"Ah sneeze!"
However, what is somewhat troublesome is that although Lu Zhou has studied differential manifolds and topology, he has not done much research on differential topology, a branch of mathematics.
As the sky outside the window gradually darkened, not only did the originally smooth strokes of his writing gradually slow down, beads of sweat gradually seeped out from Lu Zhou's forehead.
In the villa of Zhongshan International, Lu Zhou was sitting in his study room, writing something at the desk with a pen, when he sneezed without warning.
According to the description in its abstract, the main content of this paper is to improve the Surgery theory and transform the problem of manifold classification into the calculation problem of certain edge groups.
Xiao Ai: [Master, there is no need to add sugar to instant coffee? (°ー°〃)]
"Ah... it's so difficult!"
However, things don't seem to be heading in a more optimistic direction.
"Who is thinking about me again..."
Not to mention the agreed-upon competition to see who could get this result first, even if he didn't pretend to be so cool, it was not his style to give up in the face of difficulties.
After selecting a few tags and sorting them according to the number of citations, Lu Zhou quickly picked out a few top-ranked papers.
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
After sniffing and muttering to himself, Lu Zhou continued to look at the draft paper in front of him, tapping the ballpoint pen in his hand lightly on the table.
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
The author of the paper is Professor Kreck, a well-known expert in the fields of partial differential equations and topology. This paper was published in the "Annals of Mathematics" in 1999 and has been cited more than 100 times. A little high.
[Okay, good master!]
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
"It's a bit difficult."
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
"that's it!"
[... When n is greater than 2, two n-dimensional complexes completely intersect X^n(d) and X^n(d') diffeomorphisms, if and only if their Euler numbers, total degrees, and Pontrjagin classes are all equal.]
As time passed, more and more papers were piled on the table.
"It's really embarrassing for me, Fat Tiger... Should I just leave it alone?"
"That's not right! If the proposition is true, I wouldn't be able to figure it out after thinking about it for so long..."
His thumb opened the cap of the pen and he wrote the first line of text on the paper.
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
Strictly speaking, this is not a complex analysis problem, nor is it a partial differential equation problem in the traditional sense, but a very interesting classification problem about smooth manifolds.
His thumb opened the cap of the pen and he wrote the first line of text on the paper.
[At this time, X is called a complex complete intersection. If the complex dimension of
"It's a bit difficult."
This statement may be a bit confusing, but in fact, in differential topology, this is a relatively popular research direction, mainly studying the invariant properties of differential manifolds under differential homeomorphism mapping.
Talking to himself, Lu Zhou held the scrap paper and sat down on the chair again. He spread the draft paper in his hand on the table, and his eyes rekindled a blazing fighting spirit.
As he muttered softly, Lu Zhou's eyes suddenly lit up, and he keenly captured an interesting title from the vast database.
"But the strange thing is that it can't prove that the proposition is wrong... No matter how many sets of parameters are brought in, results consistent with the proposition can be obtained."
"It's a bit difficult."
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
What's more, the research on the Riemann Hypothesis is now stuck in a bottleneck. Instead of being stuck on a dead end road, it's better to try to look up and see if there are any other noteworthy clues around you.
However, what is somewhat troublesome is that although Lu Zhou has studied differential manifolds and topology, he has not done much research on differential topology, a branch of mathematics.
"that's it!"
The situation didn't seem as optimistic as he imagined.
It can even be said that this is a completely new field for him.
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
Strictly speaking, this is not a complex analysis problem, nor is it a partial differential equation problem in the traditional sense, but a very interesting classification problem about smooth manifolds.
"Ah... it's so difficult!"
Not to mention the agreed-upon competition to see who could get this result first, even if he didn't pretend to be so cool, it was not his style to give up in the face of difficulties.
"... That's a long way to go. Anyway, make me a cup of coffee."
As time passed, more and more papers were piled on the table.
However, there is nothing wrong with such a situation. After all, Professor Chen Yang studies the Hodge Hypothesis, and the Riemann Hypothesis he studies are two completely different problems.
