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. 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, T. Shulman. “Elements of C*-algebras attaining their norm in a finite-dimensional representation,” Canad. J. Math. 71 (2019), Issue 1,
K. Courtney, A. Duwenig, M. Georgescu, A. an Huef, M. G. Viola, “Nuclear Dimension of the reduced C*-algebra of a twist.”
K. Courtney, W. Winter, “CPC*-systems.”
K. Courtney, “Nuclear C*-algebras and cpc systems.”