Why isn't differential Galois theory widely used?Prerequisites for Differential Galois theoryWhy should I...
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Why isn't differential Galois theory widely used?
Prerequisites for Differential Galois theoryWhy should I care about fields of positive characteristic?Sheaf cohomology: what is it and where can I learn it?Nilpotent infinitesimals comparisonBest book ever on Galois theory (and differential galois theory)Galois Theory for Differential Equations?Prerequisites for Differential Galois theoryReference request: algebraic methods in geometryWhitney's Embedding TheoremHow can a non-mathematician intuitively understand the importance of algebraic varieties?Mistake (?) in differential Galois theory
$begingroup$
Ellis Kolchin developed differential Galois theory in the 1950s. It seems to be a powerful tool that can decide the solvability and the form of the solutions to a given differential equation.
Why isn't differential Galois theory widely used in differential geometry? It is plausible that we can solve some problems of differential/integral geometry using this theory.
So, what is the major pullback in this theory that prevents its wide application to other fields rather than discrete geometry (e.g., Diophatine geometry)?
abstract-algebra differential-geometry soft-question galois-theory differential-algebra
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
$endgroup$
This question has an open bounty worth +50
reputation from Rodrigo de Azevedo ending in 2 days.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
|
show 1 more comment
$begingroup$
Ellis Kolchin developed differential Galois theory in the 1950s. It seems to be a powerful tool that can decide the solvability and the form of the solutions to a given differential equation.
Why isn't differential Galois theory widely used in differential geometry? It is plausible that we can solve some problems of differential/integral geometry using this theory.
So, what is the major pullback in this theory that prevents its wide application to other fields rather than discrete geometry (e.g., Diophatine geometry)?
abstract-algebra differential-geometry soft-question galois-theory differential-algebra
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
$endgroup$
This question has an open bounty worth +50
reputation from Rodrigo de Azevedo ending in 2 days.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
$begingroup$
I haven't had much exposure to Galois theory yet, but I have heard that it is not widely taught, so I conjecture that the teachers of these courses aren't sufficiently comfortable with it.
$endgroup$
– user142198
Mar 27 '15 at 0:32
$begingroup$
@Incurrence The question is about differential Galois theory, not ordinary (algebraic) Galois theory, and it's about research in differential geometry, not courses. When you write "I have heard that it is not widely taught" and "the teachers of these courses aren't sufficiently comfortable with it", if you're talking about algebraic Galois theory, you're wrong on both counts.
$endgroup$
– Alex Kruckman
Apr 25 '16 at 2:04
1
$begingroup$
The question is now posted on MathOverflow: Why is differential Galois theory not widely used?
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:01
$begingroup$
@MartinSleziak thanks for the reminder, I am doing a few edits on some of my old questions, please leave it to me before further moderation, thank you!
$endgroup$
– Henry.L
Nov 19 '18 at 14:07
$begingroup$
@HenryL The only thing I wanted was to have link to MO question at least in the comments (so that the users who stumble upon this question find also the question on MO). As you probably now, it is recommended to link both copies to each other when posting on multiple sites. (So I was planning no further actions other than posting the above comment.)
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:09
|
show 1 more comment
$begingroup$
Ellis Kolchin developed differential Galois theory in the 1950s. It seems to be a powerful tool that can decide the solvability and the form of the solutions to a given differential equation.
Why isn't differential Galois theory widely used in differential geometry? It is plausible that we can solve some problems of differential/integral geometry using this theory.
So, what is the major pullback in this theory that prevents its wide application to other fields rather than discrete geometry (e.g., Diophatine geometry)?
abstract-algebra differential-geometry soft-question galois-theory differential-algebra
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
$endgroup$
Ellis Kolchin developed differential Galois theory in the 1950s. It seems to be a powerful tool that can decide the solvability and the form of the solutions to a given differential equation.
Why isn't differential Galois theory widely used in differential geometry? It is plausible that we can solve some problems of differential/integral geometry using this theory.
