In fact, as for whether he is still a human or not, Lu Zhou himself may not be able to answer this question now.
Not far away.
Everyone was waiting for him to continue.
Every minute from now on belongs to a new world!
Now, however, solving it is as easy as breathing.
"In fact, grand unified theory is the theme of this report meeting."
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
"I may need a little time... maybe, I am really old."
Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the models of rockets.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
These are known.
If he remembered correctly, when he first entered Princeton, about six years ago, Professor Deligne invited him to join the research on the standard conjecture.
Without pausing for too long, Lu Zhou glanced around the silent venue and continued speaking in an unhurried tone.
It was as if the whole world had been wound up again, from silent silence to starting to tick again.
"As we all know, the standard conjecture can be divided into two parts. The first half is Professor Grothendieck's generalization of the Hard-Lefschetz theorem when he was studying the Weil conjecture, which is also known as the Lefschetz standard conjecture."
"If not, then this report meeting will end here."
Six years have passed now.
Without pausing for too long, Lu Zhou glanced around the silent venue and continued speaking in an unhurried tone.
The audience was completely silent.
Schultz, who was sitting not far from him, had almost the same reaction, and even exclaimed in disbelief.
No one spoke.
Just like the beauty of mathematics, it itself will not be open to everyone.
It was too far away and Lu Zhou couldn't see clearly, but as far as he could see, the faces of young and old people were all filled with shock and madness.
"His thinking speed is too fast... To use an inappropriate metaphor, the average person may be riding a rocket... Maybe I am riding a Space-X Falcon, but it is still a rocket, and there is no essential difference from other rockets. But he It was different. He had already boarded something similar to a warp engine. While I was still following a line of thought step by step, he had already folded the entire piece of paper in half, starting from the stem of the proposition. , jumping directly to the results part.”
However, at this point, its historical mission has come to an end.
Obviously, there has been no significant progress on this topic until now.
"His thinking speed is too fast... To use an inappropriate metaphor, the average person may be riding a rocket... Maybe I am riding a Space-X Falcon, but it is still a rocket, and there is no essential difference from other rockets. But he It was different. He had already boarded something similar to a warp engine. While I was still following a line of thought step by step, he had already folded the entire piece of paper in half, starting from the stem of the proposition. , jumping directly to the results part.”
Deligne was silent, looking at the stage with a complicated expression, and said no more.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
He didn't look at the shocked faces behind him, nor did he listen to the exclamations and unbelievable comments that resounded throughout the venue.
"If not, then this report meeting will end here."
Now, however, solving it is as easy as breathing.
These are known.
Just like the beauty of mathematics, it itself will not be open to everyone.
…
Under the gaze of countless expectant eyes, Lu Zhou's frown suddenly relaxed, and in a relaxed tone, Lu Zhou continued.
"What do you think?"
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
"The above is the proof of the standard conjecture."
"Anyone else has any questions?"
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
He didn't look at the shocked faces behind him, nor did he listen to the exclamations and unbelievable comments that resounded throughout the venue.
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
Almost knocking off the ceiling of the stadium.
Even in his own eyes.
And what he wants to prove now is that under general circumstances, it is also true!
"The proof of the standard conjecture is just a starting point. I hope that through my presentation, I can bring some inspiration to your future exploration of beautiful things."
Everything is quiet.
Obviously, there has been no significant progress on this topic until now.
Lu Zhou took a deep breath of cold air to cool down the restless emotions in his chest. He looked at the line on the whiteboard that read "Lefschetz standard conjecture, established!" After being silent for a long time, he slowly spoke.
As the last punctuation mark falls.
The audience was completely silent.
Now, however, solving it is as easy as breathing.
Even for him, it is quite challenging to keep up with this rhythm.
In fact, as for whether he is still a human or not, Lu Zhou himself may not be able to answer this question now.
Perelman, who was sitting in the audience with a frown on his face and his arms folded, suddenly sat up straight and his pupils, which were looking directly at the whiteboard, shrank to a single point.
Obviously, there has been no significant progress on this topic until now.
"As we all know, the standard conjecture can be divided into two parts. The first half is Professor Grothendieck's generalization of the Hard-Lefschetz theorem when he was studying the Weil conjecture, which is also known as the Lefschetz standard conjecture."
These are known.
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
where Intersection is a subalgebraic variety of X.
"...Everyone knows this kind of obvious thing even if you don't say it."
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
The dull or solemn expressions of the audience in the front row have already told everything about their mood and state at this moment. No one has recovered from the visual and spiritual shock, so naturally they can't talk about their feelings.
"The second half is Hodge's standard conjecture."
The dull or solemn expressions of the audience in the front row have already told everything about their mood and state at this moment. No one has recovered from the visual and spiritual shock, so naturally they can't talk about their feelings.
If he remembered correctly, when he first entered Princeton, about six years ago, Professor Deligne invited him to join the research on the standard conjecture.
"The second half is Hodge's standard conjecture."