The more he delved into this problem, the more he discovered how complex the maze behind it was.
The ballpoint pen in his hand was spinning faster and faster. Lu Zhou, who was frowning, stared at the original question and opened and closed his lips slightly.
"At least you should be able to find something similar."
[Okay, good master!]
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
It was only because the hyperelliptic curve analysis method could be improved and used to study the Cauchy-Riemann equation and the generalized surface of the Riemann surface that it triggered his association with this issue...
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
Strictly speaking, this is not a complex analysis problem, nor is it a partial differential equation problem in the traditional sense, but a very interesting classification problem about smooth manifolds.
[Let f1...fr be homogeneous polynomials with respect to the complex coefficients of variables z0...zn+r. This set of polynomials defines a complex algebraic variety X in the complex projective space CP^(n+r)...]
"But the strange thing is that it can't prove that the proposition is wrong... No matter how many sets of parameters are brought in, results consistent with the proposition can be obtained."
"It's really embarrassing for me, Fat Tiger... Should I just leave it alone?"
"That's not right! If the proposition is true, I wouldn't be able to figure it out after thinking about it for so long..."
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
However, things don't seem to be heading in a more optimistic direction.
About ten minutes later, when he read the paper carefully to the end, the look of interest in his eyes suddenly turned into excitement.
Although this feeling was very weak, he had a clear hunch that he had found the right path to the end of the maze.
"Ah sneeze!"
In the villa of Zhongshan International, Lu Zhou was sitting in his study room, writing something at the desk with a pen, when he sneezed without warning.
Lu Zhou's eyes shone slightly with excitement.
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
However, there is nothing wrong with such a situation. After all, Professor Chen Yang studies the Hodge Hypothesis, and the Riemann Hypothesis he studies are two completely different problems.
Xiao Ai was lying on the bookshelf, just quietly watching. Since Lu Zhou banned it from turning on the camera at will, it was the only camera on the drone that it could use freely.
This statement may be a bit confusing, but in fact, in differential topology, this is a relatively popular research direction, mainly studying the invariant properties of differential manifolds under differential homeomorphism mapping.
Not to mention the agreed-upon competition to see who could get this result first, even if he didn't pretend to be so cool, it was not his style to give up in the face of difficulties.
The sky outside the window gradually darkened.
I don't know how many times he has walked into a dead end. Finally, Lu Zhou, who couldn't keep calm, instantly transformed into a grumpy old man. He crumpled up the half-finished draft paper and threw it into the wastebasket next to him. inside.
"But the strange thing is that it can't prove that the proposition is wrong... No matter how many sets of parameters are brought in, results consistent with the proposition can be obtained."
[At this time, X is called a complex complete intersection. If the complex dimension of
Rows of retrieved papers quickly appeared in front of him.
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
Lu Zhou's eyes shone slightly with excitement.
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
The author of the paper is Professor Kreck, a well-known expert in the fields of partial differential equations and topology. This paper was published in the "Annals of Mathematics" in 1999 and has been cited more than 100 times. A little high.
Lines of calculations like notes poured down from his pen like an endless river, and soon the entire draft paper was filled with dense operators and numbers.
"...It is impossible that no one has studied such an interesting problem."
What's more, the research on the Riemann Hypothesis is now stuck in a bottleneck. Instead of being stuck on a dead end road, it's better to try to look up and see if there are any other noteworthy clues around you.
The first step has been taken.
[Okay, good master!]
However, there is nothing wrong with such a situation. After all, Professor Chen Yang studies the Hodge Hypothesis, and the Riemann Hypothesis he studies are two completely different problems.
"It's a bit difficult."
Xiao Ai: [Master, there is no need to add sugar to instant coffee? (°ー°〃)]
Talking to himself, Lu Zhou held the scrap paper and sat down on the chair again. He spread the draft paper in his hand on the table, and his eyes rekindled a blazing fighting spirit.
