I work at the intersection of probability, analysis and geometry. My research to date has focused on the theory of multiplicative chaos and their applications in mathematical physics and probabilistic number theory. The following is a simulation of an approximate Gaussian free field with Dirichlet boundary condition on the unit square.

Below you can find further information about my various research topics and related simulations/visualisations.

Spectral geometry of Liouville quantum gravity

(Under construction...)

Liouville Brownian motion (at γ = 0.5) on the heatmap of underlying approximiate GFF (left) vs proportion of time spent at different field heights (right)

For general audience

Here are some slides from a talk about my interest in Gaussian multiplicative chaos as a universal random multifractal measure, aimed at a general non-mathematical audience.