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Following the line of this question, I'm in my last year of M.Sc., and I'm looking for a place where I can start my PHD. Since that question has been asked 4 years ago, I thought it may be wise to ask whether something has changed.

That is, there are new research groups/universities in the area? The old ones are still active?

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Some particular places have already been mentioned in the answers to the question you refer to, and I think it is not appropriate to give in this place advice on where to do your PhD in computational algebra concretely. That said, some general things I would do in your situation:

  • First of all, search on the internet which research groups which are located (or are sufficiently represented) in regions / countries which you would consider moving to fit best to your interests.

  • Then communicate with a couple of different members of each of these groups, preferably of different ranks (PhD student to professor / group leader). In particular ask them about

    • the working atmosphere (is it friendly / collaboratively? Is there team spirit?),

    • the funding situation (do people always get employment during their PhD studies if they wish so?, are there sufficient funds for conference travel expenses available to PhD students?),

    • the support from the group for former PhD students (recommendations / job references etc.) and its effectiveness.

    I'd suggest you to be particularly careful in case you get contrary answers to these questions from different members of the same group.

    Just in case you are interested, you are welcome to contact me with respect to GAP (I am in the GAP Group since about 15 years).

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  • $\begingroup$ Some people are forthcoming and can give what I think might be good answers to the questions above. A lot of people have political and other concerns which color their responses. If you can phrase the questions so that the answers are "less commital", you may have more success with them. In particular, approach it like " I'm looking for a group which X, is your group like that?", where X reflects your desires. The responder can judge whether you might fit in without revealing any dirty laundry about themselves or the group. Gerhard "Machiavelli Had Some Good Points" Paseman, 2015.11.09 $\endgroup$
    – Gerhard Paseman
    Commented Nov 9, 2015 at 18:17
  • $\begingroup$ @GerhardPaseman: The phrasing of the questions is of course up to the asker, and how best to formulate depends on the country (I think there are e.g. significant differences between the US and many countries in Europe), etc., etc.. -- I mentioned only some key topics to enquire about. $\endgroup$
    – Stefan Kohl ♦
    Commented Nov 9, 2015 at 18:46
  • $\begingroup$ I think it is a good list, and your caution to be careful afterwards is good. In my opinion it should be made even more clear that this is different from doing similar research for a job or applying to a graduate program. What might be natural approaches in those cases may not yield good results here. Gerhard "Obviously Likes This Especially Clear" Paseman, 2015.11.09 $\endgroup$
    – Gerhard Paseman
    Commented Nov 9, 2015 at 18:47

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