It was only because the hyperelliptic curve analysis method could be improved and used to study the Cauchy-Riemann equation and the generalized surface of the Riemann surface that it triggered his association with this issue...
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
"... That's a long way to go. Anyway, make me a cup of coffee."
This statement may be a bit confusing, but in fact, in differential topology, this is a relatively popular research direction, mainly studying the invariant properties of differential manifolds under differential homeomorphism mapping.
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
His thumb opened the cap of the pen and he wrote the first line of text on the paper.
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
Not to mention the agreed-upon competition to see who could get this result first, even if he didn't pretend to be so cool, it was not his style to give up in the face of difficulties.
"Xiao Ai, make me a cup of coffee, without sugar!"
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
Xiao Ai: [Master, there is no need to add sugar to instant coffee? (°ー°〃)]
"Fortunately, it was only a little wrinkled and not torn!"
But this time, it lasted until dawn...
Lines of calculations like notes poured down from his pen like an endless river, and soon the entire draft paper was filled with dense operators and numbers.
After saying that, the sound of swishing brush strokes sounded again in the study.
"... That's a long way to go. Anyway, make me a cup of coffee."
Lu Zhou, who was lying in front of the table, reached out and turned on the lamp on the corner of the table, but he never made any other action other than calculations.
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
[Okay, good master!]
"That's not right! If the proposition is true, I wouldn't be able to figure it out after thinking about it for so long..."
The ballpoint pen in his hand was spinning faster and faster. Lu Zhou, who was frowning, stared at the original question and opened and closed his lips slightly.
Talking to himself, Lu Zhou held the scrap paper and sat down on the chair again. He spread the draft paper in his hand on the table, and his eyes rekindled a blazing fighting spirit.
What's more, the research on the Riemann Hypothesis is now stuck in a bottleneck. Instead of being stuck on a dead end road, it's better to try to look up and see if there are any other noteworthy clues around you.
Lu Zhou, who was lying in front of the table, reached out and turned on the lamp on the corner of the table, but he never made any other action other than calculations.
Not to mention the agreed-upon competition to see who could get this result first, even if he didn't pretend to be so cool, it was not his style to give up in the face of difficulties.
"Ah sneeze!"
It can even be said that this is a completely new field for him.
The drone floated up from the bookshelf and whined as it flew outside the study.
Not to mention the agreed-upon competition to see who could get this result first, even if he didn't pretend to be so cool, it was not his style to give up in the face of difficulties.
In the villa of Zhongshan International, Lu Zhou was sitting in his study room, writing something at the desk with a pen, when he sneezed without warning.
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
Strictly speaking, this is not a complex analysis problem, nor is it a partial differential equation problem in the traditional sense, but a very interesting classification problem about smooth manifolds.
"It's a bit difficult."
After selecting a few tags and sorting them according to the number of citations, Lu Zhou quickly picked out a few top-ranked papers.
Although this feeling was very weak, he had a clear hunch that he had found the right path to the end of the maze.
However, things don't seem to be heading in a more optimistic direction.
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
"Fortunately, it was only a little wrinkled and not torn!"
His thumb opened the cap of the pen and he wrote the first line of text on the paper.
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
"If the problem of manifold classification can be transformed into the calculation of some edge groups... Oh my god, this is the last piece of the puzzle I am missing!"
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
[Let f1...fr be homogeneous polynomials with respect to the complex coefficients of variables z0...zn+r. This set of polynomials defines a complex algebraic variety X in the complex projective space CP^(n+r)...]
"Ah... it's so difficult!"
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
After sniffing and muttering to himself, Lu Zhou continued to look at the draft paper in front of him, tapping the ballpoint pen in his hand lightly on the table.
"That's not right! If the proposition is true, I wouldn't be able to figure it out after thinking about it for so long..."
[At this time, X is called a complex complete intersection. If the complex dimension of
His thumb opened the cap of the pen and he wrote the first line of text on the paper.
