My research primarily concerns operator algebras, especially C*-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;
  • Families of representations of C*-algebras;
  • Lifting problems in operator spaces;
  • Interplay between topological groups/ groupoids, their representations, and their associated operator algebras; and
  • Convolution algebras associated to groupoids and the transfer of ideas and techniques between the algebraic and analytic settings.



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.

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. [] (arXiv:1910.13005)

K. Courtney, “Universal C*-algebras with the Local Lifting Property,” Math. Scand., 127 (2021), 361-381. [] (arXiv:2002.02365).

K. Courtney, D. Sherman. “The universal C*-algebra of a contraction,” J. Operator Theory, 84 (2020), Issue 1, 153-184. [] (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,
[] (arxiv:1707.01949).

K. Courtney, T. Shulman. “Free products with amalgamation over central C*-subalgebras,”  Proc. Amer. Math. Soc., 148 (2020), 765-776. [] (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.”