Given an Abelian variety on the whole domain, it is conjectured that the rank of its Modal group is equal to the zero-point order of its L function at 1, and the leading coefficient of the Taylor expansion of its L function at 1 is the same as that of the Modal group
There are precise equations between the finite part size, the free part volume, the period of all prime positions, and the sand population.
——This is the BSD conjecture, whose full name is the Birch and Swinnerton-Dyer conjecture. If you feel that the above description is too complicated, it can be roughly described as:
"Establish the connection between the arithmetic information of the finitely generated Abelian group formed by the set of rational points of the elliptic curve E and the analytical information of the Taylor expansion of the corresponding Hasse-Weil L-function L(E,s)."
Is this easier to understand?
To put it simply, the BSD conjecture is a number theory conjecture about describing the structure of rational points on elliptic curves. It is also an important conjecture in congruence numbers, and its difficulty is still higher than Fermat's last theorem.
Although in terms of mathematical significance, the BSD conjecture is not as good as the Riemann conjecture, it is also slightly less difficult. Therefore, after many mathematicians failed to attack the Riemann conjecture, they turned to the BSD conjecture. For this reason, they also invented
A large number of mathematical tools, such as the Gross-Zagier formula, are one of the most powerful tools for promoting the proof of BSD conjectures. They are also the preferred tool for studying BSD conjectures in the mainstream of mathematics. Currently, 90% of the results related to BSD conjectures rely on Gross.
-Zagier formula.
Now Professor Huffman is using an unprecedented new angle to study the BSD conjecture from the direction of matroids and group theory. How could he not arouse strong curiosity among the audience?
Although Professor Huffman is a great expert in matroids and group theory, and has done in-depth research on the Hodge conjecture, would it be too abrupt to suddenly turn to the BSD conjecture?
Amid countless doubtful and curious eyes, Professor Huffman stepped onto the podium.
Professor Huffman, who is nearly forty years old, is a typical "less hair, more knowledge". Almost all the hair on his forehead has fallen out, leaving only a few sparse strands. He stood still and spoke:
"As we all know, the BSD conjectures of order 0 and order 1 have almost been solved, and for higher-order BSD conjectures, we mainly rely on continuing to explore the potential of the Gross-Zagier formula, but so far there is not enough
Eye-catching results. It is obvious that it is very difficult to use the Gross-Zagier formula to study high-order BSD conjectures. I think so. It proves that the BSD conjecture is inseparable from group theory and elliptic curves. Can it be combined with matroids? I spent a lot of time.
It took more than half a year to do this research, and now I will talk about my understanding."
Professor Huffman is a typical mathematician who never talks nonsense. He goes straight to the topic without even making pleasantries.
"Everyone here should know the relationship between the Hasse-Weil function and the Euler product. I just skipped this part and used the Euler product directly..."
Professor Huffman's research results are very outstanding. He studies the high-level BSD conjecture from a completely new perspective. Although there is still a long way to prove it, he started with matroids, combined with group theory, Riemann zeta
Function, Gaussian conjecture in the quadratic domain, shows a promising new direction.
When the one-hour report ended, the audience burst into applause. Faltings, Professor Tao and others all applauded vigorously and nodded in admiration.
Ning Qingyun sighed quietly: "This Professor Huffman is so amazing. He is worthy of being called the mathematician most likely to win the Fields Medal besides you. Just now he skillfully quoted our hypergeometric mapping method.
, I deeply understand the essence of it, and indeed there are many strong people in the international mathematics community. I feel that there is still a lot of gap between me and him."
Qin Ke smiled and said: "He is indeed a genius. At least judging from the report just now, his research on the BSD conjecture has ranked among the top five in the world. This is the result of only half a year of research. But you don't have to
To belittle oneself, he is a super expert in matroids and group theory. He uses the tools he has studied all his life to think about the BSD conjecture. Of course, there will be more obvious results. If you use the three lime number theory methods to study the BSD conjecture, you will also
Achieve outstanding results that are eye-catching.”
Ning Qingyun nodded, her confidence slightly restored. It is indeed true. Professor Huffman has achieved dazzling results starting from matroids and group theory, but whether this direction is correct and whether it can completely prove the BSD conjecture is still a question.
The unknown number.
Just like the original "Hardy-Ramanujan System" and "Jacques Solomon Adamard System", they have been used by countless people to study the Riemann Hypothesis for more than half a century, and have achieved many amazing results.
But in the end it was overturned by Qin Ke. The directions of these two systems can only be very close to the end point of the Riemann Hypothesis, but what is wrong is wrong. No matter how close it is, it is impossible to reach the real end point.