Lu Zhou, who was lying in front of the table, reached out and turned on the lamp on the corner of the table, but he never made any other action other than calculations.
The first step has been taken.
"At least you should be able to find something similar."
After saying that, the sound of swishing brush strokes sounded again in the study.
Lu Zhou's eyes shone slightly with excitement.
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
The situation didn't seem as optimistic as he imagined.
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
"It's a bit difficult."
Although this feeling was very weak, he had a clear hunch that he had found the right path to the end of the maze.
Although this feeling was very weak, he had a clear hunch that he had found the right path to the end of the maze.
"It's a bit difficult."
I don't know how many times he has walked into a dead end. Finally, Lu Zhou, who couldn't keep calm, instantly transformed into a grumpy old man. He crumpled up the half-finished draft paper and threw it into the wastebasket next to him. inside.
It was only because the hyperelliptic curve analysis method could be improved and used to study the Cauchy-Riemann equation and the generalized surface of the Riemann surface that it triggered his association with this issue...
Xiao Ai was lying on the bookshelf, just quietly watching. Since Lu Zhou banned it from turning on the camera at will, it was the only camera on the drone that it could use freely.
"Xiao Ai, make me a cup of coffee, without sugar!"
"But the strange thing is that it can't prove that the proposition is wrong... No matter how many sets of parameters are brought in, results consistent with the proposition can be obtained."
However, there is nothing wrong with such a situation. After all, Professor Chen Yang studies the Hodge Hypothesis, and the Riemann Hypothesis he studies are two completely different problems.
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
About ten minutes later, when he read the paper carefully to the end, the look of interest in his eyes suddenly turned into excitement.
The more he delved into this problem, the more he discovered how complex the maze behind it was.
"Let me just say, there is no way that such an interesting problem has not been studied by anyone before... at least someone must have studied similar topics!"
The drone floated up from the bookshelf and whined as it flew outside the study.
"Xiao Ai, make me a cup of coffee, without sugar!"
What's more, the research on the Riemann Hypothesis is now stuck in a bottleneck. Instead of being stuck on a dead end road, it's better to try to look up and see if there are any other noteworthy clues around you.
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
However, there is nothing wrong with such a situation. After all, Professor Chen Yang studies the Hodge Hypothesis, and the Riemann Hypothesis he studies are two completely different problems.
Once a breakthrough is opened in thinking, inspiration will flow out like a flood, and there is no way to stop it.
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
In the villa of Zhongshan International, Lu Zhou was sitting in his study room, writing something at the desk with a pen, when he sneezed without warning.
Lines of calculations like notes poured down from his pen like an endless river, and soon the entire draft paper was filled with dense operators and numbers.
The sky outside the window gradually darkened.
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
[... When n is greater than 2, two n-dimensional complexes completely intersect X^n(d) and X^n(d') diffeomorphisms, if and only if their Euler numbers, total degrees, and Pontrjagin classes are all equal.]
"It's a bit difficult."
As the sky outside the window gradually darkened, not only did the originally smooth strokes of his writing gradually slow down, beads of sweat gradually seeped out from Lu Zhou's forehead.
As time passed, more and more papers were piled on the table.
Once a breakthrough is opened in thinking, inspiration will flow out like a flood, and there is no way to stop it.
The situation didn't seem as optimistic as he imagined.
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
"If the problem of manifold classification can be transformed into the calculation of some edge groups... Oh my god, this is the last piece of the puzzle I am missing!"
The situation didn't seem as optimistic as he imagined.
Xiao Ai was lying on the bookshelf, just quietly watching. Since Lu Zhou banned it from turning on the camera at will, it was the only camera on the drone that it could use freely.
[... When n is greater than 2, two n-dimensional complexes completely intersect X^n(d) and X^n(d') diffeomorphisms, if and only if their Euler numbers, total degrees, and Pontrjagin classes are all equal.]
With a look of interest gradually appearing in his eyes, Lu Zhou quickly downloaded the paper and read line by line along the main text of the paper.
