In the lecture hall, Professor Deligne, dressed in a blue shirt and graying hair, was preparing materials for his lecture.

Looking at Deligne's appearance as he looked through the materials, Chen Zhou sighed slightly.

In contrast to his sometimes overconfidence, Deligne was the kind of mathematician who was really, very pure, confident and humble.

It is no exaggeration to say that even if Deligne had not prepared in the slightest, his lecture would have been wonderful and would have been packed.

But now, what Chen Zhou sees is that the other party has a serious attitude.

Actually, Deligne is really a real mathematical genius.

In middle school, he learned the Principia Mathematica of the Bourbaki School in France from his mathematics teacher, Nitz.

The Principia Mathematica of the Bourbaki school is not an ordinary mathematical book.

This is a reinterpretation and cognition of modern mathematics, and the content is very abstract, and it is a very broad and profound work.

It's basically a math book that belongs to the graduate level of a university.

However, Deligne read several of them smoothly and gained a lot of mathematical knowledge.

So much so that before Déligne entered the university, his practical level had reached or even surpassed the level of a mathematics undergraduate.

Later, when Deligne entered the Universiteit de Bruxelles to study mathematics, he became a student of the mathematician Titz.

Professor Teetz is also a math guru, winner of the Wolf Prize in Mathematics and the Abel Prize, and is a typical algebraist known for his research on group theory.

And Titz and Deligne are still old acquaintances.

When Deligne was still in high school, he often went to the university to audit Titz's classes and seminars, and was deeply appreciated by this teacher.

Chen Zhou remembered that in one document, he saw the story of Deligne and Titz.

It is said that once Deligne went on an outing with his classmates and would have missed a seminar.

But when Titz found out, he simply postponed the seminar in order to allow Deligne to attend the lecture smoothly.

It is precisely because of a teacher like Titz that there was the later Deligne.

It was also at the suggestion of Titz that Deligne went to Paris to study algebraic geometry and algebraic number theory.

It was also because he went to Paris that Deligne met the most important teacher of his life, and the one who had a great influence on him, the emperor of algebraic geometry, Grothendieck.

At that time, Paris was full of masters, and it was the golden age of the French school of mathematics.

Grothendieck and Searle, the youngest winner in the history of the Fields Medal, happened to hold a seminar in Paris to discuss the most cutting-edge problems in mathematics.

Grothendieck was responsible for algebraic geometry, and Searle was responsible for algebraic number theory.

It was in this kind of discussion that Deligne was once again sublimated, and he quickly grasped the essence of the mathematical ideas of these two masters.

Even Grothendieck, who many people found odd and difficult to get along with, was more than happy to lend his notes to Deligne for him to sort out and study.

And Grothendieck also bluntly said that Deligne's mathematical level is already on par with him.

You know, Deligne was only in his twenties at that time.

In addition, Deligne received his Ph.D. from the Free University of Brussels at the age of 24 and was directly employed as a professor of mathematics at the same time.

Later, at the age of 26, Deligne became one of the four tenured professors at the Institut des Hautes Etudes des Sciences in France.

At that time, the French mathematical community was a real gathering of stars.

In Chen Zhou's own words, this Nima is the real open life......

In fact, there are quite a few geniuses like Deligne.

This is also one of the reasons why Chen Zhou has been spurring himself to work hard.

"Ahem...... Deligne on the stage coughed lightly and glanced at the crowd in the audience, "First of all, welcome to my lecture today......

"Many years ago, I proved the proposition of the Wey conjecture by ingenuity, despite the fact that there were many new and different main ideas. ”

However, my proof avoids the question of whether the standard conjecture is correct or not, which has left many people, including me, with a lot of regret. ”

"Because of this, I have not given up the study of standard conjectures for a long time after that, especially two years ago, and this regret has been with me all day long......"

The words that Deligne used to open the scene were something that many people did not expect.

Although it is certain that today's lecture is related to the standard conjecture, such an opening ......

Chen Zhou took a deep look at Deligne on the stage.

