I live in an Asian country and completed my master's in Math in June 2020. I want to do a PhD in Europe, but I have had some difficulties in finding a suitable position. I do not believe doing a PhD in my country is a good option due to extreme racism and corruption, abuse. These issues had already taken a toll on my mental health and the system is delibrately and very heavily gamed against my group in the country I was born.
I wrote to professors in Europe 3 weeks ago whose interests align with mine to discuss the possibility of an internship. This would had help me get my foot in the door, and hopefully strengthen my PhD application. However, I don't have funding.
I sent an e-mail along with SOP that explained my situation (including past hardships, issues in my country, etc.) and providing my CV and master's thesis.
Many professors have already replied back negatively due to various reasons and hopes are not high that I will get an internship in Europe. It was already suggested by answers in this question: What is the best way to approach professors in Europe about the possibility of an internship (as an unfunded, international student)?. But I really want to do an internship. I was also thinking of writing to profs in China but I came to know that they are not much specialized in Pure maths and hence I didn't wrote to them.
A professor of France suggested that I should apply to USA, Canada as this sort of arrangement is more common there and there is no money for internships in France.
Before, writing to professors in USA and Canada, I wanted to make sure by letting know of your opinion that can such a plan with internship of atleast 2 months and atmost 1 year can materialize in the system in USA and Canada when a student is unfunded?