Overall, Professor Huffman's report was very successful. The biggest highlight was the innovation and the profound mathematical skills shown in it.
It can be inferred from the enthusiastic applause of the audience that Professor Huffman has a more than 90% chance of locking in a Fields Medal.
In front of Professor Huffman's "jewels", the following academic reports all turned into "bricks", which made people feel lackluster.
Secondly, there were no such amazing reports in the academic report on the third day. It was not until the fourth day that the famous German mathematician Professor Lepe gave a report titled "Research on Hodge Theory of P-ary System", which once again
Caused a sensation.
This outstanding mathematician, who won the Leibniz Prize, the highest award in the German scientific community, and has high hopes from the German mathematics community, used his original "p-adic analysis technology" to find a breakthrough in the Hodge conjecture.
, winning a warm applause that was almost as warm as Professor Huffman’s.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Two heavyweight seed players in a row launched a charge towards the seven millennium mathematical problems, and both achieved excellent results with innovative methods.
As a result, it can be seen that the competition for this year's Fields Medal is fierce, and it can also be seen that Qin Ke proved the great impact of the Riemann Hypothesis on them - now if the seven millennium problems are not used as the theme of the report, it seems that there is no
I had the nerve to stand on the stage and receive the award with Qin Ke.
The performance of Professors Huffman and Lepe also caused many mathematicians who originally wanted to compete for the Fields Medal to be so shocked that they almost gave up, including Professor Maynard of Eagle Country.
Professor Maynard is indeed a bit unlucky. Every time he worked up his energy to defeat Qin Ke, he was hit again and again. Especially at the last Steele Award academic report meeting, he was directly deduced by Qin Ke on the spot.
The scenario of the fifth set of expressions of the Riemann Hypothesis devastated my confidence, and it has not been fully restored to this day.
At this time, faced with the extremely outstanding performance of the two competitors, Professor Maynard's confidence in winning the prize was shaken violently again. The saddest thing is that his report was just after Qin Ke's report. When he saw the meeting agenda
When the schedule was arranged, Professor Maynard even considered going home.
The only thing that supports him to stay is the thought of "it's time to come" and his final stubbornness as a mathematician.
In the next two days, the mathematicians who gave presentations on stage competed with each other. Professor Emilie Bolivar, a Hungarian mathematician who won the Cher Tibor Memorial Medal, and a female mathematician who won the National Science Award.
Professor Mari Siegel, both of whom performed equally well.
The strong fighting spirit and "big moves" displayed by the popular candidates for this year's Philippine Awards eclipsed the performances of other speakers.
It was under such tremendous pressure that Ning Qingyun gave her 45-minute report.
Judging from the level of reporting time, the young Ning Qingyun only has a 45-minute second gear. Compared with the one-hour first gear of popular candidates such as Huffman, Lepe, Bolivar, and Siegel, it is much longer.
Inferior.
But Ning Qingyun was aroused to fight. After she and Qin Ke gave each other a light slap, she took a deep breath, moved her legs that were slightly trembling due to nervousness, and walked to the reporting platform with firm will.
"Hello everyone, I am Ning Qingyun from Xiaguo Qingmu University. The topic of my report today is "Research on N-S Equations Using Infinite Flow Algorithm for Nonlinear Partial Differential Equations"!"
The girl's soft and melodious voice echoed in the lecture hall that could accommodate thousands of people. The whole audience was slightly startled at first, and then exploded.
Another millennium conjecture!
The report given by Ning Qingyun is not the previous wave guessing, ice guessing, or three lime number theory processing methods, but a brand new, never published research on the N-S equation!
No one thought that Ning Qingyun would unleash such a hidden ultimate move!
Professor Siegel, who had been paying attention to Ning Qingyun, changed his expression.
Currently, many media and academic experts are speculating on the list of winners of this year's Fields Medal. Among them, there are only two female mathematicians in the top ten, namely the female mathematician Mari Siegel of China and Xia Guo.
Ning Qingyun!
Among them, 37-year-old Professor Siegel ranked sixth, while Ning Qingyun ranked ninth.
Professor Siegel understands that when it comes to academic achievements and the number of awards, he is slightly inferior to Ning Qingyun. His biggest advantage is his age.
This is the last International Congress of Mathematicians where she can win the Fields Medal, and among female mathematicians of the same age, no one can match her.
In addition, no female mathematician has won the award in the past three years.
Judging from the gender balance and IMU's history of encouraging women to engage in mathematics research, it is speculated that her probability of winning this Fields Medal is much higher.
In order to steadily surpass Ning Qingyun, Professor Siegel spent countless efforts and mobilized the best graduate students in the school to do research together, and finally formed the "Geometric Analysis and Low-Dimensional Topology in Shimura" reported yesterday.
