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I work in functional analysis and specialize in the study of linear operators on Hilbert space. Specifically, I research C*-algebras associated to dynamical systems of various sorts. Such algebras have been used to study a wide range of topics including topology, representations of groups, and group actions. The goal of my research is to show that properties of the dynamical systems force certain nice properties of the associated algebra. My current collaborators include Lisa Clark, Adam Fuller, Astrid an Huef, David Pitts, and Sarah Reznikoff.
Publications:
Publications:
Accepted
Accepted
B. Armstrong, J. Brown, L.Clark, K. Courtney, Y. Lin, K. McCormick, and Jacqui Ramagge, The local bisection hypothesis for twisted groupoid C*-algebras, to appear in Semigroup Forum, 11 pages.
Published
Published
J. Brown, A. Fuller, D. Pitts, and S. Reznikoff, Regular Ideals and graph algebras, Rocky Mountain Journal of Mathematics, 52 (2022), 43 - 48.
J. Brown, A. Fuller, D. Pitts, and S. Reznikoff, Graded C*-algebras and twisted groupoid C*-algebras, New York Journal of Mathematics 27 (2021), 205 - 252.
J. Brown, R. Exel, A. Fuller, D. Pitts, and S. Reznikoff, Intermediate C*-algebras of Cartan embeddings, Proceedings of the American Mathematical Society, Series B 8 (2021), 27 - 41.
J. Brown, L. Clark, and A. an Huef. Dense subalgebras of purely infinite simple groupoid C*-algebras. Proceedings of the Edinburgh Mathematical Society, 63 (2020), 609 - 629.
J. Brown, L. Clark, and A. an Huef. Diagonal preserving ring *-isomorphisms of Leavitt path algebras. Journal of Pure and Applied Algebra, 221 (2017), 2458-2481.
J. Brown, H. Li, and D. Yang. Cartan Subalgebras of Topological graph algebras and k-graph C*-algebras. Munster Journal of Mathematics, 10 (2017), 367-381.
J. Brown and D. Yetter. Discrete Conduche Fibrations and C*-algebras. Rocky Mountain Journal, 47 (2017), 711-756.
J. Brown, L. Clark, A. Sierakowski, and A. Sims. Purely infinite C*-algebras that are principal groupoid C*-algebras. Journal of Mathematical Analysis and Applications, 439 (2016), 213–234.
J. Brown, G. Nagy, S. Reznikoff, A Sims, and D. Williams. Cartan Subalgebras in C*-algebras of Hausdorff etale groupoids. Intergral Equations and Operator Theory, 85 (2016), 109-126.
J. Brown, L. Clark and A. Sierakowski, Purely infinite C*-algebras associated to etale groupoids. Ergodic Theory and Dynamical Systems, 35 (2015), 2397-2411.
J. Brown, G. Goehle and D. Williams, Groupoid equivalence and the iterated crossed product.Houston Journal of Mathematics 41 (2015), 153-175.
J. Brown and A. an Huef, The socle and semisimplicity of a Kumjian-Pask algebra Communications in Algebra, 43 (2015), 2703-2723.
J. Brown and L. Clark, A groupoid formulation of the Baire Category Theorem. Fundamenta Mathematicae 226 (2014), 123–130.
J. Brown, L. Clark, C. Farthing and A. Sims, Simplicity for groupoid algebras. Semigroup Forum 88 (2014) , 433–452.
J. Brown and G. Goehle, The Brauer semigroup for groupoid dynamical systems. Transactions of the American Mathematical Society 366 (2014), 1943–1972.
J. Brown and I. Hirshberg, The Rokhlin property for endomorphisms. Illinois Journal of Mathematics, 58, 619-627.
J. Brown and A. an Huef, Centers of algebras associated to higher-rank graphs. Revista Matematica Iberoamericana 30 (2014),1387–1396.
J. Brown and A. an Huef, Decomposing the C*-algebras of groupoid extensions. Proceedings of the American Mathematical Society 142 (2014), 1261–1274.
J. Brown, G. Nagy and S. Reznikoff, Generalized Cuntz-Krieger uniqueness for k-gaphs.Journal of Functional Analysis 266 (2014), 2590–2609.
J. Brown, Proper actions of groupoids on C*-algebras. The Journal of Operator Theory 67 (2012), 437– 467.
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