My research in mathematics explores the deep connection between the type of analysis that a (metric) space supports and its geometry. Here analysis encompasses the extensions of tools from calculus, measure theory, potential theory and PDE's. Geometry of a space concerns its embeddability into more familiar spaces, its path connectivity (quantitatively), its Hausdorff and other dimensions, its rectifiability, etc.

My research has also concerned conformal and quasiconformal mappings and uniformization of metric spaces.

I enjoy teaching mathematics just as much as it is reminder of how elegant and intuitive math should end up at the end. My teaching is always evolving according to the new challenges and based on feedback from my students. Currently, I am looking for ways to utilize AI technology as a resource for both students and instructors, rather than fight it!