I am a PhD student in Stochastic analysis, obsessing over Deep Learning. My research focuses on diffusion approximations aka stochastic modified equations for stochastic gradient descent and other stochastic optimization methods.
I used to be mostly interested in category theory. While I don't plan on doing research in that area any time soon I think the fairly new field of applied category theory looks fascinating.
I wrote a song about Gauss, which you can listen to here: https://www.youtube.com/watch?v=93Bab7S3hjA