Soon, Cai Peng's report meeting began.

The problem of minimum differential calculation of dimensional polynomials of differential equations is not very well-known in the mathematical world, but it is a 'fundamental' problem.

Its solution is not only a new approach to the concept of the intensity of partial differential equations in Einstein's 'physics', but also involves the development of mathematical disciplines such as geometry, algebra, and statistics.

In addition, polynomials are also an important concept that can be used to derive many concepts.

For example, the concept of symmetry can be deduced from the symmetry relation of the coefficients of a polynomial, while in calculus, the concepts of integration and differentiation can also be derived from the form of the polynomial and the law of change.

On the whole, its solution will be an important advance in differential algebra and its applications, and its impact on mathematics will be considerable.

On the lecture stage, Cai Peng went from being nervous and rusty at the beginning, to slowly starting to be fluent, and then to becoming more and more handy, and the nervousness of giving a report at this international conference for the first time also faded.

Looking at Cai Peng, Xu Chuan nodded approvingly.

Although this student has taken a lot of detours in mathematics, when he really enters the field that interests and is talented for him, the potential to burst out is quite good.

On the other side, in the corner of the lecture hall, looking at Cai Peng, who was sitting on the stage to report, Professor Zhou Hai, who had been successfully promoted to the director of the School of Mathematics of Nanjing University, couldn't help but feel a little emotional.

"I didn't expect this kid to follow him and come to this height today."

On the side, Rong Zhizhuan, the dean of the Academy of Mathematics, said with a smile: "Cai Peng is also a genius, but he didn't find his suitable field before, but now he has entered the right major, coupled with the training of Academician Xu, it is not surprising that he has this achievement." ”

"Speaking of which, he should be graduating from the smallest differential problem that can prove the dimensional polynomial of a differential equation."

"After the report meeting, you can be pulled to our school as a professor of mathematics, this is also a very good talent, it just happened that the department was reorganized into a college two years ago, and there is an urgent shortage of excellent professors."

Zhou Hai said with a smile: "It's not difficult to pull him over to take up his post, after all, Academician Xu is still here, I believe Cai Peng is also willing, and I'll talk to him later." ”

After a pause, he seemed to think of something, and continued with some emotion: "I don't know if this kid has a chance to win another Fields Medal for our country and our NTU." ”

Up to now, Xu Chuan has only won the Fields Medal medal won by Chinese scholars.

Thinking of Amelia, who won the award before, he couldn't help but hope that his former student could win back a Fields Medal.

After all, this is the crowning glory of mathematics.

On the side, Rong Zhizhuan smiled and said: "There is a chance, if I remember correctly, he seems to be less than thirty this year." The results have already been made in the field of differential equations and polynomials, and if the remaining polynomial calculations of the smallest differential dimension can be solved, there is still a lot of hope. ”

Half an hour has passed, and the report will gradually come to an end.

After the last calculation report was completed, Cai Peng breathed a long sigh of relief, but quickly concentrated his energy again, and he did not dare to relax in the slightest.

Because the next question session is the core part of the whole report meeting.

Especially if he has proved a phased achievement, but has not yet passed the peer review, there must be many peers who have doubts in their hearts.

The first to ask questions was Professor Tao Zhexuan from the University of California.

In the world of mathematics, as the saying goes, mathematical problems and proofs without Tao Zhexuan's support are unqualified, and this 'all-round mathematician', who is known as the new generation, got up and spoke briefly.

"I noticed the expression on page 11, line 6, and there is an interesting line that says that if R,R[x] is a condensation ring, then 1

"Page 11, line 6?"

Cai Peng flipped through the paper and said: "Derived from lemma 1.4, the performance dimension of any loop R is not 1, and the FPD(R) = 0 and 1

"Thank you."

After listening to Cai Peng's statement, Tao Zhexuan nodded approvingly, a very good seedling, no, he should be called a 'mathematician'.

After all, solving part of the problem of the smallest differential calculation of the dimensionality polynomial of a differential equation is enough to deserve the title of a mathematician.

After Tao Zhexuan's questioning ended, the questioning session continued.

Fifteen minutes of questioning is not a long time, and it is impossible to take care of everyone. However, for Cai Peng, as long as he solves the doubts in the hearts of those bigwigs sitting in the front row, this report meeting will be successful.

