Available positions for grads/undergrads/postdoctoral fellows: Yes
Jobs that my graduate students now hold include:
- Mission Engineer at the European Space Agency
- Software Engineer
- Financial Analyst
My early research included solving several outstanding problems in the analytic theory of polynomials, including Schoenberg’s [conjecture], Katsoprinakis’ [conjecture], and the De Bruijn-Spring conjecture. My current research explores classical and functional analysis, matrix theory and quantum information. Key areas of focus include:
- Matrix theory: I explore many interesting questions related to matrix theory. I've shown how the theory of diagonal matrix scalings can be used to find symmetric states with maximum geometric entanglement. I [and coauthors] have solved the Perfect-Mirsky conjecture on the spectra of doubly stochastic matrices for n=4. I have extended a theorem of Wielandt from matrices to Banach algebras, thereby giving spectral inclusion bounds for the sum and products of elements of a Banach algebra. I have also studied complete positivity of matrices over semirings or inclines.
- Quantum information: I am also interested in discovering new [mathematical] properties of quantum fidelity, (entanglement, quantum coherence and quantum privacy, and studying some mathematical tools such as completely positive linear maps and the majorization order which are very useful in quantum information.)