#### Biography

I received my B.Sc. and M.Sc in Mathematics from Department of Mathematics of University of Salahaddin in 1996 and 2003 respectively. My Ph.D. degree in Mathematics from Cardiff School of Mathematics Cardiff University , United Kingdom, in 2012. From 2003 to 2006, I was Assistant lecturer at University of Salahaddin, College of Science, Department of Mathematics, and from 2006 to 2008 I was lecture at University of Salahaddin, College of Science, Department of Mathematics, and from 2008 to 2012 I was PhD student at Cardiff School of Mathematics Cardiff University , United Kingdom, and from September 2012 to 2018 lecture , at University of Salahaddin, College of Science, Department of Mathematics.

My research lie in the fields of functional analysis, operator theory and spectral theory. I am particularly interested in numerical range of operator matrices, numerical range of operator polynomials, c-numerical range of operator matrices, q-numerical range of operator matrices, q-numerical range of operator polynomials, S-numerical range of operator matrices, S-numerical range of operator polynomials and quadratic numerical range of block operator matrices (theory and numerics). 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.