Although it feels a little distressing to see the owner working so hard, it really can't help much with this kind of creative work.
His thumb opened the cap of the pen and he wrote the first line of text on the paper.
However, there is nothing wrong with such a situation. After all, Professor Chen Yang studies the Hodge Hypothesis, and the Riemann Hypothesis he studies are two completely different problems.
The first step has been taken.
"Xiao Ai, make me a cup of coffee, without sugar!"
What's more, the research on the Riemann Hypothesis is now stuck in a bottleneck. Instead of being stuck on a dead end road, it's better to try to look up and see if there are any other noteworthy clues around you.
I don't know how many times he has walked into a dead end. Finally, Lu Zhou, who couldn't keep calm, instantly transformed into a grumpy old man. He crumpled up the half-finished draft paper and threw it into the wastebasket next to him. inside.
But this time, it lasted until dawn...
It was only because the hyperelliptic curve analysis method could be improved and used to study the Cauchy-Riemann equation and the generalized surface of the Riemann surface that it triggered his association with this issue...
The sky outside the window gradually darkened.
After saying that, the sound of swishing brush strokes sounded again in the study.
"It's really embarrassing for me, Fat Tiger... Should I just leave it alone?"
Lu Zhou, who was lying in front of the table, reached out and turned on the lamp on the corner of the table, but he never made any other action other than calculations.
Once a breakthrough is opened in thinking, inspiration will flow out like a flood, and there is no way to stop it.
"It's about to begin!"
Strictly speaking, this is not a complex analysis problem, nor is it a partial differential equation problem in the traditional sense, but a very interesting classification problem about smooth manifolds.
The author of the paper is Professor Kreck, a well-known expert in the fields of partial differential equations and topology. This paper was published in the "Annals of Mathematics" in 1999 and has been cited more than 100 times. A little high.
However, things don't seem to be heading in a more optimistic direction.
[... When n is greater than 2, two n-dimensional complexes completely intersect X^n(d) and X^n(d') diffeomorphisms, if and only if their Euler numbers, total degrees, and Pontrjagin classes are all equal.]
The situation didn't seem as optimistic as he imagined.
As the sky outside the window gradually darkened, not only did the originally smooth strokes of his writing gradually slow down, beads of sweat gradually seeped out from Lu Zhou's forehead.
After saying that, the sound of swishing brush strokes sounded again in the study.
[Okay, good master!]
"At least you should be able to find something similar."
Once a breakthrough is opened in thinking, inspiration will flow out like a flood, and there is no way to stop it.
According to the description in its abstract, the main content of this paper is to improve the Surgery theory and transform the problem of manifold classification into the calculation problem of certain edge groups.
This statement may be a bit confusing, but in fact, in differential topology, this is a relatively popular research direction, mainly studying the invariant properties of differential manifolds under differential homeomorphism mapping.
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
The situation didn't seem as optimistic as he imagined.
After sniffing and muttering to himself, Lu Zhou continued to look at the draft paper in front of him, tapping the ballpoint pen in his hand lightly on the table.
"At least you should be able to find something similar."
According to the description in its abstract, the main content of this paper is to improve the Surgery theory and transform the problem of manifold classification into the calculation problem of certain edge groups.
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
However, there is nothing wrong with such a situation. After all, Professor Chen Yang studies the Hodge Hypothesis, and the Riemann Hypothesis he studies are two completely different problems.
The more he delved into this problem, the more he discovered how complex the maze behind it was.
Rows of retrieved papers quickly appeared in front of him.
"If the problem of manifold classification can be transformed into the calculation of some edge groups... Oh my god, this is the last piece of the puzzle I am missing!"
"It's a bit difficult."
"...It is impossible that no one has studied such an interesting problem."
[... When n is greater than 2, two n-dimensional complexes completely intersect X^n(d) and X^n(d') diffeomorphisms, if and only if their Euler numbers, total degrees, and Pontrjagin classes are all equal.]