Following Tao Zhexuan, several bigwigs in the field of differential equations and polynomials also stood up and asked a few questions, and finally got a perfect explanation.

Overall, the presentation went quite smoothly.

"Professor, I did it!"

After the report meeting, Cai Peng quickly ran over, with an excited face.

Xu Chuan patted him on the shoulder and said with a smile: "Very wonderful report, very good." I hope you can climb the new level on the road of mathematics in the future! ”

Cai Peng nodded firmly and said seriously: "I will, professor!" ”

Xu Chuan smiled and said, "Come on." ”

There is nothing more rewarding than watching the students you teach thrive step by step.

Whether it is Gu Bing and Amelia before, or Cai Peng now, or Ding Rui, Tong Yang and others who are studying with him.

Watching batches of students grow up from his hands is really a kind of old fatherly relief.

The core of the International Congress of Mathematicians is always on academic exchanges, with 20 groups and academic reports in different fields during the conference, and a large number of wonderful papers and reports have emerged.

During the conference, Xu Chuan's harvest was also quite rich, whether it was the Gauss Award or the Fields Medal Special Award, it was a new achievement in life.

Of course, the more important thing is the academic gain.

The theory related to space-time holes has enough ideas and is being improved, and the fields of number theory and pure mathematics, which have been relatively rarely touched before, have also seen a number of wonderful reports and papers at this symposium.

Time flies, and in the blink of an eye, the International Congress of Mathematicians has come to its last day.

There will be a presentation on the Young-Mills mass gap, which will be the grandest of the mathematics conference.

In order to meet the needs of not only mathematicians, but also many physicists, the IMU committee that organized the conference specially placed the report in the large lecture hall that presided over the opening ceremony of the conference.

It can accommodate more than 3,000 people at the same time, but it is still full at the moment.

It can be said that most of the scholars who participated in this conference were present.

Not only that, but many physicists who were not very interested in mathematics conferences before also came from all over the world on this day.

Everyone looked eagerly at the lecture desk, and their eyes fell on the young figure standing on it.

If an ordinary person or an ordinary scholar were standing here, facing the black and oppressive heads of the audience, facing this huge pressure, I am afraid that he would be so nervous that he would not even be able to speak.

But for Xu Chuan, who is used to this kind of large-scale report meeting, this is not a scene worth making his heart beat faster.

For him, whether it is to give a report on the stage or to answer the doubts in the minds of those who ask questions, it is not much difficult.

After all, this is not the first time that he has stood on such a stage to face the whole world, nor is it the first time that he has solved such a problem.

Responding to the eyes of the audience, Xu Chuan, who was standing on the newspaper platform, slowly spoke.

"Regarding the Yang-Mills quality gap problem, I'm sure you've read my paper before you come here. So I won't waste your time. ”

After a pause, he continued: "I will briefly explain the proof process in the paper, and explain in detail some of the ideas I used to prove this problem. ”

"If there are still any doubts, you can point them out in the final question session, and I will leave enough time for you."

As he spoke, Xu Chuan clicked on the PPT that had been prepared a long time ago and projected it on the huge screen behind him.

For arbitrary, compact single-group G, there is a massive quantum Yang-Mills field with G as the gauge group on R4, and there is a mass gap > 0！ 》

The caption on the picture is long, but it's the best response to the Jan Mills existential and quality gap issues.

Looking at the screen beside him, Xu Chuan began to explain step by step.

Let all spatial derivatives of the canonical field A = A(t,xk) disappear faster than any power of xk xk as xk xk →∞, uniformly distributed, with respect to bounded t. (This condition does not depend on the Lorentz coordinate system.) Let AdG denote the local Lie algebra of such gauge fields, and G denote the corresponding infinite-dimensional local Lie groups."

【tAk = Ek，tEk =jFjk[Aj，Fjk]， Fjk =jAkkAj[Aj，Ak]】

"Here, the invariant coupling of differentiable structures on high-dimensional manifolds is introduced, and by the characterization theorem, the S-transform is a topological linear isomorphism of (C)."

On the lecture platform, Xu Chuan compared the PPT behind him and explained the proof steps and key nodes of the Yang-Mills quality gap.

