I'm worried this might not be fitting for this forum, but it's basically a literature and reference request.
I'm looking to do a project in algebra where we are supposed to research some topic (preferrably something fresh) for a few months and write about it.
Such a new subject that has catched my fancy is that of tropical geometry (in the sense of min/max-plus algebras), but upon researching it, it seems that the only applications to actual problems are in fairly advanced algebraic geometry, which I don't know much about.
So my question is: are there any open questions or recent theory in tropical settings or similar that is comprehensible for an undergraduate to understand, investigate and perhaps speculate a bit about?
I've heard that there is theory for transfering from normal geometry to tropical that maps multiplication to addition via the additivity of the logarithm and a limit process for the addition to maximum part, but I was unable to extract something along those lines from the articles google led me to.
Basically, I'm looking for something that is new, but not super technical or overly messy. Is it perhaps better to investigate some related aspect of algebraic geometry? Any literature reference or insight into these branches of mathematics would be greatly appreciated. If you have a wildly different, but interesting suggestion for a subject you could share that too.
For reference about the level I'm looking for, I'm familiar with subjects such as vector calculus, complex analysis, baby rudin level analysis, basic probability theory, linear algebra, basic fourier theory, basic abstract algebra and so on.