"It's a bit difficult."
As the sky outside the window gradually darkened, not only did the originally smooth strokes of his writing gradually slow down, beads of sweat gradually seeped out from Lu Zhou's forehead.
"Ah... it's so difficult!"
The author of the paper is Professor Kreck, a well-known expert in the fields of partial differential equations and topology. This paper was published in the "Annals of Mathematics" in 1999 and has been cited more than 100 times. A little high.
As he muttered softly, Lu Zhou's eyes suddenly lit up, and he keenly captured an interesting title from the vast database.
Lu Zhou, who was lying in front of the table, reached out and turned on the lamp on the corner of the table, but he never made any other action other than calculations.
I don't know how many times he has walked into a dead end. Finally, Lu Zhou, who couldn't keep calm, instantly transformed into a grumpy old man. He crumpled up the half-finished draft paper and threw it into the wastebasket next to him. inside.
Talking to himself, Lu Zhou held the scrap paper and sat down on the chair again. He spread the draft paper in his hand on the table, and his eyes rekindled a blazing fighting spirit.
As the sky outside the window gradually darkened, not only did the originally smooth strokes of his writing gradually slow down, beads of sweat gradually seeped out from Lu Zhou's forehead.
"That's not right! If the proposition is true, I wouldn't be able to figure it out after thinking about it for so long..."
After selecting a few tags and sorting them according to the number of citations, Lu Zhou quickly picked out a few top-ranked papers.
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
I don't know how many times he has walked into a dead end. Finally, Lu Zhou, who couldn't keep calm, instantly transformed into a grumpy old man. He crumpled up the half-finished draft paper and threw it into the wastebasket next to him. inside.
"But the strange thing is that it can't prove that the proposition is wrong... No matter how many sets of parameters are brought in, results consistent with the proposition can be obtained."
The ballpoint pen in his hand was spinning faster and faster. Lu Zhou, who was frowning, stared at the original question and opened and closed his lips slightly.
"It's a bit difficult."
Rows of retrieved papers quickly appeared in front of him.
[Let f1...fr be homogeneous polynomials with respect to the complex coefficients of variables z0...zn+r. This set of polynomials defines a complex algebraic variety X in the complex projective space CP^(n+r)...]
The situation didn't seem as optimistic as he imagined.
As he muttered softly, Lu Zhou's eyes suddenly lit up, and he keenly captured an interesting title from the vast database.
"But the strange thing is that it can't prove that the proposition is wrong... No matter how many sets of parameters are brought in, results consistent with the proposition can be obtained."
"That's not right! If the proposition is true, I wouldn't be able to figure it out after thinking about it for so long..."
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
Once a breakthrough is opened in thinking, inspiration will flow out like a flood, and there is no way to stop it.
The first step has been taken.
Rows of retrieved papers quickly appeared in front of him.
Talking to himself, Lu Zhou held the scrap paper and sat down on the chair again. He spread the draft paper in his hand on the table, and his eyes rekindled a blazing fighting spirit.
After selecting a few tags and sorting them according to the number of citations, Lu Zhou quickly picked out a few top-ranked papers.
After selecting a few tags and sorting them according to the number of citations, Lu Zhou quickly picked out a few top-ranked papers.
What's more, the research on the Riemann Hypothesis is now stuck in a bottleneck. Instead of being stuck on a dead end road, it's better to try to look up and see if there are any other noteworthy clues around you.
After selecting a few tags and sorting them according to the number of citations, Lu Zhou quickly picked out a few top-ranked papers.
"It's a bit difficult."
"Who is thinking about me again..."
"It's a bit difficult."
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
But this time, it lasted until dawn...
"Ah sneeze!"
"...It is impossible that no one has studied such an interesting problem."
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
"It's about to begin!"
[... When n is greater than 2, two n-dimensional complexes completely intersect X^n(d) and X^n(d') diffeomorphisms, if and only if their Euler numbers, total degrees, and Pontrjagin classes are all equal.]
