi has not obtained the result of "almost all" like Tao, the law he found can be regarded as another path or direction to the final proof.

The direction is very important in the proof of mathematical problems.

Just like a tree, there may be quite a lot of branches, but there is only one branch that can lead to the highest point.

Of course, there may be more than one "highest point" in mathematics, but by the same token, once you go in the wrong direction, you may not be able to reach the final answer in the end.

"But now the last question is..."

"Is there a unified method to generate invariant vectors in each representation space?"

Xiao Yi pondered.

This is the most difficult problem in the next research.

He has been thinking about this problem for almost two weeks.

The other questions above only stopped him for a while, but this question alone still made him unable to find a good idea.

"Perhaps, we should try other angles?"

Xiao Yi thought for a while.

However, at this moment, the door of the office was knocked.

"Please come in."

He looked at the door, and then Liang Qiushi opened the door and walked in.

"Teacher! I can't stand it anymore! Help!"

Liang Qiushi shouted as soon as he came in.

Xiao Yi asked with a puzzled look on his face: "What's wrong?"

Liang Qiushi said helplessly: "My thesis has encountered the last problem now, and I still don't know how to solve it!"

"I can only ask the teacher for help!"

Xiao Yi laughed and said: "Wow, you only know to come to me now, there is only one and a half months left before the deadline."

Liang Qiushi put his hands together, bowed and said: "I really have no way, teacher, this problem is too difficult!"

Xiao Yi shook his head and said: "Okay, okay, I told you when you chose the topic that your question is difficult. To be honest, you are just stumped now, and you are already a little bit ahead of me. Expected.”

Hearing what the teacher said, Liang Qiushi smiled and seemed a little proud.

Xiao Yi didn't care about his appearance, and then said: "Okay, show me where you are stuck now."

"OK."

Liang Qiushi then took out a stack of draft paper from the bag in his hand, and then began to show it to Xiao Yi.

"That's the problem..."

"I still can't figure out the proof that the friendly measure μ on the function field F^n must be a non-uniform strong extreme value, and the proof that extends to the non-homogeneous Baker-Sprindzuk conjecture."

There was a rather troubled look on his face, and it was obvious that this question had stumped the mathematical genius.

Xiao Yi took it and carefully watched Liang Qiushi's proof process.

Liang Qiushi's thesis topic involves extending the method of non-homogeneous Diophantine approximation in the real number domain to the function domain.

Diophantine approximation theory has always been a very difficult topic in the field of number theory. It studies the approximation of rational numbers or algebraic numbers to real numbers, as well as related measurement theory and counting theory. It has a long history of research, which can be traced back to ancient times. The research work of Diophantus in the Greek era has also been one of the subjects that has been studied over and over again in the mathematical community.

Of course, Liang Qiushi's subject is quite difficult.

It may be quite difficult for ordinary doctoral students to figure out this paper.

So when Liang Qiushi chose this topic, Xiao Yi also tried to persuade him.

What I didn't expect in the end was that he was able to research this topic to the present point, which is quite unexpected.

Moreover, in fact, Liang Qiushi has already completed a result before. He gave the equivalence property between the extreme value measure and the non-uniform extreme value measure, which can be regarded as the transfer principle in the non-homogeneous case.

This result is enough to be completed as a master's graduation thesis. It is trivial to post anything in a section, and even to be rated as an excellent graduation thesis is completely casual.

When Liang Qiushi completed this result, it was already last year, so he was not satisfied with that result and continued to conduct in-depth research, and finally reached this level.

Xiao Yi looked at it briefly, and then said: "I remember that you seemed to have proved that the friendly measure was strongly contracted before, right?"

"Yes." Liang Qiushi asked doubtfully, "But what is the connection between this and the current problem?"

Xiao Yi smiled and said: "Now that you have completed this step, then what should you do next? In fact, you just need to think about it carefully."

"For example, think more about your previous results, the equivalence between extreme value measures and non-uniform extreme value measures. In other words, your method can also prove that strong extreme values ​​and non-uniform strong extreme values It’s also equivalent.”

Hearing Xiao Yi's reminder, Liang Qiushi's eyes flashed with thought, and then he entered a state of thinking.

As time passed slowly, he suddenly realized it and said in surprise: "The principle of transfer!"

"Yes, that's it." Xiao Yi snapped his fingers: "Now, we already know that the friendly measure μ is a strong extreme value. This is the result proved by Ghosh. You have already cited it in your previous results. On the one hand, μ is also strongly contracted, so you know what to do next.”

Liang Qiushi nodded repeatedly: "I understand."

But then a puzzled expression appeared on his face: "So how should we solve the non-homogeneous Baker-Sprindzuk conjecture next?"

Xiao Yi smiled slightly and said: "For a conjecture problem, we must first figure out what kind of problem this conjecture wants us to discuss."

"For Y∈F^(m×n) and θ∈F^m, we define the non-homogeneous Diophantine exponent ω(Y, θ) as the real number ω that enables the set of inequalities to have solutions for any large T "The true realm."

“Here, the set of inequalities describes the approximation relationship between Yq+p+θ and q. Similarly, we can define the multiplicative version of the non-homogeneous exponent ω × (Y, θ).”

“This conjecture shows that from homogeneous approximation in almost every sense to non-homogeneous approximation that holds for any translation θ, this transfer principle is established under certain conditions. It reflects the mathematical community’s support for Diophantine approximation theory. The pursuit of promotion from homogeneous to non-homogeneous.”

"Now that we have proved that friendly measures are non-uniformly strong extrema on the function domain, the key is that we need to create a connection between natural measures and friendly measures on analytical non-degenerate manifolds."

"However, in fact, this problem is already obvious so far. Here I recommend a paper to you. You can probably figure it out after you go back and read it."

Xiao Yi then turned on the computer, searched for a while, and finally found a paper.

"Yes, it's this paper, "Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation", published in 2007."

Xiao Yi sent the link of this paper to Liang Qiushi's WeChat.

"Please read this paper carefully later. If you still don't understand it after reading it, come to me again."

Liang Qiushi's eyes widened immediately. He didn't expect that his teacher solved his problem almost casually and even directly recommended a paper to him.

And it was published in 2007?

Is this the strength of the youngest mathematical master in history?