Is it possible to ask about student research project ideas in this website?
In the past, I have seen several such requests and one answer that always shows up and is usually the most popular is:
This is not the right place to ask this. It would be better to ask your teacher/adviser who will be helping you and who knows you better.
On top of what Graphth says, and I agree with, if you are looking for projects which might lead to publishable original work and can be worked on by an undergraduate in the course of a few months, it is really hard to find such questions. I have a very small number saved up for the REU program at Michigan this summer, and I don't want to give them away. I suspect that most mathematicians who mentor undergraduate research feel the same way.