The audience was completely silent.
Lu Zhou seemed to be tangled up in some troublesome matter. He frowned and thought for a long time.
There are also theories yet to be discovered.
Still no one spoke.
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
The audience was completely silent.
The two old men sat there, staring motionless at the whiteboard.
It was too far away and Lu Zhou couldn't see clearly, but as far as he could see, the faces of young and old people were all filled with shock and madness.
At this moment, he was not only ascending to the throne of the temple of mathematics, but also the pinnacle of human mind.
There are more and more calculations on the whiteboard.
Everyone was waiting for him to continue.
It's not easy though.
"Anyone else has any questions?"
Of course they won't understand.
The standard conjecture is one of the most profound propositions in algebraic geometry.
Under the gaze of countless expectant eyes, Lu Zhou's frown suddenly relaxed, and in a relaxed tone, Lu Zhou continued.
Schultz, who was sitting not far from him, had almost the same reaction, and even exclaimed in disbelief.
"In fact, grand unified theory is the theme of this report meeting."
"never mind."
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
And what he wants to prove now is that under general circumstances, it is also true!
"Although it is just to demonstrate the application of grand unified theory in studying algebraic geometry problems..."
About ten minutes passed before he turned around, faced the silent venue, and spoke slowly.
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
It was too far away and Lu Zhou couldn't see clearly, but as far as he could see, the faces of young and old people were all filled with shock and madness.
Still no one spoke.
At this moment, he was not only ascending to the throne of the temple of mathematics, but also the pinnacle of human mind.
"But now that it's all written down."
Although there is no sound, it is like a song.
Just like the beauty of mathematics, it itself will not be open to everyone.
After so many years of friendship, this was the first time he heard this guy admit that he was old.
About ten minutes passed before he turned around, faced the silent venue, and spoke slowly.
"I may need a little time... maybe, I am really old."
"The second half is Hodge's standard conjecture."
Not far away.
"It's better to solve it together."
It was as if the whole world had been wound up again, from silent silence to starting to tick again.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
Lu Zhou retracted his strokes on the whiteboard, took two steps back, and looked at his results as if he were looking at a work of art for a long, long time.
There are more and more calculations on the whiteboard.
…
Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the models of rockets.
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
He didn't look at the shocked faces behind him, nor did he listen to the exclamations and unbelievable comments that resounded throughout the venue.
If he remembered correctly, when he first entered Princeton, about six years ago, Professor Deligne invited him to join the research on the standard conjecture.
Under the gaze of countless expectant eyes, Lu Zhou's frown suddenly relaxed, and in a relaxed tone, Lu Zhou continued.
Schultz, who was sitting not far from him, had almost the same reaction, and even exclaimed in disbelief.
After so many years of friendship, this was the first time he heard this guy admit that he was old.
"...Everyone knows this kind of obvious thing even if you don't say it."
The audience was completely silent.
"As we all know, the standard conjecture can be divided into two parts. The first half is Professor Grothendieck's generalization of the Hard-Lefschetz theorem when he was studying the Weil conjecture, which is also known as the Lefschetz standard conjecture."
From the perspective of species and civilization, all of this is too small.
Lu Zhou, who said these words lightly, walked to the blank whiteboard next to him with many complex emotions such as awe, emotion, and calm, and stopped for a moment.
After about half a minute, he shook his head.
Regarding this strange metaphor, Mr. Qiu said nothing, but silently moved his gaze to the almost filled whiteboard.
The standard conjecture is one of the most profound propositions in algebraic geometry.
Under the gaze of countless expectant eyes, Lu Zhou's frown suddenly relaxed, and in a relaxed tone, Lu Zhou continued.
Bathed in the applause that resounded throughout the venue, Lu Zhou gently placed the marker in his hand, destined to become a historical relic, on the podium, took a half step back, bowed slightly, and turned to walk towards the audience.
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
The applause sounded like a downpour.
The same conversation was taking place on the other side of the venue.
"I will be here these three days. If you have any new questions later, you can come here to find me."
Standing in front of this whiteboard that connects the universe, no matter nationality, race, or cultural background, everything seems pale and loses its meaning.
Even in his own eyes.
Its profundity lies not only in its complex beauty, but also in its profound inferences.
From the perspective of species and civilization, all of this is too small.
Lu Zhou seemed to be tangled up in some troublesome matter. He frowned and thought for a long time.
Schultz, who was sitting not far from him, had almost the same reaction, and even exclaimed in disbelief.
It's just that the person who asked the question was Mr. Qiu Chengtong, and the person who answered was Professor Tao.
Most directly, if the standard conjecture is true, it can directly deduce the Weil conjecture, and it can be deduced that the role of Frobenius on the cohomology group of smooth projective algebraic varieties is semi-simple, and it can even be deduced that the algebraic closed chain in the algebraic variety ( The numerical equivalence and homological equivalence of algebraic cycle are the same equivalence relationship, etc.
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
"The second half is Hodge's standard conjecture."