It is no exaggeration to say that the proof of the Wey conjecture is the greatest achievement of algebraic geometry in recent decades.

Throughout the 60s of the 20th century, the Wey conjecture was the central research topic of algebraic geometry.

And the main battlefield of Wey's conjecture research is France.

In fact, Grothendieck's series of research, and the mathematical ideas he proposed, basically revolved around the Wey conjecture.

But even a great master of algebraic geometry like Grothendieck failed to solve this dilemma.

Of course, the reason why Grothendieck did not solve the Wey conjecture may not be a problem of his knowledge.

Just because he didn't want to get around the unsolved puzzle of standard conjecture.

This is also what Deligne just said.

In addition, two years ago was the time of Grothendieck's death.

Thinking of this, Chen Zhou suddenly felt that Deligne might be using this report meeting to vent a certain emotion in his heart.

Otherwise, no mathematician would have used such an opening statement.

After Deligne said this, without the slightest pause, he officially began his report meeting.

The topic of standard conjecture is the only topic he is currently working on.

It is also the only subject that he is willing to spend his heart and soul on arguing in the future.

"If we use the cohomology theory defined by algebraic closed chains, and then use the topological theory of the category, we can get a good cohomology theory from the cohomology theory......"

"This upper cohomology theory can be called the dual ...... of cohomology theory"

Although Deligne's voice, from the beginning to the present, is flat.

However, there is an inexplicable firmness in the voice.

The blueprint of modern mathematics that Chen Zhou had combed and drawn at the invitation of Nott had a place for standard conjecture.

At this moment, listen to Deligne's narration.

Chen Zhou has a deeper understanding of this most important proposition in algebraic geometry.

Algebraic geometry is the study of algebraic plurality, or algebraic clusters, defined by polynomial equations.

It's probably similar to the manifold defined by a continuous function in topology.

However, manifolds are generalizations of the concepts of curved surfaces, which can be arbitrarily dimensional.

An important feature of polynomials is their global nature.

However, this does not prevent the study of algebraic geometry and algebraic topology, both of which are extremely powerful theories of cohomology and supercohomology, as important tools.

Unlike the singular upper cohomology theory of manifolds in algebraic topology, the upper cohomology theory in algebraic geometry is not so clear.

Just like the close connection between the singular cohomology in algebraic topology and another group now known as topological K-theory, a lot of information can be obtained about the topology of manifolds, etc.

Mathematicians naturally hope to have a similar theory in the cohomology theory of algebraic geometry.

Although the algebraic K-theory was quickly constructed, the corresponding theory of upper cohomology has been constructed only in a few very special cases.

This was already seen as a good advance in the study of algebraic geometry at that time.

On the other hand, the existing theory of upper homology in algebraic geometry is also flawed.

These theories of cohomology often require topological and analytic structures other than the algebraic diversity itself.

Take, for example, the consonance and Hodge structures on Betty.

Moreover, the connection between the various cohomology groups is not close.

Therefore, Grothendieck, who has always been committed to the study of the theory of cohomology in algebraic geometry, predicted the existence of a special class of mathematical objects formed by algebraic closed chains, that is, the multiplicity of algebraic subtypes.

From these objects, a "universal" theory of upper cohomology can be constructed, which has the common essence of all other good theories of upper cohomology.

This "omnipotent" theory of upper cohomology should have the role of singular upper cohomology in algebraic topology.

In particular, there should be a similar sequence of the Atia-Hertzbruch spectrum, linking the theory of upper cohomology with the theory of algebraic K-.

And this particular mathematical object is Grothendieck's Motive theory, or the standard conjecture.

What Deligne is talking about is that in the study of the standard conjecture, this possibility is the long-sought "omnipotence" on the homology.

"Here, we replace the closed interval [0,1]...... in topological homotopy theory with affine straight lines"

Deligne's words clearly entered Chen Zhou's ears and drove Chen Zhou's sensitive mathematical nerves.

The research work that Deligne referred to at the seminar was in fact an extremely abstract and formal work.

In particular, the establishment of the theory of upper cohomology involves the construction of a series of triangular categories and derived categories.

