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Copyright © 2019 L.W. Marcoux, Esq.
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Welcome to my homepage

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For be a man's intellectual superiority what it will, it can never assume the practical, available supremacy over other men, without the aid of some sort of external arts and entrenchments, always, in themselves, more or less paltry and base. This it is, that for ever keeps God's true princes of the Empire from the world's hustings; and leaves the highest honors that this air can give, to those men who become famous more through their infinite inferiority to the choice hidden handful of the Divine inert, than through their undoubted superiority over the dead level of the mass. Such large virtue lurks in these small things when extreme political superstitions invest them, that in some royal instances even to idiot imbecility they have imparted potency.

Herman Melville: Moby Dick

Things I do

    A bunch of research.

    I teach a bunch of math and pure math courses.

    I currently supervise two graduate students and 1 nserc usra.

    I serve on a bunch of committees.

Teaching testimonials

His innuendos kept me focused.

2017 - Math 147

The course contains a lot of propositions that sound like they should be true, but aren't (or maybe I just lost track, and they actually are true? I dunno).

2016 - Math 148

Persists admirably at making dry jokes despite the near total absence of student encouragement.

2012 - PMath 334

Very good at math for a guy raised by chickens.

2012 - Math 228

No comment.

2002 - Math 247
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Research

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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 permanence properties of compressions of operator algebras.

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

A selection of recent papers

    Marcoux, L.W. and Popov, A., Abelian, amenable operator algebras are similar to C*-algebras, Duke Math. J. 165 (2016), 2391-2406.

    Clouâtre, R. and Marcoux, L.W., Compact ideals and rigidity of representations for amenable operator algebras, Studia Math. 244 (2019), 25-41.

    Clouâtre, R. and Marcoux, L.W., Residual finite-dimensionality and representations of amenable operator algebras, J. Math. Anal. Appl. 472, (2019), 1346-1368.

    Livshits, L., MacDonald, G., Marcoux, L.W. and Radjavi, H., Hilbert space operators with compatible off-diagonal corners, J. Funct. Anal. 275 (2018), 892-925.

    Bernik, J., Marcoux, L.W., Popov, A.I., and Radjavi, H., On selfadjoint extensions of semigroups of partial isometries, Trans. Amer. Math. Soc. 2016 (2016), 264-304.

    Marcoux, L.W., Radjavi, H. and Yahaghi, B.R., Reducibility of operator semigroups and values of vector states, Semigroup Forum 95, (2017), 126-158.

Preprints

    Marcoux, L.W., On norm-limits of algebraic quasidiagonal operators, 2018.

    Aghamollaei, G., Marcoux, L.W., and Radjavi, H., Linear preservers of polynomial numerical convex hulls, 2018.

    Marcoux, L.W., Radjavi, H., and Yahaghi, B.R., On *-similarity in C*-algebras, 2019.

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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.

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Supervision

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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. Thesis in progress.
  • 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. Thesis in progress.
  • 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

  • Suan, C. (2019) Essay in progress, University of Waterloo.
  • Sarkowicz, P. (2018) Nuclear C*-algebras and Kadison's similarity problem, University of Waterloo.
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L.W. Marcoux
Department of Pure Mathematics
University of Waterloo
Waterloo, Ontario
Canada, N2L 3G1

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