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i worked on writing numerical integration routines for weight functions with border-singularities. i can send you the paper if you want. It’s not very theoretical, moreso computational :)
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Currently finishing up my bachelor's thesis. The content can roughly be described as extreme value theory of stochastic processes.

The main part of the thesis is based on a very recent paper (july 2022). It basically extended known results for time series (stochastic processes in discrete time) to continuous-time stochastic processes. Therefore i'm explaining the results given in this new paper and perhaps compare them with previous results about time series.

Additionally, and this will almost always be necessary for a bachelor's thesis, you'll need to give some brief introduction to relevant prerequisite marerial. In my case this means writing a bit about multivariate extreme value theory and about (càdlàg) stochastic processes, their topology (J1 topology) and weak convergence.

Then as some 'bonus', i develope some original results (though not too novel results imo) for special cases of stochastic processes, specifically Markov processes. For a bachelor's thesis you aren't really expected to develope original results, but it's certainly possible to some degree and it'll likely lead to a better grade.

As to how i found the topic i wanted to write about: I just looked at a journal my professor was an editor of and searched for something that seemed interesting. Then contacted that professor to ask whether it would be possible to write my thesis about this paper and it was quickly approved.
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My Bachelor thesis was about fix point theorems with focus on Brouwer, Schauder and some game theoretical application.
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Currently doing my thesis on the connections between group theory and formal languages. In particular, discussing the Muller-Schupp theorem and some more recent results.
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My undergraduate thesis was on representation varieties of the Heisenberg group (original research).
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Hausdorff dimensions, but If I could do it over I would  have definitely done something with graphs or combinatorics.
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My undergraduate thesis was on the definition of variety in non commutative algebraic geometry.
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