"In fact, grand unified theory is the theme of this report meeting."
Use this moment as a watershed moment.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
These are known.
At the moment when Lu Zhou successfully extended the Hodge theory on compact manifolds to complete non-compact manifolds, Professor Deligne suddenly broke the silent agreement and spoke.
"Thanks."
Lu Zhou seemed to be tangled up in some troublesome matter. He frowned and thought for a long time.
After looking at the stunned Schultz, Perelman, who had been silent until now, muttered a rare word.
The sound echoed in the empty venue.
There are also theories yet to be discovered.
"It's better to solve it together."
There are also theories yet to be discovered.
Almost knocking off the ceiling of the stadium.
However, for those who can understand it, this kind of beauty is shocking to the heart and reaches the depths of the soul.
"Thanks."
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
Six years have passed now.
And what he wants to prove now is that under general circumstances, it is also true!
As the last punctuation mark falls.
In fact, as for whether he is still a human or not, Lu Zhou himself may not be able to answer this question now.
However, at this point, its historical mission has come to an end.
Not far away.
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
After about half a minute, he shook his head.
"The above is the proof of the standard conjecture."
Everything is quiet.
These are known.
As he raised his hand, the pen on the whiteboard moved.
As he raised his hand, the pen on the whiteboard moved.
This is a property of L^2 cohomology theory mentioned by Sir Attiyah in his paper on the study of discrete groups and elliptic operators published in the "Annals of Mathematics" in 1976.
The applause sounded like a downpour.
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
Obviously, there has been no significant progress on this topic until now.
"In fact, grand unified theory is the theme of this report meeting."
[… When i≤n/2, the quadratic form x→(-1)^i·L^(r-2i) on A^i(X)∩ker(L^(n-2i+1)) xx is positive...]
The audience was completely silent.
Sitting next to him, Faltings said nothing.
There are more and more calculations on the whiteboard.
Now, however, solving it is as easy as breathing.
where Intersection is a subalgebraic variety of X.
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
However, for those who can understand it, this kind of beauty is shocking to the heart and reaches the depths of the soul.
"As we witness together at this moment, our theory has once again been verified that our universe is perfect and it is in line with mathematical beauty."
As the last punctuation mark falls.
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
"The second half is Hodge's standard conjecture."
After so many years of friendship, this was the first time he heard this guy admit that he was old.
About ten minutes passed before he turned around, faced the silent venue, and spoke slowly.
Many people sitting in the audience could not absorb information as fast as he could write on the blackboard.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
Its profundity lies not only in its complex beauty, but also in its profound inferences.
And what he wants to prove now is that under general circumstances, it is also true!
"Thanks."
The standard conjecture is one of the most profound propositions in algebraic geometry.
"The second half is Hodge's standard conjecture."
Everyone was waiting for him to continue.
That smile is like the wind in early spring in March. Although there is no special tension, it blows into the hearts of every listener. Wherever it blows, the ice melts, the snow melts, and the clouds bloom and the sun rises.
Just like the beauty of mathematics, it itself will not be open to everyone.
"The second half is Hodge's standard conjecture."
Time passed by minute by minute.
However, for those who can understand it, this kind of beauty is shocking to the heart and reaches the depths of the soul.
At this moment, he was not only ascending to the throne of the temple of mathematics, but also the pinnacle of human mind.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
Although this is an indisputable fact, hearing this guy admit it in person still makes him a little melancholy...
Although there is no sound, it is like a song.
Everything is quiet.
"Anyone else has any questions?"
Every minute from now on belongs to a new world!
There are more and more calculations on the whiteboard.
After so many years of friendship, this was the first time he heard this guy admit that he was old.
He didn't look at the shocked faces behind him, nor did he listen to the exclamations and unbelievable comments that resounded throughout the venue.
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
Every minute from now on belongs to a new world!
At the moment when Lu Zhou successfully extended the Hodge theory on compact manifolds to complete non-compact manifolds, Professor Deligne suddenly broke the silent agreement and spoke.
Schultz, who was sitting not far from him, had almost the same reaction, and even exclaimed in disbelief.
The silence in the audience continued.
Many people sitting in the audience could not absorb information as fast as he could write on the blackboard.
"The above is the proof of the standard conjecture."
Even for him, it is quite challenging to keep up with this rhythm.
No one spoke.
"Thanks."
At this moment, he was not only ascending to the throne of the temple of mathematics, but also the pinnacle of human mind.
He didn't look at the shocked faces behind him, nor did he listen to the exclamations and unbelievable comments that resounded throughout the venue.
where Intersection is a subalgebraic variety of X.
Not far away.
Perelman, who was sitting in the audience with a frown on his face and his arms folded, suddenly sat up straight and his pupils, which were looking directly at the whiteboard, shrank to a single point.
"In fact, grand unified theory is the theme of this report meeting."
[… When i≤n/2, the quadratic form x→(-1)^i·L^(r-2i) on A^i(X)∩ker(L^(n-2i+1)) xx is positive...]
