# Applied Math Seminar I Krishan Rajaratnam, Vortex lattice solutions of the ZHK Chern-Simons equations

Thursday, December 6, 2018 — 2:30 PM EST

MC 6460

## Speaker

Krishan Rajaratnam | Department of Mathematics, University of Toronto

## Title

Vortex lattice solutions of the ZHK Chern-Simons equations

## Abstract

We study the ZHK Chern-Simons equations which occur in the study of the fractional quantum hall effect of condensed matter physics. We first give a background of these equations and briefly describe their relation to physics. Then we state and sketch ideas behind our first result on the existence of vortex lattice solutions of these equations. Then we shall describe the physically interesting solution whose lattice shape minimizes the average energy per lattice cell. Time permitting, we describe the generalization of these results to find solutions of the ZHK Chern-Simons equations on Riemann surfaces of higher genus $g$. Finally, we shall present a result on the orbital stability of the vortex lattice solutions under perturbations which preserve the lattice‎.

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