"Applications of Andre Ault's Conjecture of Clusters", the applause from the audience made Professor Siegel see that the Fields Medal was waving towards him.
But at this moment, Ning Qingyun suddenly released a big move, and it was a big move related to the N-S equation, which made Professor Siegel feel a chill in his heart.
Andre Ault guessed that both fame and significance are inferior to the N-S equation. If Ning Qingyun makes any major breakthrough in the N-S equation, her winning rate will suddenly drop!
Under the anxious and even frightened gaze of Professor Siegel, Ning Qingyun began her 45-minute academic report.
This is the first time that Ning Qingyun has stood on such a high-end stage. Almost all the world's most famous mathematicians have gathered here to listen to her share her latest research results.
Recalling that a few years ago, she was not confident enough to even enter the Provincial Mathematical Olympiad, but now she was on the presentation stage at the International Congress of Mathematicians, which made her feel as if she was in another world.
Ning Qingyun knew that this was because Qin Ke kept pulling her to run, and she gritted her teeth and chased after Qin Ke, putting in unimaginable hardships and efforts, studying hard for countless days and nights.
The results obtained in exchange for this.
"Don't worry, I will always be behind you and try my best to be your second best."
Ning Qingyun met Qin Ke's eyes in the audience, and a strong determination surged in her heart. Her voice, which was originally trembling with nervousness, became fluent. She looked around the dark audience, and combined the stylus and PPT display to display
He spoke the speech he had memorized by heart.
Nonlinear partial differential equations are also a field that Ning Qingyun is extremely good at, mainly due to studying Goldbach's conjecture with Qin Ke.
The N-S equation is a new direction that she has been focusing on in the past six months. She has received the knowledge imparted by Qin Ke through "thinking resonance" and the experience of participating in the "Turbulence" research group of Academician Jiang Weixian in the past two months.
It turned into lines of gorgeous and eye-catching mathematical calculations at this time.
This chapter is not over yet, please click on the next page to continue reading! Qin Ke nodded secretly after hearing this. The outstanding scientific talent that Ning Qingyun had always hidden and inherited from her parents, an academician, has been fully realized through her hard work and study in the past few years.
The discovery made her unknowingly surpass her own limits again and again, and finally bloomed with colorful light at this moment!
45 minutes later, Ning Qingyun bowed slightly: "...Based on the above derivation, I came to the following conclusion that through the infinite flow algorithm of nonlinear partial differential equations, about a quarter of the N-S equations under normal circumstances can be solved.
I will continue to study new mathematical methods in the next three years and strive to achieve greater breakthroughs in the N-S equation. Thank you all, my report ends here!"
Ning Qingyun responded with warm applause that resounded throughout the audience.
Although Ning Qingyun, like Professor Huffman and Professor Lepe, failed to crack the Millennium Conjecture, all three of them have achieved important results in different Millennium Conjectures that no one can ignore.
Originally, many people's impression of Ning Qingyun was "the partner with Qin Ke" and "the girl who was led away by Qin Ke", but her wonderful performance this year made almost everyone look up to her.
This extremely young girl is indeed a mathematician who has reached the top international level! Especially in the fields of number theory and partial differential equations, she will never be inferior to senior mathematics professors in the same field!
Professor Siegel's face was uncontrollably pale. When it came to her performance at the academic seminar, she was still inferior to Ning Qingyun.
Now she only has two chances of winning, one is age, the other is nationality...
Professor Siegel was confused. Everyone present was actually thinking about the same question as her.
"Will IMU resist the pressure of age and give a Fields Medal to 20-year-old Qin Ke, and then give another Fields Medal to Ning Qingyun, who is from the same country and is also only 20 years old?
?”
Ning Qingyun walked off the stage, and Qin Ke gave her a high-five again: "It's great, you are worthy of being my Jun'er."
Ning Qingyun blushed and whispered: "It's your turn next, come on!"
"Don't worry, your excellent performance has given me a lot of motivation."
Qin Ke stood up with a smile and walked to the side of the stage.
At this time, the host was already reading: "Next, I would like to invite Professor Qin Ke from the Department of Mathematics of Xia Guoqingmu University and Qiuzhen Academy to give you a one-hour report. The topic of his report is-"Conjecture from Hailstones"
, Goldbach’s conjecture, and the proof of Riemann’s conjecture, thinking about the future direction of the unification of mathematics!”
The auditorium that had just calmed down was like boiling water with hot oil poured into it, and it boiled instantly!
The unification of mathematics! The number one candidate for this year’s Fields Medal actually chose this unifying theme of mathematics that has attracted countless people’s admiration and discouraged countless others!
Chapter completed!