Great Country Academician

Fefferman stared at the boy with dark circles in front of his eyes for a long time.

In the end, he sighed softly and said, "You won."

He only sleeps six hours a day, and 14 hours are all spent on research. Fefferman thinks that he has never been so crazy when he was young.

He clearly remembers that when he was the craziest and most serious in his research, he was only studying the local solvability of non-degenerate linear partial differential equations, working more than ten hours a day for more than half a month.

In contrast, his level of explosive liver can be said to be nothing at all.

I worked fourteen hours a day for more than a month and a half.

Thinking about it, I feel terrible. If this state is placed on him, I am afraid that he will die suddenly, right?

The most desperate thing in this world is that a genius who is better than you works harder than you.

But this also made Fefferman sigh.

It's good to be young, you can explode your liver wantonly.

At his age, even if he wanted to stay up late, he couldn't do it.

Now he finally understood why the young man in front of him was able to stand at the top of the mathematics world at the age of twenty.

Ultimate talent + ultimate concentration + ultimate effort, who will succeed if he doesn't succeed?

However, this kind of morbid research method is undesirable, and we still need to find an opportunity to persuade him.

At least, he doesn't want to see such a genius who can promote the development of mathematics die young, or suffer from illnesses in his later years.

On the other side, Deligne, who was immersed in the manuscript, looked up at Xu Chuan, said nothing, and looked down at the manuscript again.

Xu Chuan's research method that almost overdraws his own future has already been criticized many times when he was still a student.

If you don't find a way to solve the problem, that's okay.

But when he found an idea, he, the student, would shut himself in the room and study continuously until he solved the problem or proved that his idea was wrong.

This research method, in Deligne's view, is a joke about his own health.

He has persuaded him many times, hoping that he can relax when researching problems, and not stay up all night and devote all his time to research.

You can go out to play football, basketball, watch concerts, listen to operas and so on.

But it didn't work.

Geniuses are stubborn, just like Perleman rejects all fame and fortune, his student's desire for knowledge and problem solving has also reached an almost morbid state.

Xu Chuan didn't care what the two big shots thought of him.

In fact, although his research on the problem is a bit exhausting, it is not really morbid.

Coupled with the fact that he is young and runs every day, the consumption of his body by staying up late and bursting his liver is actually not as serious as the two of them thought.

Compared with the concerns of the two bosses, he is now more curious about where Fefferman is stuck.

"May I ask, where are you stuck in the research on isospectral problems?"

Xu Chuan's curious question, in his opinion, it is obviously easier for Fefferman to propose ideas.

Hearing the inquiry, Fefferman came back to his senses and said: "I can't construct a regular Borel measure and a sequence of smooth functions that decrease monotonically. This is where I get stuck."

"I tried to use Dirichlet function, I also tried to use Riemann function, and even analytic function, but I couldn't construct a regular Borel measure."

After thinking about it, he added another sentence: "Do you have any good suggestions? If so, please tell me."

Xu Chuan was stunned for a moment, he didn't expect that Fefferman would be stuck in such a place: "If you just simply build a regular Borel measure and a sequence of smooth functions that decrease monotonically, why don't you try to use high-dimensional cobud smooth functions Woolen cloth?"

Hearing this, Fefferman was a little confused, thought for a while, and after confirming that he had never heard of this kind of function, he asked hesitantly: "High-dimensional residual bud function? What is that?"

On the side, Deligne also raised his head curiously, not only Fefferman, even he had never heard of this function name.

Being stared at by the two, Xu Chuan froze again, the memories in his mind flipped quickly, and then he wanted to slap himself in annoyance.

It is now 2018, and the high-dimensional cobud function, a function applied to the identification of function extreme points and singular points, has not yet appeared.

It would take two years for this function to be formally proposed by him and applied to the physical discoveries at that time.

He has memories of the future, but Fefferman and Deligne don't.

However, since this function has been released in advance, there is no other way but to release it in advance.

Fortunately, this research result was developed by himself in the future, not someone else's.

Otherwise, he really thought about whether to write it out.

After all, in his opinion, publishing other people's future research results in advance is tantamount to plagiarism, even if the original owner has no relevant ideas in mind.

No wonder he found Fefferman's idea easier, but Fefferman himself got stuck on this issue.

The reason why he finds it easier is because he has more knowledge of the next ten years, and some of the current problems will be solved in the future.

Exhaling, Xu Chuan dragged out a blackboard from the corner of Xu Chuan's study room. This was what he asked for from Princeton University specifically for the convenience of daily mathematical research.