"As we all know, the standard conjecture can be divided into two parts. The first half is Professor Grothendieck's generalization of the Hard-Lefschetz theorem when he was studying the Weil conjecture, which is also known as the Lefschetz standard conjecture."
Without pausing for too long, Lu Zhou glanced around the silent venue and continued speaking in an unhurried tone.
After looking at the stunned Schultz, Perelman, who had been silent until now, muttered a rare word.
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
Schultz, who was sitting not far from him, had almost the same reaction, and even exclaimed in disbelief.
Sitting next to him, Faltings said nothing.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
Not far away.
Even in his own eyes.
It's not easy though.
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
Lu Zhou took a deep breath of cold air to cool down the restless emotions in his chest. He looked at the line on the whiteboard that read "Lefschetz standard conjecture, established!" After being silent for a long time, he slowly spoke.
"... Use the L^2 cohomology method to obtain the topological information of the compact quotient of complete manifolds, and extend the Hodge theory on compact manifolds to complete non-compact manifolds!"
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
Its profundity lies not only in its complex beauty, but also in its profound inferences.
No one spoke.
"God...he, he is a genius!"
Obviously, there has been no significant progress on this topic until now.
Now, however, solving it is as easy as breathing.
This is a property of L^2 cohomology theory mentioned by Sir Attiyah in his paper on the study of discrete groups and elliptic operators published in the "Annals of Mathematics" in 1976.
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
Not far away.
What was surprising was not only the ingenuity of his conception, but what really shocked Schulz was that he used these mathematical tools as easily as breathing.
Regarding this strange metaphor, Mr. Qiu said nothing, but silently moved his gaze to the almost filled whiteboard.
His shoulders relaxed.
No, to be precise, it’s not just the Chinese mathematics community.
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
His shoulders relaxed.
The applause sounded like a downpour.
Obviously, there has been no significant progress on this topic until now.
It was as if those mathematical tools were created just for him.
Everyone was waiting for him to continue.
"The above is the proof of the standard conjecture."
After looking at the stunned Schultz, Perelman, who had been silent until now, muttered a rare word.
Six years have passed now.
Not far away.
"...Everyone knows this kind of obvious thing even if you don't say it."
Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the models of rockets.
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
After about half a minute, he shook his head.
At the moment when Lu Zhou successfully extended the Hodge theory on compact manifolds to complete non-compact manifolds, Professor Deligne suddenly broke the silent agreement and spoke.
Not far away.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
After so many years of friendship, this was the first time he heard this guy admit that he was old.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
The era of standard conjecture is over.
The two old men sat there, staring motionless at the whiteboard.
At this moment, he was not only ascending to the throne of the temple of mathematics, but also the pinnacle of human mind.
Although there is no sound, it is like a song.
At the moment when Lu Zhou successfully extended the Hodge theory on compact manifolds to complete non-compact manifolds, Professor Deligne suddenly broke the silent agreement and spoke.
Its profundity lies not only in its complex beauty, but also in its profound inferences.
Time passed by minute by minute.
[… When i≤n/2, the quadratic form x→(-1)^i·L^(r-2i) on A^i(X)∩ker(L^(n-2i+1)) xx is positive...]
"Although it is just to demonstrate the application of grand unified theory in studying algebraic geometry problems..."
where Intersection is a subalgebraic variety of X.
Everyone was waiting for him to continue.
"What do you think?"
Sitting next to him, Faltings said nothing.
This is a property of L^2 cohomology theory mentioned by Sir Attiyah in his paper on the study of discrete groups and elliptic operators published in the "Annals of Mathematics" in 1976.
As he raised his hand, the pen on the whiteboard moved.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
Sitting next to him, Faltings said nothing.
"Thanks."
"In fact, grand unified theory is the theme of this report meeting."
Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the models of rockets.
No, to be precise, it’s not just the Chinese mathematics community.
These are known.
After about half a minute, he shook his head.
"It's better to solve it together."
The standard conjecture is one of the most profound propositions in algebraic geometry.
"As we all know, the standard conjecture can be divided into two parts. The first half is Professor Grothendieck's generalization of the Hard-Lefschetz theorem when he was studying the Weil conjecture, which is also known as the Lefschetz standard conjecture."
"I may need a little time... maybe, I am really old."
Bathed in the applause that resounded throughout the venue, Lu Zhou gently placed the marker in his hand, destined to become a historical relic, on the podium, took a half step back, bowed slightly, and turned to walk towards the audience.
There are more and more calculations on the whiteboard.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
"Anyone else has any questions?"
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
Six years have passed now.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
Of course they won't understand.
"...Everyone knows this kind of obvious thing even if you don't say it."
After so many years of friendship, this was the first time he heard this guy admit that he was old.
Even in his own eyes.
It was as if those mathematical tools were created just for him.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
The era of standard conjecture is over.
Although there is no sound, it is like a song.
