My research interest lies in partial differential equations, in particular mathematical fluid dynamics ( MHD equations) and also nonlinear waves and dispersive equations such as the Benjamin–Bona–Mahony (BBM) equation and the Dirac equation. Over the past year, I have become interested in turbulence theory. Most of this has involved learning and doing some research in Hall and electron MHD turbulence. I find turbulence theory very fascinating, and I look forward to learning more and doing some research in this area in coming years.
For the first two years of my PhD, I worked in differential geometry, focusing on Higgs bundles and Hitchin systems. Although I did not publish in this area, I picked up a number of geometric tools and perspectives that I’m excited to bring into my research in PDEs in the future.
In past when I was in physics, I did some research on non-Hermitian Hamiltonians in quantum mechanics, and some of the results of that resrach can be found in the publication #6. Before that, I participated in a research group working in solid-state physics and its applications to solar cells which leaded to publications #7 and #8.
Local well-posedness of BBM equation on half-line with Robin boundary conditions (Under Preparation.) - Joint work with Jerry L. Bona.
Local and global well-posedness for 1D nonlinear Dirac equation on half-line with Dirichlet boundary conditions (Completed and will appear on Arxiv very soon.) - Joint work with Jerry L. Bona.
Rigorous analysis for the Dirac system on the quarter-plane. [arXiv:2606.19326] (49 pages) - Joint work with Jerry L. Bona and Andreas Chatziafratis.
Determining wavenumbers for Hall and electron MHD turbulence. (2026) [arXiv: 2604.10804 ] (39 pages) - Joint work with Mimi Dai.
Local well-posedness for electron MHD with partial resistivity (2025) Submitted for a publication, [arXiv: 2503.18149 ] (15 pages) - Joint work with Mimi Dai.
Quantum Mechanics of a Photon, Journal of Mathematical Physics, 58, 082302 (2017) - Joint work with Ali Mostafazadeh.
The effects of recombination lifetime on efficiency and J-V characteristics of InxGa1-xN/GaN quantum dot intermediate band solar cell, Journal of Physica E, 42, pp. 2353-2357, (2010) - Joint work with Nima E. Gorji, Hossein Movla, Foozieh Sohrabi, Ahmad Hosseinpour, and Meisam Rezaei.
Photocurrent and Surface Recombination Mechanisms in the InxGa1-xN/GaN Different-sized Quantum Dot Solar Cells, Turkish Journal of Physics, 34, 97-106, (2010) - Joint work with Hossein Movla, Foozieh Sohrabi, Jafar Fathi, Arash Nikniazi, and Khadije Khalili.