Research

I am a theoretical mathematician working in the area of Operator Algebras and related fields. My research primarily concerns C*-algebras (pronounced “C-star-algebras”), and related objects such as operator systems and topological groups and groupoids. My projects thus far have focused on the following themes:

  • Structural and regularity properties of C*-algebras;
  • Finite dimensional approximations of C*-algebras;
  • Lifting problems;
  • Interplay between topological groups/ groupoids, their representations, and their associated operator algebras;
  • Convolution algebras associated to groupoids and the transfer of ideas and techniques between the algebraic and analytic settings; and
  • Quantum channels and quantum confusability graphs.

Articles:

Published:

B. Armstrong, G. G. de Castro, L. Orloff Clark, K. Courtney, Y-F. Lin, K. McCormick, J. Ramagge, A. Sims, and B. Steinberg. “Reconstruction of twisted Steinberg algebras,” Int. Math. Res. Not., rnab291, 2021. https://doi.org/10.1093/imrn/rnab291.  arXiv:2101.08556.

B. Armstrong, L. Orloff Clark, K. Courtney, Y-F. Lin, K. McCormick, and J. Ramagge. “Twisted Steinberg algebras,” J. Pure Appl. Algebr., 226 (2022), Issue 3. [https://doi.org/10.1016/j.jpaa.2021.106853] (arXiv:1910.13005)

K. Courtney, “Universal C*-algebras with the Local Lifting Property,” Math. Scand., 127 (2021), 361-381. [https://doi.org/10.7146/math.scand.a-126018] (arXiv:2002.02365).

K. Courtney, D. Sherman. “The universal C*-algebra of a contraction,” J. Operator Theory, 84 (2020), Issue 1, 153-184. [http://dx.doi.org/10.7900/jot.2019mar11.2229] (arXiv:1811.04043).

K. Courtney, T. Shulman. “Elements of C*-algebras attaining their norm in a finite-dimensional representation,” Canad. J. Math. 71 (2019), Issue 1,
[http://dx.doi.org/10.4153/CJM-2017-040-x] (arxiv:1707.01949).

K. Courtney, T. Shulman. “Free products with amalgamation over central C*-subalgebras,”  Proc. Amer. Math. Soc., 148 (2020), 765-776. [https://doi.org/10.1090/proc/14746] (arXiv:1809.09134).

Preprints and In Preparation:

K. Courtney, A. Duwenig, M. Georgescu, A. an Huef, M. G. Viola, “Alexandrov groupoids and the nuclear dimension of twisted groupoid C*-algebras.” arXiv:2211.00547.

K. Courtney, W. Winter, “Nuclearity and CPC*-systems.”

K. Courtney, “Completely positive approximations and inductive systems.”