"Xiao Ai, make me a cup of coffee, without sugar!"
"Ah... it's so difficult!"
In the villa of Zhongshan International, Lu Zhou was sitting in his study room, writing something at the desk with a pen, when he sneezed without warning.
"At least you should be able to find something similar."
"It's really embarrassing for me, Fat Tiger... Should I just leave it alone?"
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
It was only because the hyperelliptic curve analysis method could be improved and used to study the Cauchy-Riemann equation and the generalized surface of the Riemann surface that it triggered his association with this issue...
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
Even if differential topology is not his research direction, with his understanding of differential manifolds and topology theory, it is not a big problem to quickly become familiar with the key points of research in this field.
[Let f1...fr be homogeneous polynomials with respect to the complex coefficients of variables z0...zn+r. This set of polynomials defines a complex algebraic variety X in the complex projective space CP^(n+r)...]
As he muttered softly, Lu Zhou's eyes suddenly lit up, and he keenly captured an interesting title from the vast database.
After thinking for a while, Lu Zhou shook his head and finally drove this unfulfilling thought out of his mind.
Not to mention the agreed-upon competition to see who could get this result first, even if he didn't pretend to be so cool, it was not his style to give up in the face of difficulties.
Strictly speaking, this is not a complex analysis problem, nor is it a partial differential equation problem in the traditional sense, but a very interesting classification problem about smooth manifolds.
The author of the paper is Professor Kreck, a well-known expert in the fields of partial differential equations and topology. This paper was published in the "Annals of Mathematics" in 1999 and has been cited more than 100 times. A little high.
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
The situation didn't seem as optimistic as he imagined.
"It's a bit difficult."
However, things don't seem to be heading in a more optimistic direction.
As he muttered softly, Lu Zhou's eyes suddenly lit up, and he keenly captured an interesting title from the vast database.
Xiao Ai: [Master, there is no need to add sugar to instant coffee? (°ー°〃)]
After sniffing and muttering to himself, Lu Zhou continued to look at the draft paper in front of him, tapping the ballpoint pen in his hand lightly on the table.
"Ah sneeze!"
According to the description in its abstract, the main content of this paper is to improve the Surgery theory and transform the problem of manifold classification into the calculation problem of certain edge groups.
In the villa of Zhongshan International, Lu Zhou was sitting in his study room, writing something at the desk with a pen, when he sneezed without warning.
"But the strange thing is that it can't prove that the proposition is wrong... No matter how many sets of parameters are brought in, results consistent with the proposition can be obtained."
With a look of interest gradually appearing in his eyes, Lu Zhou quickly downloaded the paper and read line by line along the main text of the paper.
Once a breakthrough is opened in thinking, inspiration will flow out like a flood, and there is no way to stop it.
But this time, it lasted until dawn...
"Ah... it's so difficult!"
Putting aside the distracting thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.
"... That's a long way to go. Anyway, make me a cup of coffee."
If a bridge can be built between topology problems and complex analysis problems, maybe his hyperelliptic curve analysis method will be able to work wonders in the study of the Riemann zeta function...
About ten minutes later, when he read the paper carefully to the end, the look of interest in his eyes suddenly turned into excitement.
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
Lines of calculations like notes poured down from his pen like an endless river, and soon the entire draft paper was filled with dense operators and numbers.
Lines of calculations like notes poured down from his pen like an endless river, and soon the entire draft paper was filled with dense operators and numbers.
"It's about to begin!"
"that's it!"
With a look of interest gradually appearing in his eyes, Lu Zhou quickly downloaded the paper and read line by line along the main text of the paper.
[Let f1...fr be homogeneous polynomials with respect to the complex coefficients of variables z0...zn+r. This set of polynomials defines a complex algebraic variety X in the complex projective space CP^(n+r)...]
"It's about to begin!"
"Ah sneeze!"
After saying that, the sound of swishing brush strokes sounded again in the study.
