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I was an undergrad student with Professor X a few years back. Prof. X used to be a co-author in all the publications with Prof. Y. Prof. Y is very popular in the field.

Now, I am working in a university. I have keen interest to work with Prof. Y on a few problems of interest.

I have less idea on how to collaborate in such a situation where I don't have indirect contact apriori. The option that I have is to send a mail to him which looks as follows:

Subject: Request for collaboration -- Problem A and Problem B

Dear Prof. Y

Greetings!

I have learned about you from Prof. X during my works with him.

I have gone through your recent papers: [this] and [this]. I am good in Method1 and Method2 which could suitably address your problem.

My recent works can be found in [this profile link].

Looking forward to hearing from you.

Sincerely,

me

-- [my signature]

Is this approach a suitable for my collaboration with Prof. Y?

Update: I had sent an email to Prof. Y after incorporating the suggestions from the fellow academia.SE community members here. I got a response from Prof. Y and looks like he is also interested in working together.

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    Your draft seems a little bit informal and you are not asking anything. You are saying "Here I am, now please ask me to collaborate!". You should probably ask directly if a collaboration is of interest for Prof Y. – Ian Nov 15 '16 at 9:36
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    You say "looking forward to hearing from you", but you didn't ask for anything. I think you need to put in more effort up front so you can say, e.g. "I believe method 1 could be used to solve problem X, which I know you are interested in. I've attached my notes showing how this works, but some details are missing and I think you have the right expertise to complete the proof/experiment/computation. Would you like to work with me on this?" – David Ketcheson Nov 15 '16 at 10:09
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    In my field, it is more customary to skype or visit to discuss a potential collaboration before a collaboration actually occurs. I would be much more open to people asking to collaborate if they ask to first discuss the topic at hand instead of immediately asking for a commitment in collaboration. – T K Nov 15 '16 at 11:15
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    Maybe you can asl Prof X to introduce you two. His email will certainly be read by Prof Y, and his word will mean you are not a crank. – Davidmh Nov 15 '16 at 12:18
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    @Coder I would not send something too long, it would get glanced over typically. I would just say something short and say "I would like to talk to you further about your work and possible new directions in your work using my ideas and techniques." – T K Nov 15 '16 at 12:46
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Let's elaborate on my comment in this answer. Here are the issues:

  1. There are just statements in your draft, no actual question.
  2. The tone of the mail is a bit informal for the case you don't know Prof. Y (at least in my opinion). Leaving out the "Greetings" will make it better.

Here's my proposal for the mail:

Subject: Request for collaboration -- Problem A and Problem B

Dear Prof. Y,

I have learned about you from Prof. X during my works with him.

I have gone through your recent papers: [this] and [this]. Recently, I have worked with Method1 and Method2 which could suitably address your problem. Would you be interested to (Removed: collaborate on [thing] with me?) talk with me about the topic in a phone call or meeting? It would be a pleasure to work with you on this topic.

My recent works can be found in [this profile link].

Looking forward to hearing from you.

Sincerely,

me

-- [my signature]

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    I still think this is too informal, and I'd personally be surprised to receive an email straight out asking to collaborate. I would suggest allowing them the initiative, something more along the lines of: -- "I have been reading through your recent papers: [this] and [this] and I have some ideas which may be of interest. Would you be available for a meeting where I could discuss them? I have recently worked with Method1 and Method2 and I think they could possibly address your problem. It would be a pleasure to work with you on this topic." – Daniel Nov 15 '16 at 11:51
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    @Daniel: Good point, I'll rework that sentence. – Ian Nov 15 '16 at 12:05
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    Simply stating "I have worked with ... " the methods is not good. Probably many people have worked with the methods. Why should he collaborate with you and not someone else? Don't make him click through and read all your publications; explicitly say "In [publication], I used Method X to [do something], and in [publication] I used Method Y to [do something else]". Show that you are expert enough in the methods that you can get publications with them. If you haven't, an experienced researcher is not going to be interested in working with you. – iayork Nov 15 '16 at 13:39
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Of course it can work, it is done all the time. Right now we got several projects running with other groups all around the world, some of them started with a mail basically saying "hey, you are doing nice work, we got an idea and would need your help, are you interested?".

For your situation it depends on what you want from this collaboration. Do you want them to do a part of that project because they can do it (better)? Or do you want to go there and learn how to do it yourself, which is more like an internship. Or do you have a solution to a problem they are having, which is in my opinion not a common reason to start a cooperation.

I agree with @ian_itor that your mail basically doesn't say anything about what you want from that Prof. Y. And especially this part is kind of strange:

I am good in Method1 and Method2 which could suitably address your problem.

Is beeing good in that method something special? Couldn't they do it alone/find someone else? Do they really need YOU? Did they explicitly stated that they have this problem? And do you need them?

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