Although this is an indisputable fact, hearing this guy admit it in person still makes him a little melancholy...
"What do you think?"
However, at this point, its historical mission has come to an end.
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
Use this moment as a watershed moment.
After a while, he clenched his fists and sighed softly.
After a while, he clenched his fists and sighed softly.
The same conversation was taking place on the other side of the venue.
Its profundity lies not only in its complex beauty, but also in its profound inferences.
"Although it is just to demonstrate the application of grand unified theory in studying algebraic geometry problems..."
Lu Zhou seemed to be tangled up in some troublesome matter. He frowned and thought for a long time.
This is a property of L^2 cohomology theory mentioned by Sir Attiyah in his paper on the study of discrete groups and elliptic operators published in the "Annals of Mathematics" in 1976.
It's just that the person who asked the question was Mr. Qiu Chengtong, and the person who answered was Professor Tao.
"I will be here these three days. If you have any new questions later, you can come here to find me."
The audience was completely silent.
"Although it is just to demonstrate the application of grand unified theory in studying algebraic geometry problems..."
About ten minutes passed before he turned around, faced the silent venue, and spoke slowly.
It's not easy though.
"... Use the L^2 cohomology method to obtain the topological information of the compact quotient of complete manifolds, and extend the Hodge theory on compact manifolds to complete non-compact manifolds!"
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
"I will be here these three days. If you have any new questions later, you can come here to find me."
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
It's not easy though.
His shoulders relaxed.
"The proof of the standard conjecture is just a starting point. I hope that through my presentation, I can bring some inspiration to your future exploration of beautiful things."
"But now that it's all written down."
And what he wants to prove now is that under general circumstances, it is also true!
Standing in front of this whiteboard that connects the universe, no matter nationality, race, or cultural background, everything seems pale and loses its meaning.
Even for him, it is quite challenging to keep up with this rhythm.
"It's better to solve it together."
Time passed by minute by minute.
[… When i≤n/2, the quadratic form x→(-1)^i·L^(r-2i) on A^i(X)∩ker(L^(n-2i+1)) xx is positive...]
"His thinking speed is too fast... To use an inappropriate metaphor, the average person may be riding a rocket... Maybe I am riding a Space-X Falcon, but it is still a rocket, and there is no essential difference from other rockets. But he It was different. He had already boarded something similar to a warp engine. While I was still following a line of thought step by step, he had already folded the entire piece of paper in half, starting from the stem of the proposition. , jumping directly to the results part.”
At this moment, he was not only ascending to the throne of the temple of mathematics, but also the pinnacle of human mind.
There are also theories yet to be discovered.
"The above is the proof of the standard conjecture."
It's just that the person who asked the question was Mr. Qiu Chengtong, and the person who answered was Professor Tao.
Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the models of rockets.
The standard conjecture is one of the most profound propositions in algebraic geometry.
Lu Zhou seemed to be tangled up in some troublesome matter. He frowned and thought for a long time.
Regarding this strange metaphor, Mr. Qiu said nothing, but silently moved his gaze to the almost filled whiteboard.
Sitting next to him, Faltings said nothing.
Standing in front of this whiteboard that connects the universe, no matter nationality, race, or cultural background, everything seems pale and loses its meaning.
After a while, he clenched his fists and sighed softly.
Standing in front of this whiteboard that connects the universe, no matter nationality, race, or cultural background, everything seems pale and loses its meaning.
"I may need a little time... maybe, I am really old."
"Well done!"
"The proof of the standard conjecture is just a starting point. I hope that through my presentation, I can bring some inspiration to your future exploration of beautiful things."
These are known.
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
…
Lu Zhou, who said these words lightly, walked to the blank whiteboard next to him with many complex emotions such as awe, emotion, and calm, and stopped for a moment.
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
At the moment when Lu Zhou successfully extended the Hodge theory on compact manifolds to complete non-compact manifolds, Professor Deligne suddenly broke the silent agreement and spoke.
It's not easy though.
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
Lu Zhou took a deep breath of cold air to cool down the restless emotions in his chest. He looked at the line on the whiteboard that read "Lefschetz standard conjecture, established!" After being silent for a long time, he slowly spoke.
Even in his own eyes.
No, to be precise, it’s not just the Chinese mathematics community.
"If not, then this report meeting will end here."
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
However, for those who can understand it, this kind of beauty is shocking to the heart and reaches the depths of the soul.
Lu Zhou took a deep breath of cold air to cool down the restless emotions in his chest. He looked at the line on the whiteboard that read "Lefschetz standard conjecture, established!" After being silent for a long time, he slowly spoke.
Even in his own eyes.
Even if we look around the world and look back in history, we may not be able to find a more glorious moment.
There was no applause either.
Lu Zhou, who said these words lightly, walked to the blank whiteboard next to him with many complex emotions such as awe, emotion, and calm, and stopped for a moment.
Everything is quiet.
At this moment, he was not only ascending to the throne of the temple of mathematics, but also the pinnacle of human mind.
