Is it possible to obtain a PPL after having a brain surgery?
According to AOPA's medical guru on their discussion board (members only, or I would link to an example) it is possible to get a medical certificate following a tumor removal but only after a 5-year wait and a battery of tests.

But having said that, medical issues are very individual and the FAA's AME guidance suggests that one year is enough in some cases. In the end the only way to get a definite answer is to find a good AME who can review your case in detail and advise you. Note that standard advice is to schedule a consultation first, rather than go straight for the actual flight medical.

Disclaimer: I'm not a doctor or AME and I have no idea how brains work :-)