Mathematics GRE

I'm a third year mathematics student from Middle-east. My university is best in the country and yet not a lot of our professors are active researchers. Either their research area is not within my area of interests or they are not really good mathematicians or that simply they don't want to do research with undergraduates. Moreover, My designated supervisor won't answer any of my questions (Ignores).

I need to find a professor i can link with, for doing research, for study guidance, for general help really. My field of interests so far are Analysis and geometry (But of course, as an undergraduate, I'm intrinsically confused among all the areas of maths there are).

I don't how to write an email asking for this. I can find many great professors within my area of interests sure but when i check out their publications, I can't really make sense of their work. It's highly advanced for me (Even though i have taken multiple advanced courses in geometry). So I don't know how to ask to work with them if i don't understand their work properly! How to ask for guidance without being ignored?

I see that many of undergrad students here have research experiences with prestigious professors. I would really really appreciate it if you could share your experience of linking with professors. How? What to email (I'm particularly shy in this matter)? What to do and What not to do?

Apply to the Polymath JR REU next year: it is a remote research experience that accepts most people and has tons of options + great research projects.

But as for your main question, maybe try to email researchers you've found with your exact question and seek their advice too. Ask for a short 20/30 minute meeting, and try to get their advice on what is reasonable or not to ask for. Then, email more new people asking for that (unless they are willing to help you more proactively already).

Try to aim for researchers in "top" and less highly ranked programs, and especially those whose websites have a strong teaching component. Especially try to email researchers from your own background and culture - they'd relate to your problems the best.