I am a PhD student in mathematics in the US. I got a 3 year postdoc position at a R1 university in USA and I was extremely happy about that as the department is pretty strong in my research area and my postdoc mentor, say Prof., is a top researcher in my area and also works on similar things as me. But Prof. informed me that he has accepted a position in Austria (he is Austrian) but he can offer me a postdoc there for 3 years and it will also include teaching (which I prefer).
I am now really confused about making a decision as to where to go. Since I am from Mauritius, staying in US or going to Austria are bot fine with me. One of the main reasons for accepting the US offer was that I was excited about working with Prof. I am hesitating a bit about moving to Austria because 1) I have heard that the North American job market for tenure track is a bit harder for candidates from Europe and 2) my partner is in the US. I asked my advisor and he suggested that I stay in the US. Below are my questions:
1) How common is it for math postdocs to work without a "mentor"? If I end up staying in the US, then even though the department has a good research group in my area but they work on different type of problems and there won't be anyone "officially" assigned to me as a mentor and I am a bit scared that I might feel to lonely there in terms of research.
2) Will it be considered ok, if I ask the department in the university in the US to maybe defer my position for a year, during which I go to Austria and (hopefully) start a collaboration with Prof. and then come back to the US? Is this something which is common with postdocs? Are universities in US, generally ok with such an arrangement (I haven't consulted the university yet)?Comments from people who had similar experience (either as a postdoc themselves or as a faculty who have seen this happen) will be greatly appreciated? Thanks.