So, what is the major pullback in this theory that prevents its wide application to other fields rather than discrete geometry (e.g., Diophatine geometry)?
abstract-algebra differential-geometry soft-question galois-theory differential-algebra
abstract-algebra differential-geometry soft-question galois-theory differential-algebra
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
edited Mar 10 at 23:13
Rodrigo de Azevedo
13k41960
13k41960
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
asked Mar 26 '15 at 12:59
Henry.LHenry.L
543417
543417
This question has an open bounty worth +50
reputation from Rodrigo de Azevedo ending in 2 days.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
This question has an open bounty worth +50
reputation from Rodrigo de Azevedo ending in 2 days.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
$begingroup$
I haven't had much exposure to Galois theory yet, but I have heard that it is not widely taught, so I conjecture that the teachers of these courses aren't sufficiently comfortable with it.
$endgroup$
– user142198
Mar 27 '15 at 0:32
$begingroup$
@Incurrence The question is about differential Galois theory, not ordinary (algebraic) Galois theory, and it's about research in differential geometry, not courses. When you write "I have heard that it is not widely taught" and "the teachers of these courses aren't sufficiently comfortable with it", if you're talking about algebraic Galois theory, you're wrong on both counts.
$endgroup$
– Alex Kruckman
Apr 25 '16 at 2:04
1
$begingroup$
The question is now posted on MathOverflow: Why is differential Galois theory not widely used?
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:01
$begingroup$
@MartinSleziak thanks for the reminder, I am doing a few edits on some of my old questions, please leave it to me before further moderation, thank you!
$endgroup$
– Henry.L
Nov 19 '18 at 14:07
$begingroup$
@HenryL The only thing I wanted was to have link to MO question at least in the comments (so that the users who stumble upon this question find also the question on MO). As you probably now, it is recommended to link both copies to each other when posting on multiple sites. (So I was planning no further actions other than posting the above comment.)
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:09
|
show 1 more comment
$begingroup$
I haven't had much exposure to Galois theory yet, but I have heard that it is not widely taught, so I conjecture that the teachers of these courses aren't sufficiently comfortable with it.
$endgroup$
– user142198
Mar 27 '15 at 0:32
$begingroup$
@Incurrence The question is about differential Galois theory, not ordinary (algebraic) Galois theory, and it's about research in differential geometry, not courses. When you write "I have heard that it is not widely taught" and "the teachers of these courses aren't sufficiently comfortable with it", if you're talking about algebraic Galois theory, you're wrong on both counts.
$endgroup$
– Alex Kruckman
Apr 25 '16 at 2:04
1
$begingroup$
The question is now posted on MathOverflow: Why is differential Galois theory not widely used?
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:01
$begingroup$
@MartinSleziak thanks for the reminder, I am doing a few edits on some of my old questions, please leave it to me before further moderation, thank you!
$endgroup$
– Henry.L
Nov 19 '18 at 14:07
$begingroup$
@HenryL The only thing I wanted was to have link to MO question at least in the comments (so that the users who stumble upon this question find also the question on MO). As you probably now, it is recommended to link both copies to each other when posting on multiple sites. (So I was planning no further actions other than posting the above comment.)
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:09
$begingroup$
I haven't had much exposure to Galois theory yet, but I have heard that it is not widely taught, so I conjecture that the teachers of these courses aren't sufficiently comfortable with it.
$endgroup$
– user142198
Mar 27 '15 at 0:32
$begingroup$
I haven't had much exposure to Galois theory yet, but I have heard that it is not widely taught, so I conjecture that the teachers of these courses aren't sufficiently comfortable with it.
$endgroup$
– user142198
Mar 27 '15 at 0:32
$begingroup$
@Incurrence The question is about differential Galois theory, not ordinary (algebraic) Galois theory, and it's about research in differential geometry, not courses. When you write "I have heard that it is not widely taught" and "the teachers of these courses aren't sufficiently comfortable with it", if you're talking about algebraic Galois theory, you're wrong on both counts.
$endgroup$
– Alex Kruckman
Apr 25 '16 at 2:04
$begingroup$
@Incurrence The question is about differential Galois theory, not ordinary (algebraic) Galois theory, and it's about research in differential geometry, not courses. When you write "I have heard that it is not widely taught" and "the teachers of these courses aren't sufficiently comfortable with it", if you're talking about algebraic Galois theory, you're wrong on both counts.
