How to know whether a Faculty member has done good work or not I have completed my Masters in Pure Mathetics in India and I want to join a Ph.D. program in Algebra and Number Theory.

For that reason, I am checking the profiles of the faculty members of the different institutes where I can join.

But the problem is I don't understand how to judge the profiles of the faculty members and what are the parameters.

Should I look into the following:


From where the faculty member has done his Ph.D., is it from India or from abroad.
Under whom has he done his PhD
What are his publications? Where has he published them?


Though I can check 1 and 2 but how do I know about his publications?
How do I know that he has done good work in Algebra and  Number Theory or not?
It's not possible for me to know about all journals in Algebra and Number Theory as I have not done any publication before?

I really need some help as I don't want to join an institute where no good faculty members are available?

How to judge? Please help.
The institution and the advisor give you very limited information. Of course, a very bad person would not be admitted at a very good institution, but even god institutions and great advisors have mediocre students. The same goes for journal names. All but the top 10 journals sometimes publish mediocre papers, and some great papers appeared in middle ranked journals.

A better way to judge people is by looking at the reviews of their papers in MathSciNet or Zentralblatt. Citation numbers are easy to manipulate, so having many citations does not necessarily mean that you are good, but few citations are a bad sign. A good indicator is by how many different authors someone was cited. If you have many citations by few people, something seems fishy. You can also look at their most cited papers. If many of them are surveys, books, or pose many open problems, the citation number is exaggerated. Worse, if there are many self citations. Next, you should read the reviews themselves. Since you want to know what the faculty members are doing, you should do so anyway. The personality of the reviewer plays a role, but I would expect that every decent advisor has some papers that are praised by the reviewer. If all reviews are short summaries of the main results, the reviewer was either lazy or didn't find anything important in the article. Articles without a review are usually worse.

A big red flag is the use of predatory journals. Some people might be too innocent to see through this scam, but every half way decent research can be published in a real journal. Not necessarily a good one, but one which has actual peer review going on. On the other hand, publishing in a little known journal, or conference proceedings is not a bad sign, unless it is always the same journal/conference, or more than a quarter of all publications are of this type.