I am an Assistant Professor in the Department of Mathematics-College of Sciences at Salahaddin University-Erbil
I completed my PhD. at the Cardiff School of Mathematics, Cardiff University, United Kingdom (Thesis Approximation of quadratic numerical range of block operator matrices, 2014), under the supervision of Professor Marco Marletta.
§ Spectral approximation for linear operators ( spectral pollution ).
§ Computation of numerical range, block numerical range
§ Differential operators, e.g. Schrödinger operators, Hain-Lust operators and Stokes operators .
§ Applications in mathematical physics, e.g. in magnetohydrodynamics
One of the main achievements of my research to date has been the absence of quadratic numerical range-pollution, which is new result in operator theory because in general, discretization of differential operators may result in spectral pollution. I have shown that this does not happen for finite difference discretizations of the Hain-Lüst operator is a little more tricky than proving that every point of the quadratic numerical range can be approximated.