I've seen many posts in this website about changing fields (sample: 1, 2, 3, etc...). This is very reassuring for me, since I wanted to do just that. Just to sum up, I want to study an area of mathematics which no one works on at my university - Group Theory, to be precise (mostly finite G.T., but I'm very open-minded about it).
I've done my best to do my undergraduate and masters degrees in as close a field as possible at my university, and kept studying some material on my own to make sure of my desire to switch gears for a PhD at another institution in the future.
That said, everywhere I look pretty much assures that, when contacting a prospective advisor, you should always establish a link between what you have done and what they have done. This leads me to pose:
How to overcome the disadvantage of being relatively unfamiliar with a new field of research when contacting a potential advisor?
What I've studied, I've done on my own, meaning I have no certificates or the like to testify my studies and put on a CV, for instance. Furthermore, I won't even pretend to know as much as I could had my MSc been on finite group theory.
Are advisors actually willing to take on students that don't have as much familiarity with their field of research? And what can I do to level the playing field against competition which is (presumably) more acquainted with the area? I am planning to apply to positions in the US, UK, Canada, and possibly elsewhere in Europe.
Thanks in advance!