Time passed little by little, and when the last mathematical formula was completed, Xu Chuan turned his head to look at the lecture hall, and after scanning the crowd for a while, he slowly spoke.

"When it comes to the Yang-Mills existential and quality gap conundrum, I think we've got an adequate answer. The predictions based on the Yang-Mills equation and the wave-particle duality of matter can describe the objective existence of elementary particles, which we have been able to explain in concrete terms with new mathematical concepts. ”

"I believe this will increase our understanding of the nature of matter, and it will also be an important step in our long-term exploration of understanding the universe through mathematics and physics."

"This concludes my report, thank you for listening."

The moment the words fell, the applause spread from the front row to the back row like a tide, and instantly filled the entire report meeting.

Sitting next to Deligne, Edward Witten clapped and smiled as he spoke, his tone filled with emotion: "Another epic problem has come to an end in his hands. ”

Looking at the young figure standing on the lecture platform, Deligne nodded and said, "Indeed, in today's mathematical world, unless someone completes the Riemann conjecture and achieves the unity of algebra and geometry, I am afraid that no one can surpass him." ”

Witten smiled and said, "Isn't he already interested in the Riemann conjecture?" What if he got rid of this problem again? ”

Hearing this question, Deligne turned his head to look at his friend, and after thinking for a moment, he said: "If he solves the Riemann conjecture and completes the unification of algebra and geometry, I am afraid that his status in the mathematical world is no longer something I can evaluate." ”

After a pause, he added, "At the very least, he will surpass my mentor completely." ”

The applause came in waves in the lecture hall like a tidal wave, and it lasted for a long time.

Looking at the audience, Xu Chuan continued to speak: "The following will be the question session, if you have a problem with the proof of the existence and quality gap problem of Yang Mills, you can raise your hand to ask questions." ”

After the words fell, the arms of the audience were raised in unison, starting from the front row, Xu Chuan selected the audience to answer questions.

He originally thought that there would be a lot of people who had a lot of doubts about this proof, but in fact, in addition to some scholars, more scholars were more interested in when the strong and weak currents would be unified, and he was not interested in other millennial problems.

As for the paper itself, perhaps the scholars who asked these questions no longer have doubts, or perhaps it has conquered everyone!

After the last Yang-Mills mass gap presentation, this year's International Congress of Mathematicians is coming to an end.

According to the usual practice, before the closing ceremonies of Tsarist Russian opera, classical music, etc., the secretary general of the International Union of Mathematicians will announce the location of the next International Congress of Mathematicians.

This is the finale of the International Congress of Mathematicians, second only to the Fields Medal, and is selected by the International Mathematical Union Committee from a list of cities in various countries.

Unlike the Olympic Games, which were once rushed to be held, and now almost no one bids for them, the International Congress of Mathematicians theoretically does not need the support of the applicant country and the applicant city.

Because its funding is paid by the International Mathematical Union itself, whether it is the cost of the hotel or some other support, it is an internal expense.

Of course, generally speaking, no matter which city or country the International Congress of Mathematicians is located, the corresponding city will give a considerable part of the support.

For example, transportation, security, management, and even communication with the hotel to reduce some or even all of the fees.

After all, holding such a grand event has a huge effect on the improvement and promotion of a country's mathematical strength, influence, academic prestige and other aspects.

However, it is not easy to host such an event in your own city.

Because everyone wants to hold such a grand event at their doorstep, it is not only convenient and face-saving, but also can promote the development of the field of mathematics in the motherland.

After all, going abroad for exchange is a very difficult thing for 'poor' mathematicians, especially those who are graduate and doctoral students. In most cases, they can only rely on the professor to take him out to see the world.

But it is completely different in your own country, it only takes a little time and money to communicate with many top experts face-to-face.

This is extremely beneficial for promoting the development of mathematics in a country.

Standing on the lecture platform, Professor Herder Holden, Secretary General of the International Mathematical Union, faced the blazing eyes of the audience, cleared his throat with a smile, and said in a loud and clear voice:

"After consultation with the International Mathematical Union Committee, the venue of the thirtieth International Congress of Mathematicians is—"

"Huaguo Jinling!"

(End of chapter)