The direction Liu Yichen chose for mathematics was not the field of number theory that he was famous for, but the field of algebraic geometry, because Professor Delinie was a big master in the field of algebraic geometry.

Algebraic geometry is an important tool for studying analytical number theory. The two actually have similarities. To be honest, Liu Yichen's attainments in the field of algebraic geometry are not low.

If he is an ordinary professor, he is not qualified to be Liu Yichen's tutor because it is very simple. Then he did not win the Fields Medal at the International Mathematician Conference, but he is still a popular candidate at the International Mathematician Conference four years later, even if he has not made any mathematical achievements in the past four years.

Of course, Professor Delinie has this qualification. Professor Delinie is a student of Grothendick and one of the leaders of the Grothendick School. In terms of the awards he won, he only won three awards in the history of mathematics: the Fields Medal, the Wolf Medal and the Crafford Medal.

With Professor Delinie's knowledge, Liu Yichen believed that he would definitely learn a lot from him.

Professor Delinie met Liu Yichen in the office and said with a smile: "Welcome to the Princeton family. I have been waiting for you for a year and a half."

"For me, there will be no rigid requirements on you and will not restrict your development. According to my observations, you are a scholar who is good at independent research. Of course, if you are willing to join my project, I am very welcome. If you are not interested, you can complete the tasks I give you like other doctoral students and prepare your graduation thesis, and you can also get your doctorate degree." Professor Delinie said with a smile.

"Of course, my expectations and requirements for you will be higher than others. After all, with your math level, you are already a world-class mathematician, so my requirements for your graduation thesis are, at least at the Philippine Award level. Work hard, don't be too lazy to yourself and waste your talent. In that case, not only will I be sorry for yourself, but also for many people who have high expectations for you!" Professor Delin Nai said.

Liu Yichen almost spurted out blood.

The achievement of the Philippine Award-level as your graduation thesis!?

Liu Yichen couldn't help but smile bitterly, which meant that he had to make a very small model program such as the first and second question, or the result of the hail conjecture.

This standard is really not very high.

On this day, Liu Yichen also met his seniors, two seniors and one senior. But the three of them looked at Liu Yichen with strange eyes and very polite attitude.

Because this young master who was just starting out was more famous than them, he also won several heavyweight mathematics awards, but they had not even obtained a doctorate degree.

At the same time, Liu Yichen also learned that Professor Delinie is working on a topic - ‘Standard Conjecture’!

Speaking of standard conjecture, we can’t help but talk about Riemann’s conjecture, Wei Yin’s conjecture and ‘Popular Mathematics’ Grothendiek!

The Riemann conjecture, unlike the Zhou conjecture, hail conjecture and other series of relatively independent mathematical problems, although it seems to be simple to describe, it can even be summarized by the sentence "The zero point of the zeta function is on the straight line res(s)=1/2".

But in fact, it is a very big project, similar to a building.

Just like Ponca's conjecture, without Smael introducing it into the high-dimensional concept in the 1960s, without the theory of "studying geometric structures with nonlinear differential equations" developed by Yu Chengtong when proving the Karabi conjecture, there would be no Hamilton's later breakthrough in "i-flow" and the paper on the theory of singularity in 1993, and there would be no final proof of Perelmann.

This is a considerable law proof of a mathematical proposition at the level of millennial puzzles. Even a genius, as introverted as Perelman, cannot skip all the previous work and directly draw the Ponca conjecture.

Only by being able to achieve such achievements can Newton, Gauss, Euler, and Grothendieck join forces to directly jump out of all previous work and directly prove it.

The same is true for Riemann's conjecture, and this building is larger than the Poncalai's conjecture.

It is like an isolated mountain. All mathematicians stand at the foot of the mountain and look up at the mountain. They are not even sure how high the mountain is, whether there are roads or levels during the process of walking up.

The only thing that is confirmed is that there are as many problems as there are mountains in front of you, and no one has solved them yet. Whoever can solve all the problems leading to the ultimate proposition of Riemann's conjecture, then the results born during this period will be enough to win more than ten people in the Fields Medal.

The mathematics community has never stopped studying Riemann's conjecture. "The most brilliant pearl in number theory" is not an easy task. Everyone wants to pick this bright pearl, let their name appear in the history of mathematics and shine brightly, and it is comparable to mathematics masters such as Gauss and Euler.

Therefore, in the past century, many research results have been born, such as the "40% zero point" of Kangrui's critical line theorem, and the "introducing the Riemann conjecture into a quantum mechanic system under special circumstances for explanation" proposed by three mathematicians such as Karl Bend, are all considered as solutions to the Riemann conjecture.

Of course, taking algebraic geometry as the entry point is also an idea for studying the Riemann conjecture.

