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
  • Operator system inductive systems

Articles:

Published:

K. Courtney, N. Galke, L. van Luijk, A. Stottmeister. “Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem.” to appear in J. Operator Theory, arXiv:2510.02019.

K. Courtney, P. Ganesan, M. Wasilewski. “Connectivity for quantum graphs via quantum adjacency operators.” arXiv:2505.22519. to appear in Int. Math. Res. Not..

K. Courtney and W. Winter. “Images of order zero maps,” to appear in Special Issue of Münster J. Math. in honor of Eberhard Kirchberg. arXiv:2312.08215.

K. Courtney, A. Duwenig, M. Georgescu, A. an Huef, M. G. Viola. “Alexandrov groupoids and the nuclear dimension of twisted groupoid C*-algebras.” J. Funct. Anal., 286 (2024), no. 9, 49pp. [https://doi.org/10.1016/j.jfa.2024.110372] arXiv:2211.00547.

K. Courtney and W. Winter. “Nuclearity and CPC*-systems,” Forum Math., Sigma, 13 (2025), e59.
[https://doi.org/10.1017/fms.2024.123] (arXiv:2304.01332).

B. Armstrong, J.H. Brown, L. Orloff Clark, K. Courtney, Y-F. Lin, K. McCormick, and J. Ramagge. “The local bisection hypothesis for twisted groupoid C*-algebras,” Semigroup Forum, 2023. https://doi.org/10.1007/s00233-023-10392-9. (arXiv:2307.13814).

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).

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).

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 and 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).

K. Courtney and 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 and 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).

Preprints

K. Courtney. “Completely positive approximations and inductive systems.” arXiv:2304.02325.