Rajesh Pereira

Associate Chair
Associate Professor, Mathematics
Email: 
pereirar@uoguelph.ca
Phone number: 
519-824-4120 x53552
Office: 
MacNaughton 519

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

Research Themes: 

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:

  1. 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.
  2. 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.)

Media Coverage: 

Quantum Information

  • Matrix Analysis
  • Classical Analysis
  • Analytic Theory of Polynomials
  • Quantum Information
  • Complex Matrix Scalings, Extremal Permanents, and the Geometric Measure of Entanglement
    George Hutchinson, Doctor of Philosophy (2018).
  • Degradable and Antidegradable Qubit Channels
    Connor Paul-Paddock, Master of Science (2016).
  • New Methods for the Perfect-Mirsky Conjecture and Private Quantum Channels
    Jeremy Levick, Doctor of Philosophy (2015).
  • Completely Positive Matrices over Semirings and their CP-rank
    Preeti Mohindru, Doctor of Philosophy (2014).
  • The Structure of the Space of all Game-Playing Strategies
    Jeffrey Tsang, Doctor of Philosophy (2014).
  • A Collection of Results of Simonyi's Conjecture
    Dustin Styner, Master of Science (2012).
  • B.Sc. in Applied Mathematics (McGill University), 1996.
  • M.Sc. in Mathematics (McGill University), 1998.
  • Ph.D. in Mathematics (University of Toronto), 2003.
  • 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