After pondering for a while, he picked up the chalk and began to write: "Assuming f: (R, 0) → R is a smooth function, if 0 is an Ak-type singularity of y=f(x), then there must be a diffeomorphism Mapping φ: (R, 0) → (R, 0) such that f°φ = ±xk + 1 + f(0).”

"."

On the blackboard, Xu Chuan slowly sorted out the construction and theorems of the high-dimensional co-dead function in his mind.

".For map bud f: (U, p) → (R2, 0), where UR2, f is at P point A—equivalent to 115 singular points (standard form is f(x1, x2) → (x1, x1x22+ x42+x52)) The necessary and sufficient condition is corankf=1, Hessλ(P)

Aside, Fefferman and Deligne watched intently.

From curiosity at the beginning, to surprise, to shock.

As the calculation formulas on the blackboard gradually became complete, both of them saw the value of this function.

Especially Fefferman, there is not only deep surprise and surprise in his eyes, but also incomprehensible confusion.

Judging from the data on the blackboard, this 'high-dimensional cognate function' is not a very complicated thing, and it can even be said to be very basic.

The positive definiteness of the matrix is ​​mainly used, using the Holwitz theorem and the wave front in the three-dimensional Euclidean space R3 where the curved surface is the wave front.

By these two methods a certain equivalence class mapping shoots.

But it is this seemingly basic thing that can be perfectly integrated with the Dirichlet function to construct a regular Borel measure and a monotonically decreasing smooth function sequence in a three-dimensional surface.

The basic structure and basic application can perfectly solve the problem.

It's just that this mathematical method doesn't seem to be developed specifically for mathematics.

Looking at the calculations on the blackboard, Fefferman felt a strong sense of disobedience.

Compared with Videligne, he is not a pure mathematician.

Because he also has some development in physics, and is also a distinguished professor of Fermi National Accelerator Laboratory, specializing in calculating various physical data for Fermilab, so he also has some understanding of physics.

From the calculation formulas on the blackboard, Fefferman was keenly aware of the physical uses of these formulas. In his opinion, these formulas did not seem to be developed for mathematics, but more like tailor-made for physics.

Of course, it can also be applied to mathematics.

For example, now, it happens to be able to solve the isospectrum problem for him.

In front of the blackboard, Xu Chuan made his last stroke, then stopped the chalk in his hand, turned to look at Fefferman and Deligne.

"This is the 'high-dimensional cobud function', which is a method of calculating the extreme point of constructing a smooth function. It may be applied to constructing a regular Borel measure in a three-dimensional surface."

Fefferman and Deligne nodded in unison.

It is not difficult for them to understand these things on the blackboard.

Deligne looked at the calculations on the blackboard and pushed his glasses, and said, "This method is not difficult to construct. It is a very basic thing, but it requires certain skills, and it is not irreplaceable."

"For example, starting from Morse's lemma, similar effects can also be achieved by using the qualitative properties of potential functions near non-degenerate stationary points."

On the side, Fefferman added: "Or using extreme value theory and singularity theory, it should be possible."

After Xu Chuan pointed out this key point, the two of them had some ways to solve this problem from other angles.

But on this road, they are latecomers after all.

Compared with Xu Chuan who pioneered the way, it is undoubtedly easier for latecomers to complete the conception.

After expressing his thoughts, Fefferman continued: "However, what puzzles me is that this method does not seem to be constructed specifically for mathematics, it is more like an inference for the study of physics."

As he spoke, he looked at Xu Chuan and said with certainty, "Is that so? Xu."

Xu Chuan smiled and said, "Yes, last year, I went to CERN with Witten to complete some physical experiments. This method of function derivation is part of the mathematical results derived from the calculation of physical particles."

"It can stably reduce the value of the interval, construct the sharp singularity and the swallowtail singularity, etc., thus providing the analyzability of some previously unanalyzable differential equations."

Hearing this, Fefferman showed such an expression.

On the side, Deligne said with a smile: "Young people's thinking is faster than our two old men. I communicated with Fefferman twice before, but I couldn't find a solution to this problem."

"And as soon as you came out, you provided a complete idea."

"After watching Fefferman this time, he can solve the isospectral problem within three months and complete the phased results of the NS equation."

Fefferman glanced at Deligne, always feeling that he was laughing at himself, and said: "Please don't bring me when you talk about the old man, I am still very young."

"But this time I really have to thank Xu. It seems that I will try to explode my liver after I go back."

After a pause, he looked at Xu Chuan and said with a smile, "By the way, you young people use the word 'explosive liver', right?"