Biography
I am an Assistant Professor in operator theory at the Department of Mathematics of the University of Salahaddin.
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.
Research interests
- Spectral approximation for ordinary and partial differential operators and operator pencils, ( spectral pollution ) and involve both analysis and computational mathematics.
- Numerical range for ordinary and partial differential operators and operator pencils,, and involve both analysis and computational mathematics.
- Much of my work concerns models arising in mathematical physics, including Schroedinger, Hain-Lust 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.