The same conversation was taking place on the other side of the venue.
Every minute from now on belongs to a new world!
"... Use the L^2 cohomology method to obtain the topological information of the compact quotient of complete manifolds, and extend the Hodge theory on compact manifolds to complete non-compact manifolds!"
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
Everything is quiet.
The two old men sat there, staring motionless at the whiteboard.
"Thanks."
"If not, then this report meeting will end here."
Standing in front of this whiteboard that connects the universe, no matter nationality, race, or cultural background, everything seems pale and loses its meaning.
However, for those who can understand it, this kind of beauty is shocking to the heart and reaches the depths of the soul.
Standing in front of this whiteboard that connects the universe, no matter nationality, race, or cultural background, everything seems pale and loses its meaning.
It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.
Still no one spoke.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
And what he wants to prove now is that under general circumstances, it is also true!
From the perspective of species and civilization, all of this is too small.
From the perspective of species and civilization, all of this is too small.
Obviously, there has been no significant progress on this topic until now.
After looking at the stunned Schultz, Perelman, who had been silent until now, muttered a rare word.
However, for those who can understand it, this kind of beauty is shocking to the heart and reaches the depths of the soul.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
The audience was completely silent.
Still no one spoke.
As the last punctuation mark falls.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
Everyone was waiting for him to continue.
The applause sounded like a downpour.
What was surprising was not only the ingenuity of his conception, but what really shocked Schulz was that he used these mathematical tools as easily as breathing.
These are known.
Everything is quiet.
Even for him, it is quite challenging to keep up with this rhythm.
As the last punctuation mark falls.
Sitting next to him, Faltings said nothing.
It was as if those mathematical tools were created just for him.
Now, however, solving it is as easy as breathing.
Obviously, there has been no significant progress on this topic until now.
The same conversation was taking place on the other side of the venue.
Still no one spoke.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
Lu Zhou retracted his strokes on the whiteboard, took two steps back, and looked at his results as if he were looking at a work of art for a long, long time.
"But now that it's all written down."
The audience was completely silent.
Lu Zhou took a deep breath of cold air to cool down the restless emotions in his chest. He looked at the line on the whiteboard that read "Lefschetz standard conjecture, established!" After being silent for a long time, he slowly spoke.
"never mind."
It felt like a heavy burden had been lifted off. Lu Zhou, who had been expressionless, suddenly had a pleasant smile on his face.
Lu Zhou retracted his strokes on the whiteboard, took two steps back, and looked at his results as if he were looking at a work of art for a long, long time.
The standard conjecture is one of the most profound propositions in algebraic geometry.
Regarding this strange metaphor, Mr. Qiu said nothing, but silently moved his gaze to the almost filled whiteboard.
Lu Zhou retracted his strokes on the whiteboard, took two steps back, and looked at his results as if he were looking at a work of art for a long, long time.
Lu Zhou retracted his strokes on the whiteboard, took two steps back, and looked at his results as if he were looking at a work of art for a long, long time.
"never mind."
About ten minutes passed before he turned around, faced the silent venue, and spoke slowly.
The audience was completely silent.
"If not, then this report meeting will end here."
"The above is the proof of the standard conjecture."
Although this is an indisputable fact, hearing this guy admit it in person still makes him a little melancholy...
In fact, as for whether he is still a human or not, Lu Zhou himself may not be able to answer this question now.
Every minute from now on belongs to a new world!
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the models of rockets.
His shoulders relaxed.
The sound echoed in the empty venue.
Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the models of rockets.
The era of standard conjecture is over.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
The two old men sat there, staring motionless at the whiteboard.
Even if we look around the world and look back in history, we may not be able to find a more glorious moment.
The sound echoed in the empty venue.
This is a property of L^2 cohomology theory mentioned by Sir Attiyah in his paper on the study of discrete groups and elliptic operators published in the "Annals of Mathematics" in 1976.
It was too far away and Lu Zhou couldn't see clearly, but as far as he could see, the faces of young and old people were all filled with shock and madness.
The audience was completely silent.
Still no one spoke.
Almost knocking off the ceiling of the stadium.
Sitting next to him, Faltings said nothing.
Almost knocking off the ceiling of the stadium.
Of course they won't understand.
"Thanks."
Sitting next to him, Faltings said nothing.
No one spoke.
Although this is an indisputable fact, hearing this guy admit it in person still makes him a little melancholy...
From the perspective of species and civilization, all of this is too small.
Just like the beauty of mathematics, it itself will not be open to everyone.
Even in his own eyes.
Everything is quiet.
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
There was no applause either.
"His thinking speed is too fast... To use an inappropriate metaphor, the average person may be riding a rocket... Maybe I am riding a Space-X Falcon, but it is still a rocket, and there is no essential difference from other rockets. But he It was different. He had already boarded something similar to a warp engine. While I was still following a line of thought step by step, he had already folded the entire piece of paper in half, starting from the stem of the proposition. , jumping directly to the results part.”
