Research

My research primarily concerns operator algebras with emphasis on C*-algebras. My specialized interests include structural properties of C*-algebras and maps between them, finite dimensional approximations of C*-algebras, families of representations of C*-algebras, lifting problems in operator spaces, and the interplay between topological groups, their unitary representations, and their associated C*-algebras. In a slightly different direction, I am also interested in convolution algebras associated to groupoids.

Articles:

B. Armstrong, G. G. de Castro, L. Orloff Clark, K. Courtney, Y-F. Lin, K. McCormick, J. Ramagge, Aidan Sims, and Benjamin Steinberg. “Reconstruction of twisted Steinberg algebras,” Int. Math. Res. Not., to appear.  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).