I am interested in various topics at the intersection of theoretical/mathematical physics and geometry. My current work is focused at the interface between random metrics, quantum Hall effect and Kähler geometry.

This recent work is about geometry of the integer and fractional quantum Hall states:

Work in progress on a novel approach to random metrics in two and higher dimensions using recent methods in Kähler geometry:

My PhD work (my advisor was Michael Douglas) is about physics applications of Bergman kernel and balanced metrics. We show that the Bergman kernel is equivalent to the density matrix of a particle in magnetic field, projected on the lowest Landau level. We use quantum mechanical path integral to derive its asymptotic expansion:

Paper on the connection between Liouville 2d gravity and Stochastic Schramm-Loewner Evolution:

Some earlier papers (written at Lomonosov Moscow State University and at ITEP, Moscow):