After a while, he clenched his fists and sighed softly.
The dull or solemn expressions of the audience in the front row have already told everything about their mood and state at this moment. No one has recovered from the visual and spiritual shock, so naturally they can't talk about their feelings.
The two old men sat there, staring motionless at the whiteboard.
where Intersection is a subalgebraic variety of X.
Without pausing for too long, Lu Zhou glanced around the silent venue and continued speaking in an unhurried tone.
"...Everyone knows this kind of obvious thing even if you don't say it."
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
In fact, as for whether he is still a human or not, Lu Zhou himself may not be able to answer this question now.
His shoulders relaxed.
"I may need a little time... maybe, I am really old."
Everyone was waiting for him to continue.
Many people sitting in the audience could not absorb information as fast as he could write on the blackboard.
"In fact, grand unified theory is the theme of this report meeting."
Use this moment as a watershed moment.
Lu Zhou seemed to be tangled up in some troublesome matter. He frowned and thought for a long time.
As he raised his hand, the pen on the whiteboard moved.
Deligne was silent, looking at the stage with a complicated expression, and said no more.
There was no applause either.
From the perspective of species and civilization, all of this is too small.
"I may need a little time... maybe, I am really old."
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
"The proof of the standard conjecture is just a starting point. I hope that through my presentation, I can bring some inspiration to your future exploration of beautiful things."
No, to be precise, it’s not just the Chinese mathematics community.
Many people sitting in the audience could not absorb information as fast as he could write on the blackboard.
There are more and more calculations on the whiteboard.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
"As we witness together at this moment, our theory has once again been verified that our universe is perfect and it is in line with mathematical beauty."
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
The silence in the audience continued.
The audience was completely silent.
"God...he, he is a genius!"
"I will be here these three days. If you have any new questions later, you can come here to find me."
Sitting next to him, Faltings said nothing.
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
"Anyone else has any questions?"
Almost knocking off the ceiling of the stadium.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
Schultz, who was sitting not far from him, had almost the same reaction, and even exclaimed in disbelief.
Six years have passed now.
The silence in the audience continued.
After looking at the stunned Schultz, Perelman, who had been silent until now, muttered a rare word.
Lu Zhou seemed to be tangled up in some troublesome matter. He frowned and thought for a long time.
If he remembered correctly, when he first entered Princeton, about six years ago, Professor Deligne invited him to join the research on the standard conjecture.
"Although it is just to demonstrate the application of grand unified theory in studying algebraic geometry problems..."
Most directly, if the standard conjecture is true, it can directly deduce the Weil conjecture, and it can be deduced that the role of Frobenius on the cohomology group of smooth projective algebraic varieties is semi-simple, and it can even be deduced that the algebraic closed chain in the algebraic variety ( The numerical equivalence and homological equivalence of algebraic cycle are the same equivalence relationship, etc.
Still no one spoke.
Still no one spoke.
"I will be here these three days. If you have any new questions later, you can come here to find me."
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
As the last punctuation mark falls.
Under the gaze of countless expectant eyes, Lu Zhou's frown suddenly relaxed, and in a relaxed tone, Lu Zhou continued.
Just like the beauty of mathematics, it itself will not be open to everyone.
His shoulders relaxed.
"Anyone else has any questions?"
Sitting next to him, Faltings said nothing.
Not far away.
From the perspective of species and civilization, all of this is too small.
Although there is no sound, it is like a song.
Use this moment as a watershed moment.
Bathed in the applause that resounded throughout the venue, Lu Zhou gently placed the marker in his hand, destined to become a historical relic, on the podium, took a half step back, bowed slightly, and turned to walk towards the audience.
It felt like a heavy burden had been lifted off. Lu Zhou, who had been expressionless, suddenly had a pleasant smile on his face.
Use this moment as a watershed moment.
Regarding this strange metaphor, Mr. Qiu said nothing, but silently moved his gaze to the almost filled whiteboard.
It's just that the person who asked the question was Mr. Qiu Chengtong, and the person who answered was Professor Tao.
Lu Zhou, who said these words lightly, walked to the blank whiteboard next to him with many complex emotions such as awe, emotion, and calm, and stopped for a moment.
That smile is like the wind in early spring in March. Although there is no special tension, it blows into the hearts of every listener. Wherever it blows, the ice melts, the snow melts, and the clouds bloom and the sun rises.
"God...he, he is a genius!"
"God...he, he is a genius!"
Many people sitting in the audience could not absorb information as fast as he could write on the blackboard.
It was too far away and Lu Zhou couldn't see clearly, but as far as he could see, the faces of young and old people were all filled with shock and madness.
"If not, then this report meeting will end here."
[… When i≤n/2, the quadratic form x→(-1)^i·L^(r-2i) on A^i(X)∩ker(L^(n-2i+1)) xx is positive...]
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
If he remembered correctly, when he first entered Princeton, about six years ago, Professor Deligne invited him to join the research on the standard conjecture.
