The importance of having a "big name" as your thesis advisor When it comes to postdoc positions in mathematics in the US, does it make any difference for the hiring committees if your thesis adviser is a big name (say, someone like Gromov or Milnor)?
I'm surely not the most qualified person on this site to answer, but I have been on a postdoc hiring committee in pure mathematics and I quite disagree with the existing answers. The single most important factor is going to be your letters of recommendation (with second on the list being your publications and preprints). I think having a famous advisor is going to be of minor importance in comparison; most people understand that also great mathematicians sometimes have students that are just mediocre, so that it's no great predictor of future success. In fact I heard in a sense the opposite argument being made, that if an applicant from a smaller university with a less famous advisor has strong letters from big names, then this is more impressive than if a student at a "top" university had the exact same letters.