## Departmental PhD Thesis Exam – Krishan Rajaratnam

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Friday, October 19, 2018
2:10 p.m.
BA6183

PhD Candidate:  Krishan Rajaratnam
Supervisor:   Michael Sigal
Thesis title: Abrikosov lattice solutions of the ZHK Chern-Simons equations

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In this thesis we study the ZHK Chern-Simons equations which occur in the study of the fractional quantum hall effect of condensed matter physics. After stating basic properties of these equations, we first prove the existence of Abrikosov lattice solutions of them.  Among these solutions, we find the physically interesting one whose lattice shape minimizes the average energy per lattice cell. In addition to the Abrikosov lattice solutions, we find solutions of the ZHK Chern-Simons equations on Riemann surfaces of higher genus $g$, by utilizing similar results for the Ginzburg-Landau equations.

Finally, we study the orbital stability of the Abrikosov lattice solutions under perturbations which preserve the lattice.

A copy of the thesis can be found here: