theoretical macroeconomic topic for bachelor project? A lot of my peers are writing empirically oriented bachelor projects, where they take some topic ("tax evasion", "pollution", "ricardian equivalence", "liquidity trap", "fiscal multiplier") and look at the data, and seek to explain the mechanics behind the data by use of models. So it's mostly empirical and investigative, with a bit of theory to support the arguments made.

My question is, what would be a good idea for a purely theoretical bachelor project in macroeconomics? Is there something like that which would be a good idea for a bachelor project, as opposed to an empirical study? 

The reason is that I have a very strong background in mathemathics, so I would like to use that to my benefit and write a technical project, but I am not sure what kind it would be.
I would be careful about confusing topics and tools. Theoretical mathematics and data analysis are ways that you can approach a specific topic. No matter what topic you choose, you can apply your mathematical tools. I would recommend looking for something that interests you at a conceptual level and then seeing how you can apply your given set of tools to answer it.