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Yesterday I attended a seminar talk titled "Cluster presentation of reflection groups", and before it I tried to ask Google what is a "cluster presentation" --- but all one can find on this request is about databases or social studies.

Another example: try to find something on "geometrical groups" and not "geometric group theory".

I think this is a very common problem, when you are interested in some area you don't know anything about and trying to find some texts on it --- but it's very hard if you don't know what exactly to look for. Of course if you have someone to ask, it's not a problem anymore, but usually you don't.

So the question is: how to start learning an advanced topic if you don't have any texts or guidelines about it (and have nobody to ask except for MO community)?

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In the old days, before the internet, I used to wander through the math library glancing at random math books that seemed interesting. This gave me a sense of where everything was. I would also browse through newly arrived journals and sometimes even bound volumes of old ones. This gave me a sense of what was out there and what things were called. Then if I wanted to learn something specific, I had some sense of which part of the library to look in and I would just look through the books or journals I suspected were relevant. And do this while you're young. You won't have the time later. –  Deane Yang Oct 22 '11 at 14:25
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In the case of a seminar you can try to look up some articles by the speaker and see if you can find any useful references. –  Pieter Naaijkens Oct 22 '11 at 14:25
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Why would you be interested in "Cluster presentations of reflection groups" if you don't know what the words mean? Surely whereever you are, there must be some talks of which you can understand the title, at least? –  Igor Rivin Oct 22 '11 at 14:37
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@Deane Yang - well, the library in SPbSU (Russia) doesn't allow to "wander through" --- you can only ask for specific book, but that's all. And it also doesn't have any new books and journals. –  Andrei Smolensky Oct 22 '11 at 14:41
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Andrei, that's quite disappointing to learn. I find random luck to be a great way to stumble onto new things I like and want to learn about. Anyway, posting a question on math.stackexchange.com or MO seems like a reasonable thing to do when you have some vague idea of something you want to learn more about. –  Deane Yang Oct 22 '11 at 14:58
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3 Answers

Fundamentally, your question seems to be about having or acquiring strong library skills. Researchers in any area will have trouble finding specific or accessible articles and texts, and the difficulty in knowing where to start looking is not unique to mathematics.

I am going to be a bit critical, but you need to learn to fully utilize the existing online resources. Sometimes it takes a lot longer, so have patience, and search:

Searching the key terms separately immediately yields hits on Wikipedia. Specifically, we find the following articles:

Presentation of a Group

Reflection Groups

Of course, after reading the wikipedia article, we will know a little more, but fortunately many books and papers are given as references at the bottom of the page. This tells us exactly where to look for a more in depth discussion.

Next, the word Cluster in this context does not seem to be widespread. No hits come up on Math Sci Net for Cluster Presentation. (hopefully your university gives access to it!) This might mean that the lecturer at the presentation you went to is one of the first to use those words in that particular order.

Lastly, if you search "Geometrical groups" with the quotations in Google you get several results. One of which is a book, and from reading a few lines it is possible to determine that geometrical groups refer to groups which are given by geometric objects.

Google Scholar is also very useful, but I did not use it for any of the above searches. Also, your home universities library catalog can come in handy some times. Keep these in mind.

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This is just about your first frustrating seminar talk. You might borrow a book by James Humphreys, Reflection Groups and Coxeter Groups. I borrowed this because of this course announcement: http://www.ma.utexas.edu/users/allcock/teaching/Coxeter_groups/Coxeter.html and first homework http://www.ma.utexas.edu/users/allcock/teaching/Coxeter_groups/index.html by Daniel Allcock of U. T. Austin.

I got plenty of stuff on Google with: presentation "reflection groups" so it is the word "cluster" that is a bit too specific.

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How basic is basic? An ideal presentation announcement will mention the intended audience, as well as what prerequisites will be assumed and not covered. A bibliography also will give a few clues.

If the subject has old enough roots or foundations, one can turn to certain compilations for motivation and partial explanations that are pitched to a more general audience which possesses graduate level experience. I personally like Encylopedic Dictionary of Mathematics from MIT press; others like A Princeton Companion To Mathematics; hopefully this thread will produce a few more titles.

Gerhard "Ask Me About System Design" Paseman, 2011.10.22

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For encyclopedias there was once a question mathoverflow.net/questions/60895 –  quid Oct 22 '11 at 21:06
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