How to know whether a Faculty member has done good work or not

Question

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.

Answer 1

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.

Answer 2

If at all possible, I would ask professors at the institution where you finished your Masters.

Some additional steps you might try:

• Try to find a list of publications -- for example, these may be on a faculty member's web site or the institute's web site. There are external sites like Zentralblatt and MathSciNet which also list this data, although they require an institutional subscription. You might also try the open-access arXiv. Many researchers post preprints of their papers (which you can then read), and sometimes they also say where the paper was published.

  Generally speaking, you want to work with someone who is actively publishing in good journals. Eigenfactor is one website which rates journals, including math journals. Take these ratings with a big grain of salt: I wouldn't take the exact numerical scores too seriously. But if you're not familiar with any of these journals, then sites like this are a useful rough guide.

• You might also look at the Math Genealogy Project. If prospective advisors have graduated Ph.D. students before, this is a good sign. If you aspire to an academic career, then google the students' names and see if any of them have landed academic jobs.

• Finally, you might try emailing professors at your target institutions, say that you are considering applying to their Ph.D. programs, and asking about opportunities for research in algebra and number theory.

  Before doing so, use the Internet to find out as much about these programs as you can. If it's clear from your emails that you've done this, this increases your chances of a positive response.

Good luck!

Answer 3

Other answers have commented on how to evaluate the quality of research output. In my opinion it is at least as important to evaluate if a supervisor is a good match for you. Research excellence does not necessarily correlate with excellent mentorship of students. Sometimes (maybe even often) famous professors have little time to devote to their students due to other commitments.

A good way to find out is:

• Contact current/former group members and ask about supervision style/lab culture, does this match with how you work?
• Find out where former group members have gone afterwards. Have they moved to prestigious institutions/got faculty/industry jobs, does this match with your career goals?
• If you want to travel/visit other institutions, see if the potential supervisor has an international network of collaborators (for example look who the co-authors are on their papers).
• If possible arrange a face-to-face meeting, or a phone call, to get a sense of if this is someone you could spend the next few years working closely with.