I am currently studying the relationship between diffusion processes and geometry. Notably (and rather unsurprisingly), Diffusion Geometry plays a big role in my daily research. In particular, I mostly try to explore how to understand the geometry and the shape of data when we only have discrete observations of it. This is what I like to call the implicit manifold hypothesis, explored in this preprint, where we construct continuous-time diffusion processes on the implicit smooth underlying state space describing the data, through only point cloud observations.
This naturally also leads to me have strong interests in generative modelling and sampling of manifold-valued data. You can find some work on this in the Publications tabs.
Due to many continuous priors in physics, I am also drawn to using diffusion-geometric ideas in areas of physics, such as Lattice Field Theory.
I also have a very infrequent YouTube channel, where i talk about whatever i feel like. I've made a few albums e.g. here, some of which you can find on my Spotify.