The abstract work of this category can easily fall into an air-to-space metaphysical discussion.

In the end, it was a tirade, but there was no real result.

But Deligne handles this very well, both in developing abstract concepts and in using them to solve big practical problems.

Suffice it to say that this is very Grothendieck's style.

"The study of the standard conjecture is long and difficult, and I hope that more mathematicians can participate in this grand proposition, thank you. ”

Deligne concluded his presentation.

The duration of the briefing was not too long, only about 40 minutes.

But Chen Zhou believes that everyone who listens carefully will definitely gain a lot.

Deligne's research on standard conjectures should be regarded as the most insightful in the current world.

There are many mathematical ideas in this, which inspired Chen Zhou a lot.

So, listening to this report, although the brain is running rapidly, I feel a little tired.

But this harvest is not insignificant.

Chen Zhou felt that if it weren't for his algebraic geometry, relatively speaking, it would be a little weak.

He's sure to have a deeper understanding.

But it doesn't matter anymore.

Importantly, he seems to have found some direction......

"Chen Zhou?"

Liu Maosheng's voice beside him interrupted Chen Zhou's thoughts.

Chen Zhou turned his head suspiciously: "What's wrong?"

Liu Mao asked hesitantly: "Well, did you understand what Professor Deligne said? I see that you were engrossed in the whole process?"

Chen Zhou nodded: "I can still keep up." ”

Liu Mao let out an "oh" and stopped talking.

Chen Zhou glanced at this person strangely, and immediately reacted.

He glanced around again before asking, "Did you not understand?"

Liu Maosheng nodded a little embarrassedly.

Chen Zhou thought for a while and said, "I'll go back and sort out a copy of the content of the report meeting and send it to you." ”

When Liu Maosheng heard this, he raised his head sharply and looked at Chen Zhou incredulously.

Then he nodded frantically and said, "Thank you, thank you, junior brother, thank you, big guy......"

At this time, Zeng Zigu also silently came over and said, "Senior brother, can you give me a copy too?"

Chen Zhou nodded slightly, but also advised: "I can give it to you, but you also have to brush up more literature and enrich your ......"

Liu Maosheng and Zeng Zigu should be in a row, but they only feel that they are not following the wrong boss, and they still have soup to drink.

Looking at the appearance of the two, Chen Zhou didn't say anything more.

It's not helpful to talk too much, it's all up to the individual.

He also realized one thing at this moment, saying that it was a fruitful report meeting.

But that's based on someone who can keep up with Deligne's mathematical thinking.

And most of the students like Liu Maosheng and others here may have fallen behind at the beginning.

Except for the confused feeling that this is a book from heaven, the others are probably only a few mathematical symbols that can still be recognized.

But this is also something that cannot be helped, the more advanced the mathematical problem, the more it belongs to the domain of a few.

After all, mathematics has never been the life of the general public.

After Chen Zhou said that he was willing to give Liu Maosheng and Zeng Zigu the content of the report he had compiled.

Around him, there were a large number of people with hot eyes, staring at them in a daze.

They are still very familiar with Chen Zhou, the new Cole Award winner, the youngest winner in the history of the Cole Prize.

Therefore, they are very envious and jealous of Liu Maosheng and Zeng Zigu.

These two people look like they are the kind of people who are stunned, but they are so lucky to have a big guy to take care of them!

They also want the content of the report that Chen Zhou has compiled......

But they really can't be cheeky to open their mouths.

But then, they made their goals clear.

They looked at Liu Maosheng and Zeng Zigu's eyes, and they became hotter and hotter......

After the report meeting, Chen Zhou originally planned to go back to the hotel with Liu Maosheng and the two immediately.

After all, the harvest of this report meeting still needs to be sorted out by yourself.

It is a stone of the mountain, which can be used to attack jade.

But you have to be able to use other people's knowledge, and you have to make other people's knowledge your own.

It's just that before Chen Zhou left the lecture hall, he was stopped by Deligne.

Deligne has something to say to him alone.