I am keen to apply for Doctoral program in Europe. But I have some questions.
All my mathematical interests are centred about Hyperbolic Geometry. And I am keen to apply for PhD position (or join a research group) in the particular field. I have never done the course in my masters, because my university does not offer such course. Also, My master thesis is not in that field (in not hyperbolic geometry). Also, I can not join a internship program or summer school, and reading project on the field under some professors, because this current (Covid 19) situations. Therefore, I am planning to read the topics on my own.
To apply for a PhD program I need to write my interests to that particular professor. Since I am learning the topics on my own, and I have no document for that, then how I would convince him/her that I have read the topics and well prepared to work his/her research group.
Please help me. Thanking in advance.