Dr. Rajesh Pereira received his PhD in Mathematics at the University of Toronto in 2003. He then held a position as an Assistant Professor in the Department of Mathematics and Statistics at the University of Saskatchewan. In 2007, Pereira joined the Department of Mathematics and Statistics at the University of Guelph where he is now an Associate Professor. He is also the Associate Chair of the Department of Mathematics and Statistics.
Pereira’s 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. His current research explores classical and functional analysis, matrix theory and quantum information. Key areas of focus include:
Matrix theory. Pereira explores many interesting questions related to matrix theory. He has shown how the theory of diagonal matrix scalings can be used to find symmetric states with maximum geometric entanglement. Pereira [and his coauthors have solved] the Perfect-Mirsky conjecture on the spectra of doubly stochastic matrices for n=4. He has 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. He has also studied complete positivity of matrices over semirings or inclines.
Quantum information. Pereira is also interested in discovering new [mathematical] properties of quantum fidelity, [entanglement, quantum coherence and quantum privacy. He also studies some mathematical tools such as completely positive linear maps and the majorization order which are very useful in quantum information.]
Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery grant, 2005, 2010, 2016
Editorial Board Member, Linear and Multilinear Algebra, 2016-present.
Problem Corner editor of IMAGE, the newsletter of the International Linear Algebra Society, 2016-present
Organizer for William Lowell Putnam competition, 2013-present