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.
Collet-Eckmann type conditions and conformal welding of unicritical quadratic laminations, submitted arXiv
On convex domains maximizing the gradient of the torsion function, submitted arXiv
Many lemniscates with large diameter, arXiv
Electrostatic skeletons and condition of strict descent, arXiv
Julia sets as Conformally Balanced Dendrites, In preparation
You can also find my papers on Google Scholar