How to Add An Aspect Of Originality In My UG Research

Question

Intro

Hello, I am a fouth year undergraduate student in physics and I am interested in continuing my studies as a theoretical physicist in, hopefully, a major university. Asking my professors about what I can do to better my chances, they told me that, among other things, something that I can do to stand out is to write a good research project and ideally, get published.

Long Version Of the Question

As far as topics goes, I know from other questions in the site, that most of you guys advice that I should decide the topic of my project with the advisor. However, they offer a set of problems that students choose to tackle and when all of them are picked, they urge us to make recomendations. So if you can recommend any really interesting topic in quantum mechanics,particle physics or so , please do so.

But most importantly, I would like to know what kind of project in theoretical physics would make an undergraduate student stand out. I mean, it seems to me that its "easier" to make an experiment to measure something new. For example a friend of mine measured the dielectric properties of grey matter in some specific temperature (different from others).

But how could I do something simmilar as an undergraduate? I've been told that a way to do that is to solve a differential equation of a phenomenon making some new approximations.

Short Version

So, to recap. I would ideally like a recommendation of a topic to tackle and more importantly ways that I could give an aspect of originality to it.