Broadly, I'm interested in problems in 2D geometry that involve probabilistic models and conformal geometry techniques.
For the past year, I have been working on the geometry properties on dendrite Julia sets.
I am currently interested in 2D spectral theory in relation to the reflected Brownian motion.
On convex domains maximizing the gradient of the torsion function, arXiv
Collet-Eckmann type conditions and conformal welding of unicritical quadratic laminations, arXiv
Julia sets as Conformally Balanced Dendrites, In preparation