$endgroup$
– Alex Kruckman
Apr 25 '16 at 2:04
1
1
$begingroup$
The question is now posted on MathOverflow: Why is differential Galois theory not widely used?
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:01
$begingroup$
The question is now posted on MathOverflow: Why is differential Galois theory not widely used?
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:01
$begingroup$
@MartinSleziak thanks for the reminder, I am doing a few edits on some of my old questions, please leave it to me before further moderation, thank you!
$endgroup$
– Henry.L
Nov 19 '18 at 14:07
$begingroup$
@MartinSleziak thanks for the reminder, I am doing a few edits on some of my old questions, please leave it to me before further moderation, thank you!
$endgroup$
– Henry.L
Nov 19 '18 at 14:07
$begingroup$
@HenryL The only thing I wanted was to have link to MO question at least in the comments (so that the users who stumble upon this question find also the question on MO). As you probably now, it is recommended to link both copies to each other when posting on multiple sites. (So I was planning no further actions other than posting the above comment.)
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:09
$begingroup$
@HenryL The only thing I wanted was to have link to MO question at least in the comments (so that the users who stumble upon this question find also the question on MO). As you probably now, it is recommended to link both copies to each other when posting on multiple sites. (So I was planning no further actions other than posting the above comment.)
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:09
|
show 1 more comment
1 Answer
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$begingroup$
Among others, there is a nice concrete application differential Galois theory to the Non-Integrability of Hamiltonian Systems :
http://www.springer.com/us/book/9783034807203
answered Nov 29 '16 at 11:37
FelixFelix
712
$endgroup$
add a comment |
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$begingroup$
Among others, there is a nice concrete application differential Galois theory to the Non-Integrability of Hamiltonian Systems :
http://www.springer.com/us/book/9783034807203
answered Nov 29 '16 at 11:37
FelixFelix
712
$endgroup$
add a comment |
$begingroup$
Among others, there is a nice concrete application differential Galois theory to the Non-Integrability of Hamiltonian Systems :
http://www.springer.com/us/book/9783034807203
answered Nov 29 '16 at 11:37
FelixFelix
712
$endgroup$
add a comment |
$begingroup$
Among others, there is a nice concrete application differential Galois theory to the Non-Integrability of Hamiltonian Systems :
http://www.springer.com/us/book/9783034807203
answered Nov 29 '16 at 11:37
FelixFelix
712
$endgroup$
Among others, there is a nice concrete application differential Galois theory to the Non-Integrability of Hamiltonian Systems :
http://www.springer.com/us/book/9783034807203
answered Nov 29 '16 at 11:37
FelixFelix
712
answered Nov 29 '16 at 11:37
FelixFelix
712
answered Nov 29 '16 at 11:37
FelixFelix
712
answered Nov 29 '16 at 11:37
FelixFelix
712
712
add a comment |
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$begingroup$
I haven't had much exposure to Galois theory yet, but I have heard that it is not widely taught, so I conjecture that the teachers of these courses aren't sufficiently comfortable with it.
$endgroup$
– user142198
Mar 27 '15 at 0:32
$begingroup$
@Incurrence The question is about differential Galois theory, not ordinary (algebraic) Galois theory, and it's about research in differential geometry, not courses. When you write "I have heard that it is not widely taught" and "the teachers of these courses aren't sufficiently comfortable with it", if you're talking about algebraic Galois theory, you're wrong on both counts.
$endgroup$
– Alex Kruckman
Apr 25 '16 at 2:04
1
$begingroup$
The question is now posted on MathOverflow: Why is differential Galois theory not widely used?
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:01
$begingroup$
@MartinSleziak thanks for the reminder, I am doing a few edits on some of my old questions, please leave it to me before further moderation, thank you!
$endgroup$
– Henry.L
Nov 19 '18 at 14:07
$begingroup$
@HenryL The only thing I wanted was to have link to MO question at least in the comments (so that the users who stumble upon this question find also the question on MO). As you probably now, it is recommended to link both copies to each other when posting on multiple sites. (So I was planning no further actions other than posting the above comment.)
$endgroup$
– Martin Sleziak
Nov 19 '18 at 14:09