"Let me just say, there is no way that such an interesting problem has not been studied by anyone before... at least someone must have studied similar topics!"
"...It is impossible that no one has studied such an interesting problem."
His thumb opened the cap of the pen and he wrote the first line of text on the paper.
"If the problem of manifold classification can be transformed into the calculation of some edge groups... Oh my god, this is the last piece of the puzzle I am missing!"
This statement may be a bit confusing, but in fact, in differential topology, this is a relatively popular research direction, mainly studying the invariant properties of differential manifolds under differential homeomorphism mapping.
"It's a bit difficult."
"If the problem of manifold classification can be transformed into the calculation of some edge groups... Oh my god, this is the last piece of the puzzle I am missing!"
Lines of calculations like notes poured down from his pen like an endless river, and soon the entire draft paper was filled with dense operators and numbers.
I don't know how many times he has walked into a dead end. Finally, Lu Zhou, who couldn't keep calm, instantly transformed into a grumpy old man. He crumpled up the half-finished draft paper and threw it into the wastebasket next to him. inside.
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
"At least you should be able to find something similar."
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
According to the description in its abstract, the main content of this paper is to improve the Surgery theory and transform the problem of manifold classification into the calculation problem of certain edge groups.
In the villa of Zhongshan International, Lu Zhou was sitting in his study room, writing something at the desk with a pen, when he sneezed without warning.
The first step has been taken.
"Fortunately, it was only a little wrinkled and not torn!"
As time passed, more and more papers were piled on the table.
"That's not right! If the proposition is true, I wouldn't be able to figure it out after thinking about it for so long..."
Talking to himself, Lu Zhou held the scrap paper and sat down on the chair again. He spread the draft paper in his hand on the table, and his eyes rekindled a blazing fighting spirit.
As the sky outside the window gradually darkened, not only did the originally smooth strokes of his writing gradually slow down, beads of sweat gradually seeped out from Lu Zhou's forehead.
[At this time, X is called a complex complete intersection. If the complex dimension of
"Using the 2n-dimensional smooth closed manifold as the starting point, establishing a correlation in the complex projective space..."
After sniffing and muttering to himself, Lu Zhou continued to look at the draft paper in front of him, tapping the ballpoint pen in his hand lightly on the table.
"... That's a long way to go. Anyway, make me a cup of coffee."
What's more, the research on the Riemann Hypothesis is now stuck in a bottleneck. Instead of being stuck on a dead end road, it's better to try to look up and see if there are any other noteworthy clues around you.
"Who is thinking about me again..."
"It's about to begin!"
This statement may be a bit confusing, but in fact, in differential topology, this is a relatively popular research direction, mainly studying the invariant properties of differential manifolds under differential homeomorphism mapping.
"It's a bit difficult."
Heaving a sigh of relief, Lu Zhou grabbed the pen that was spinning rapidly, opened the computer on the corner of the desk, logged into the literature database, and entered a few lines of keywords.
As time passed, more and more papers were piled on the table.
After saying that, the sound of swishing brush strokes sounded again in the study.
The drone floated up from the bookshelf and whined as it flew outside the study.
Lu Zhou, who was lying in front of the table, reached out and turned on the lamp on the corner of the table, but he never made any other action other than calculations.
The author of the paper is Professor Kreck, a well-known expert in the fields of partial differential equations and topology. This paper was published in the "Annals of Mathematics" in 1999 and has been cited more than 100 times. A little high.
"Ah... it's so difficult!"
But this time, it lasted until dawn...
About ten minutes later, when he read the paper carefully to the end, the look of interest in his eyes suddenly turned into excitement.
Lu Zhou stood up from his chair excitedly, walked to the wastebasket, and quickly dug out the scrap paper that he had crumpled into a ball.
"At least you should be able to find something similar."
The author of the paper is Professor Kreck, a well-known expert in the fields of partial differential equations and topology. This paper was published in the "Annals of Mathematics" in 1999 and has been cited more than 100 times. A little high.
The sky outside the window gradually darkened.