In 1934, German mathematician Hassey proved the Riemann conjecture on the elliptic curve. In the 1940s, French mathematician Wei Yin proved the Riemann conjecture about the algebraic domain and thus proposed the Riemann conjecture of general clusters, that is, the famous Wei Yin conjecture: Let k be a finite domain with q elements, v is an n-dimensional virtually singular complete algebra cluster defined on k, let m of k expand to k, and the coordinates of the points of v in k are n}, then the function z(u,v) defined by d, ~,-1    nB(u,v)=au art n     , u'1' and the initial condition z(o,v)=1 is called the congruent exaggeration function of algebraic cluster v on the finite domain k, then:

1. z(u,v) is a rational function of u.

2. z(u,v) satisfies a functional equation, which is similar to the functional equations satisfied by the Riemannqua function.

3. The absolute value of the zero point of z(u,v) is the odd power of q-z, and the absolute value of the pole is the even power of q.

4. Suppose vto is a non-odd complete algebraic cluster defined on a certain finite order algebraic domain k, and vo' modularizes it into v, if v

As soon as the Wei Yin conjecture was proposed in 1949, it attracted many famous mathematicians. By the 1960s, this conjecture became the central problem of algebraic geometry. People introduced many new tools and developed some new theories to solve the conjecture.

Wei Yin himself proved some important and special circumstances of the above conjecture. In 1960, DWAK proved Conjecture 1, and Grothendiek also carried out research on Wei Yin's conjecture. In order to prove Wei Yin's conjecture, he formulated a huge algebraic geometry research plan. He proved Conjecture 1 and 2. Later, Drene was influenced by Grothendiek and basically extended and developed according to the research direction he formulated. With his extensive knowledge and keen thoughts, he proved all conjectures in 1973, thus developing a series of important achievements, which was one of the most brilliant achievements in the field of pure mathematics in the 1970s.

It can be said that Professor Deliney won three major awards for making this achievement: Fields Medal, Wolf Mathematics Prize and Crafford Prize!

However, the commonly described Wei Yin's conjecture is the Riemann conjecture in the functional domain, and it is usually nicknamed the "copycat version" Riemann conjecture.

As for the 'standard conjecture', it is a general form of Wei Yin's conjecture. It was proposed by the 'pope' Grothendiek of modern algebraic geometry. This 'standard conjecture' is also known as the crown of the algebraic geometry world.

Back then, Grothendiek explored more deep structures of motive. Corresponding to the order structure of the upper co-tuning ring implemented by motive, Grothendiek conjecture that motive should imply a similar order structure. To this end, he proposed the 'standard conjecture': each motive should have a straight sum decomposition, and the up co-tuning of all orders given to the space can be achieved through this decomposed direct sum term.

If you want to prove the Riemann conjecture, then from the perspective of algebraic geometry, this "standard conjecture" has to be faced.

The mathematics community generally believes that if Grothendieck is focused on mathematical research, then the prover of Wei Yin's conjecture is not Delinie but Grothendieck, because Delinie proves that Wei Yin's conjecture basically continues Grothendieck's research direction. With Grothendieck's mathematical strength, it is only easy to prove Wei Yin's conjecture.

Unfortunately, Grothendieck, who was only 41 years old in 1967, believed that he had established a modern algebraic geometric building. His modern algebraic geometric empire was basically built. He was 41 years old. He abandoned his believers to engage in ecological protection.

As for his proposal of the "standard conjecture", this was entirely a move of digging a hole in a straight pipe without burying people. His disciples and his followers jumped into this big hole one after another, but they couldn't get out of it.

Even Professor Deliney has studied it for thirty years, and the students he taught have also studied "standard conjectures", but unfortunately, it has not been able to solve the "standard conjectures" so far.

There is no doubt that the "standard conjecture" is the most important level leading to the Riemann Conjecture in the field of algebraic geometry. As long as this level is overcome, it is basically said that this road has been basically opened. It is not said that it is completely proved that the Riemann Conjecture can be said to be able to see the top of the mountain in the Riemann Conjecture. It is only a matter of time to prove the Riemann Conjecture.

There is no doubt that it is okay for those who prove the 'standard conjecture' to get a few Fields Medals... The question is whether one person is allowed to get so many fast Fields Medals at one time.

Liu Yichen even suspected that over the years, how many of the students Professor Deliney has been tortured by the "standard guess" and their hearts are shady?

Because there is no specific topic, Liu Yichen can study it freely. He can choose the "Standard Conjecture" research group or choose the research direction himself. He only needs to make the Philippine Award-level results, and then he can obtain a doctorate degree by graduation.
Chapter completed!