Research

My research is in Operator Algebras and Multivariate Operator Theory. All my publications can be found on the arXiv. I have research profiles on Google Scholar, ResearchGate, Semantic Scholar and MathSciNet (subscription required).

1. (with J.H. Brown, D.R. Pitts and S. Reznikoff) Regular ideals, ideal intersections, and quotients, Integral Equations and Operator Theory, 96, 3 (2024). (Article, Preprint)

2. Słociński-Wold decompositions of row-isometries, Canadian Mathematical Bulletin Vol 66 (3), 2023, 780-790. ( Article, Preprint)

3. (with J.H. Brown, D.R. Pitts and S. Reznikoff) Regular ideals of graph algebras, Rocky Mountain Journal of Mathematics vol. 52 (2022), No. 1, 43-48. (Article, Prepint)

4. (with J.H. Brown, Ruy Exel, D.R. Pitts and S. Reznikoff) Intermediate C*-algebras of Cartan embeddings, Proceedings of the American Mathematical Society Ser. B 8 (2021), 27-41 . (Article, Preprint)
   • Corrigendum: Intermediate C*-algebras of Cartan embeddings, Proceedings of the American Mathematical Society (to appear)

5. (with J.H. Brown, D.R. Pitts and S. Reznikoff) Graded C*-algebras and twisted groupoid C*-algebras, New York Journal of Mathematics 27 (2021) 205–252.. (Article, Preprint)

6. (with A.P. Donsig and D.R. Pitts) Cartan triples, International Mathematics Research Notices 2021, no. 11, 8007–8070. (Article, Preprint)

7. (with M. Hartz and M. Lupini) Boundary representations of operator spaces, and compact rectangular matrix convex sets, Journal of Operator Theory 79 (2018), no. 1, 139-172. (Article, Preprint)

8. (with A.P. Donsig and D.R. Pitts) Von Neumann algebras and extensions of inverse semigroups, Proceedings of the Edinburgh Mathematical Society 60 (2017), 57-97. (Article, Preprint)
   • Corrigendum: Von Neumann Algebras and Extensions of Inverse Semigroups, Proceedings of the Edinburgh Mathematical Society (2023).  (Article)

9. (with K.R. Davidson and E.T.A. Kakariadis) Semicrossed Products of Operator Alegbras by semigroups, Memoirs of the American Mathematical Society 247 (2017), no. 1168. (Article, Preprint)

10. (with K.R. Davidson and E.T.A. Kakariadis) Semicrossed Products of Operator Alegbras: A Survey, New York Journal of Mathematics 24a (2018) 56–86. (Article, Preprint)

11. (with D.R. Pitts) Isomomorphisms of lattices of Bures-closed bimodules over Cartan MASAs, New York Journal of Mathematics 19 (2013), 657-668. (Article, Preprint)

12. (with D. Yang) Nonself-adjoint 2-graph algebras, Transactions of the American Mathematical Society 367 (2015), No. 9, 6199-6224. (Article, Preprint)

13. (with M. Kennedy) Isometric tuples are hyperreflexive, Indiana University Journal of Mathematics 62, (2013), No. 5, 1679–1689. (Article, Preprint)

14. Nonself-adjoint semicrossed products by abelian semigroups, Canadian Journal of Mathematics 65 (2013), no. 4, 768-782. (Article, Preprint)

15. Finitely Correlated Representations of Product Systems of C*-Correspondences of Product Systems over Nk, Journal of Functional Analysis 260 (2011), no.2, 574-611. (Article, Preprint)

Theses, essays and projects

The following were written whilst a student at various institutions.  Be forewarned, they are littered with an embarrassing amount of typos.

• Representations of Operator Algebras, Ph.D. thesis, University of Waterloo (2012), supervisor: Kenneth R. Davidson.

• Free Probability Theory, essay for Part III of the Mathematical Tripos, University of Cambridge (2008), supervisor: Antony Wasserman.

• Similarity to Contractions on Hilbert Space, undergraduate project, Trinity College Dublin (2007), supervisor: Richard M. Timoney.