I am interested in various topics at the intersection of theoretical/mathematical physics and geometry. My most recent work is focused on the geometric aspects of quantum Hall states.

This recent work is about geometry of the integer and fractional quantum Hall states. Main research highlights: derivation of the gravitational anomaly and central charge in integer and fractional quantum Hall states, novel quantized coefficients in geometric adiabatic transport of QH states on moduli spaces of Riemann surfaces, definition and construction of Laughlin states on higher genus Riemann surfaces.

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):