My mathematical interests revolve around analysis. In particular, I study singular integral operators, harmonic analysis, spectral theory of self-adjoint operators and mathematical physics. This past year, I have mainly worked on finding cyclic vectors of Anderson-type Hamiltonians and rank one perturbations. My postdoc advisor is Prof. Alexei Poltoratski. I have further worked on a project with Distinguished Prof. Ronald G. Douglas on the model theory of higher rank perturbations.
I am co-organizing a workshop on `Recent advances in Harmonic Analysis and Spectral Theory' within the framework of the annual Workshop in Analysis and Probability (Summer 2012) at Texas A&M Univeristy.
I am partially supported by the National Science Foundation: DMS-1101477.
Selected publications