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Just wondering how much emphasis I should place on the following factors when 'selecting' PhD advisers to approach: 1) If a PhD adviser has a few published Top 5's versus one who has published consistently in top field and second tier general interest journals. The reason I ask this question is because I have heard that academics with Top 5's help push PhD students towards Top 5 publications more so than those without. Although, I'm not sure how true this is, it's just what I have heard. 2) The quality/rigour of the core and field courses. Assuming a strong enough Math background would someone be able to self-study sufficiently to overcome weaker courses 3) Being in a good academic location surrounded by other universities conducting good research. Maybe this network effect has good influence on further developing ideas. I know there are other considerations to have in mind such as placement ranking, supervisor compatibility, however, just wanted to know how much emphasis I should place on these in particular.