First of all, let me apologize if this is posted in the wrong forum. I did my best to find the right one.
Now to my question:
I'm a math major (senior with 13 months until graduation) who is looking to get into research. I'm wandering...what exactly is expected of undergraduate research for it to be impressive to graduate admissions of a top 20, top 50, or top 100 university? (PhD track to be specific)
For instance, if you are working on an unsolved problem, are you expected to solve it, reduce it, reformulate it, find an interesting way to view the problem, or merely discuss it? Or are there even (m)any open problems that are accessible to an undergraduate on a non-trivial level?
Also, slightly related, what areas (algebra or analysis related) are even feasible for an undergraduate to research?
I've met with my adviser but somehow this raised more questions than it really answered. I would be extremely grateful for any advice/information.