Doing research/travel between postdocs (pure mathematics, Europe) I have just finished a postdoc but will not start a new postdoc for a few months.

In the meantime, I will continue to do my research. The problem is that I registered for a conference while at my former institute and the conference will take place while I'm not officially employed at any institute. I also plan to visit collaborators during this time and will likely need a visa for at least one of the visits.

I'm hoping someone else may have been in this situation and have some advice:

What do I put as my affiliation for that and any other conference I might attend in the meantime? Will not having any affiliation affect my ability to participate in conferences or make research visits?
I was unaffiliated for a little over a year between postdocs.  I attended two conferences in that time and didn't list any affiliation.  I also made two research visits, for one of which I received some funding from my host's research grant, and being unaffiliated (or 'an independent researcher', as my host put it) was no obstacle.

This might depend somewhat on country and research area, of course.  And I didn't need a visa for either of the research visits, but I'd be quite surprised if not having an affiliation right now would be an obstacle to getting one (again a little depending on the visa-issuing country).