Hi, I hope below can be categorized under career questions.

Based on your experiences what are the major issues/concerns and differences of professor sponsored postdoc positions (compared to department sponsored ones) ?

Sometime ago, I read an article which was noting that the probability of finding a TT job is highly correlated with the perceived ranking of the university where postdoc is done. (I think it was an AMS article but I can't find it now).

Assuming productivity of a TT job candidate is constant, what do you think about the importance of the ranking of the candidates current (postdoc) university ?

For mathematics postdoc positions, what is the main difference between the named postdoc positions and regular ones ? (such as XYZ V.A.P. or just a VAP)

Thanks in advance.