Open research problems still open?

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Main Question or Discussion Point

I'm getting through a book called "Topics in Geometric Group Theory" and there are quite a few open research problems throughout the book - they are denoted as such. The book was published in 2000, so aside from googling and searching for papers published on these topics, how can I know which have been solved/discussed in great detail and which are still relatively or completely open?
 

Answers and Replies

  • #2
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By talking to someone knowledgeable in the field? That's your best bet.
 
  • #3
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By talking to someone knowledgeable in the field? That's your best bet.
the most practical solution for sure. i'm reading this book under the direction of a professor who does research in this area and i will hopefully be collaborating with him on a problem or at least working on one under his guidance in the spring but over this winter break (5 + weeks long) i would like to know which problems are worth my thought and which ones are not.
 
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If a solution has been published yet, you might be able to find it via Google. Solutions are hard to locate though if the problem has been solved as a special case of a bigger problem, or only in a special case. It is also possible that someone has already solved it but not published it yet (since publishing might take over a year), or that someone is working on the problem right now. The only way to find out is to ask someone who is on top of things.
 
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i would like to know which problems are worth my thought and which ones are not.
They probably all are. If the solution is very recent, then you may have an alternative proof, an interesting lemma, or you may gain a lot of insight. I would recommend you to use this initial period prior to actually working with your prof to get as good as possible. If you just pick out your favorite problem and work on it you will learn a lot and even if it turns out to be solved, your insights will probably help you greatly on lots of related problems.

Anyway for some more direct advice: as owlpride said it can be hard to determine if the solution is very recent, but if you know one of the most prominent papers that discusses the problem, then simply search for papers citing that. If someone publishes a solution it's very likely they start their article with "In this paper we prove a conjecture set forth in [a] and further explored in , [c] and [d] using techniques from [e] and [f]".
 
  • #6
348
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If a solution has been published yet, you might be able to find it via Google. Solutions are hard to locate though if the problem has been solved as a special case of a bigger problem, or only in a special case. It is also possible that someone has already solved it but not published it yet (since publishing might take over a year), or that someone is working on the problem right now. The only way to find out is to ask someone who is on top of things.
true, and about what i expected. i've scheduled to go back to school 2 or 3 times during the break to discuss my progress with him and i'm sure this will be among the topics we will discuss.

They probably all are. If the solution is very recent, then you may have an alternative proof, an interesting lemma, or you may gain a lot of insight. I would recommend you to use this initial period prior to actually working with your prof to get as good as possible. If you just pick out your favorite problem and work on it you will learn a lot and even if it turns out to be solved, your insights will probably help you greatly on lots of related problems.

Anyway for some more direct advice: as owlpride said it can be hard to determine if the solution is very recent, but if you know one of the most prominent papers that discusses the problem, then simply search for papers citing that. If someone publishes a solution it's very likely they start their article with "In this paper we prove a conjecture set forth in [a] and further explored in , [c] and [d] using techniques from [e] and [f]".


also very true, and i hope it didn't sound elitist or something when i said "worth my thought" i simply meant that i don't want to spend alot of time on a problem only to discover it has been thoroughly solved. however, you make a good point and one that i didn't (but should have) consider.

thanks for the replies.
 

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