Postdoc opportunities in mathematics I am expected to finish my Ph.D in mathematics (if relevant, more specifically - in commutative/homological algebra) by the end of this academic year. I am studying in a somewhat minor university, although my supervisor is a well know figure in his field.

Following my supervisor's advice, I submitted applications for postdoctoral positions in about 20 top level universities in the US. As most of these universities already finished hiring for this year, I suspect I made the mistake aiming too high, and would probably get negative answers from all the different employers.  

Assuming this is the case, I am now wondering what should be the next step in my academic career. One option is to stay at my current university for another year (but with a much lower salary, as my scholarship will come to an end). I should mention that my supervisor highly discourages this option, as he thinks that I should get more involved in the research community of my field, and my current university is a poor place to do so.

Alternatively, I am wondering if there are any other opportunities for postdocs in Europe or the US for the 2013 academic year, in my relevant field, of which the deadline still did not pass.

Any advice or idea for my situation would be helpful.

Thank you
There are several major websites on which jobs in mathematics, including postdocs, tend to be posted.  Most importantly (in the US) mathjobs.org, but also the AMS's service and others.  (See this mathoverflow question for many more.)  Postdoc positions can take a while to sort out, since many of them are filled (or even created) in response to what happened earlier in the hiring season, so there may still be opportunities, especially if you're willing to look outside the US.