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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.

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A few thoughts --

  • Don't put all your eggs in one basket. It sounds as if you've staked all your plans around working with a single professor. In general it is better to apply to multiple Ph.D. programs.

  • Go to conferences! While the pandemic is ongoing, you should be able to attend multiple conferences for free via Zoom, in your field of interest. Take advantage of this opportunity! Listen to the talks, get a sense of what people are interested in working on, and ask questions if you have a good opportunity. See here for a list; any "summer schools" or similar are even better (but might cost money).

  • Don't expect professors to read a lot of material. Unfortunately you can't send (for example) a copy of all the exercises in Hatcher and expect anyone to take a careful look. You could, however, make this material available on a website and let professors know about it.

Good luck.

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It's fairly easy for people to identify other people in the field. You need to demonstrate you know the topic during the conversation.

The easiest way is to read the professor's papers and offer intelligent comments when you first write to them: what is interesting about the paper and why, what you want to work on, etc.

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