It's not easy though.
"I will be here these three days. If you have any new questions later, you can come here to find me."
This is a property of L^2 cohomology theory mentioned by Sir Attiyah in his paper on the study of discrete groups and elliptic operators published in the "Annals of Mathematics" in 1976.
"Anyone else has any questions?"
Perelman, who was sitting in the audience with a frown on his face and his arms folded, suddenly sat up straight and his pupils, which were looking directly at the whiteboard, shrank to a single point.
Most directly, if the standard conjecture is true, it can directly deduce the Weil conjecture, and it can be deduced that the role of Frobenius on the cohomology group of smooth projective algebraic varieties is semi-simple, and it can even be deduced that the algebraic closed chain in the algebraic variety ( The numerical equivalence and homological equivalence of algebraic cycle are the same equivalence relationship, etc.
Sitting next to him, Faltings said nothing.
"Thanks."
As an all-rounder in the field of mathematics, he was probably the only person in the entire venue, other than Lu Zhou himself, who could keep up with the writing speed on the whiteboard.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
The audience was completely silent.
"...Everyone knows this kind of obvious thing even if you don't say it."
Even in his own eyes.
In fact, as early as ten lines ago, there was no suspense about the outcome, but only a few people could see it.
The applause sounded like a downpour.
Every minute from now on belongs to a new world!
As the last punctuation mark falls.
Almost knocking off the ceiling of the stadium.
Everything is quiet.
The silence in the audience continued.
It was too far away and Lu Zhou couldn't see clearly, but as far as he could see, the faces of young and old people were all filled with shock and madness.
However, at this point, its historical mission has come to an end.
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
"Well done!"
"The above is the proof of the standard conjecture."
It was as if the whole world had been wound up again, from silent silence to starting to tick again.
Although this is an indisputable fact, hearing this guy admit it in person still makes him a little melancholy...
"If not, then this report meeting will end here."
"I will be here these three days. If you have any new questions later, you can come here to find me."
This conjecture is known when X is an algebraic surface or a complex algebraic variety.
"I may need a little time... maybe, I am really old."
After a while, he clenched his fists and sighed softly.
It was as if the whole world had been wound up again, from silent silence to starting to tick again.
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what was going on.
Obviously, there has been no significant progress on this topic until now.
Almost knocking off the ceiling of the stadium.
His shoulders relaxed.
At the moment when Lu Zhou successfully extended the Hodge theory on compact manifolds to complete non-compact manifolds, Professor Deligne suddenly broke the silent agreement and spoke.
Of course they won't understand.
The silence in the audience continued.
After about half a minute, he shook his head.
Just like the beauty of mathematics, it itself will not be open to everyone.
"In fact, grand unified theory is the theme of this report meeting."
"never mind."
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
However, for those who can understand it, this kind of beauty is shocking to the heart and reaches the depths of the soul.
There are more and more calculations on the whiteboard.
"What do you think?"
Although there is no sound, it is like a song.
As he raised his hand, the pen on the whiteboard moved.
Just like the beauty of mathematics, it itself will not be open to everyone.
Bathed in the applause that resounded throughout the venue, Lu Zhou gently placed the marker in his hand, destined to become a historical relic, on the podium, took a half step back, bowed slightly, and turned to walk towards the audience.
About ten minutes passed before he turned around, faced the silent venue, and spoke slowly.
"never mind."
Lu Zhou took a deep breath of cold air to cool down the restless emotions in his chest. He looked at the line on the whiteboard that read "Lefschetz standard conjecture, established!" After being silent for a long time, he slowly spoke.
The era of standard conjecture is over.
"Anyone else has any questions?"
There is no doubt that this is the most glorious moment in the history of Chinese mathematics.
"As we witness together at this moment, our theory has once again been verified that our universe is perfect and it is in line with mathematical beauty."
Most directly, if the standard conjecture is true, it can directly deduce the Weil conjecture, and it can be deduced that the role of Frobenius on the cohomology group of smooth projective algebraic varieties is semi-simple, and it can even be deduced that the algebraic closed chain in the algebraic variety ( The numerical equivalence and homological equivalence of algebraic cycle are the same equivalence relationship, etc.
Use this moment as a watershed moment.
"The second half is Hodge's standard conjecture."
However, at this point, its historical mission has come to an end.
Although judging from the data on the physical examination test sheet, the system's strengthening does not seem to be reflected in the modification of his DNA, but his current thinking ability has obviously gone beyond what ordinary humans can achieve - or even understand.
It felt like a heavy burden had been lifted off. Lu Zhou, who had been expressionless, suddenly had a pleasant smile on his face.
Every minute from now on belongs to a new world!
It's just that the person who asked the question was Mr. Qiu Chengtong, and the person who answered was Professor Tao.
Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even aside from the conclusions that can be directly drawn through the grand unified theory, in just half an hour, Solving so many problems is also quite scary.
"I may need a little time... maybe, I am really old."