Suggestions for a math major honors thesis topic

Hello, I'm math major with fair amount of programming experience and I want get into ML/Data Science career. I'm doing a honors thesis next year and I'm looking for tentative topics, some of them are in Topological Data Analysis, Graph Theory, Optimization.

There is a chance I will apply for grad school (M.Sc.) in either applied math or computer science. So my question is:

What topic(s) will help me to get a good grasp and foundation of ML/DS?

I can't decide whether to do a broad topic (like optimization methods in ML or statistical learning theory) or niche like computing persistent homology.

Thank you very much.