Welcome to my homepage

 

He gazed up at the enormous face. Forty years it had taken him to learn what kind of smile was hidden beneath the dark moustache. O cruel, needless misunderstanding! O stubborn, self-willed exile from the loving breast! Two gin-scented tears trickled down the sides of his nose. But it was all right, everything was all right, the struggle was finished. He had won the victory over himself. He loved Big Brother.

George Orwell: 1984 Go To Top

Research

My general field of interest is Operator Theory and Operator Algebras. In particular I am interested in the approximation and structure of linear operators acting on a Hilbert space, as well as the study of non-selfadjoint and selfadjoint operator algebras. I have also dabbled in problems of interest to Linear Algebraists.

Currently my interests include: similarity of operator algebras to C*-algebras, quasidiagonality of operators and of operator algebras, consequences of the total reduction property for operator algebras, and characterising (the closures of) the set of commutators of different families of operators in B(H) and in operator algebras. At some point, through no fault of my own, I may utter the phrase "mixed unitary quantum channel", but if I do, I will mean it in the nicest possible sense of the term.

I am easily tempted to investigate new problems in operator theory and operator algebras.

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Teaching

I have produced typed course notes for a number of courses taught at the University of Waterloo. They are varying states of readiness, but at least they are available for free. Simply click on the links below.

• Course notes for Math 146, Linear algebra I.
• Course notes for PMath 334, Ring Theory.
• Course notes for PMath 351, Real Analysis.
• Course notes for PMath 450, An introduction to Lebesgue measure and Fourier series.
• Course notes for PMath 453/753, An introduction to Functional Analysis.
• Course notes for PMath 810, An introduction to operator algebras.

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Supervision

Absolutely nothing is more fulfilling than supervision. But, given how poorly remunerated doing absolutely nothing is, I have chosen to offer what humble services I can in this capacity.

All kidding aside (ok, write down this date as you will not hear me say that again), I have had the extremely good fortune to have supervised some wonderful students, at the undergraduate, Masters and Ph.D. levels.

Ph.D. students

• Cramer, Z. (2019) Compressible matrix algebras and the distance from projections to nilpotents , University of Waterloo.
• Chan, K.C. (2012) Digraph algebras over discrete pre-ordered groups, University of Waterloo.
• Dostál, M. (1998) Closures of (U+K)-orbits of essentially normal models, University of Alberta.

Masters students

• Sarkowicz, P. (2019) Exact C*-algebras and the Kirchberg-Phillips nuclear embedding theorem. University of Waterloo.
• Eifler, K. (2016) (co-supervised with M. Kennedy) Graph C*-algebras, an introduction. , University of Waterloo.
• Cramer, Z. (2015) Normal limits of nilpotent and normal operators similarity orbits in purely infinite C*-algebras , University of Waterloo.
• Haley, J. (2015) Strongly reductive operators and strongly reductive operator algebras , University of Waterloo.
• Harris, S. (2015) Kadison similarity problem and similarity degree , University of Waterloo.
• Yu, P. (2015) Spans of projections in certain C*-algebras , University of Waterloo.
• Chow, S.S. (2012) Graph algebras of real rank zero, University of Waterloo.
• Onuma, K. (2011) Linear mappings between Banach algebras that preserve spectral properties, University of Waterloo.
• Boey, E. (2010) On the modular theory of von Neumann algebras, University of Waterloo.
• Al-Ahmari, A. (2006) Almost commuting matrices versus nearly commuting matrices, University of Waterloo.
• Georgescu, M. (2006) (co-supervised with B.E. Forrest), On the similarity of operator algebras to C*-algebras, University of Waterloo.
• Pollock, D. (2004) (co-supervised with K.R. Davidson) On C*-envelopes of a special class of limit algebras, University of Waterloo.
• Gusba, S. (1999) Connectedness of the invertible group of a nest algebra, University of Alberta.

Undergraduate students

• Patrón-Fonseca, O. (2023) Quasitriangularity in Hilbert space, University of Waterloo.
• Jelinsky, A. (2022) Introduction to operator algebras, University of Waterloo.
• Xu, T. (2022) Introduction to operator algebras, University of Waterloo.
• Ala, M. (2021) Amenability of operator algebras, University of Waterloo.
• Shiner, A. (2019) Similarity, amenability and the total reduction property, University of Waterloo.
• Suan, C. (2019) The almost-invariant subspace problem, University of Waterloo.
• Sarkowicz, P. (2018) Nuclear C*-algebras and Kadison's similarity problem, University of Waterloo.

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Contact Us

Mailing Address

Department of Pure Mathematics
University of Waterloo
Waterloo, Ontario
Canada, N2L 3G1

Phone: 519-888-4567
Email: Laurent.Marcoux@uwaterloo.ca