My primary field of study is Banach space theory, but I’ve also published papers on real analysis and the interplay between descriptive set theory and Banach space theory. My focus is on the geometry of infinite-dimensional Banach spaces and the operators between them, with an emphasis on constructing Banach spaces with strict structures and using descriptive set theory to analyze operators. Below is a complete list of my research papers. An * denotes an undergraduate co-author.
38. On Schreier-type sets, partitions, and compositions. (with Hung Viet Chu) Journal of Integer Sequences, April 5, 2024.
37. The depth of Tsirelson’s norm, (with Jȩdrzej Hodor), to appear in Studia Mathematica.
36. Counting unions of Schreier sets, (with Dmitriy Gorovoy, Jȩdrzej Hodor, Daniil Homza), Bulletin Australian Mathematical Society published online 27 December 2023
35. Schreier families and F-(almost) greedy bases, (with Hung Viet Chu), Canadian Journal of Mathematics. Published online 2023:1-21.
34. Shrinking Schauder frames and their associated spaces, (with Dan Freeman), Constructive Approximation (2023)
33. Schreier sets, linear recurrences, and Turan sequences, (with Hung Viet Chu and Carrie Finch-Smith), Fibonacci Quarterly (2022), Vol. 60, no. 4. 352–356.
32. Surjective isometries on Banach sequence space: a survey, (with Leandro Antunes), Concr. Oper. 9 (2022), no. 1, 19–40.
31. An ξ-weak Grothendieck compactness principle, (with Ryan M Causey), Math. Proc. Cambridge Philos. Soc. 172 (2022), no. 1, 231–246.
30. Uniformly factoring weakly compact operators and parametrized dualization, (with Leandro Antunes and Bruno Braga), Forum Math. Sigma 9 (2021), Paper No. e22, 27 pp.
29. The Schreier space does not have the uniform 
property, (with Hung Viet Chu*), Proc. Amer. Math. Soc. 149 (2021), no. 12, 5131–5137.
28. On the Geometry of Higher Order Schreier spaces, (with Hung Viet Chu* and Leandro Antunes), Illinois J. Math. 65 (2021), no. 1, 47–69.
27. Genericity and Universality for Operator Ideals, (with Ryan M Causey), Q. J. Math. 71 (2020), no. 3, 1081–1129
26. Closed ideals of operators on the Tsirelson and Schreier spaces, (with Tomasz Kania and Niels Laustsen), J. Funct. Anal. 279 (2020), no. 8, 28 pp
25. The algebras of bounded operators on the Tsirelson and Baernstein spaces are not Grothendieck spaces, (with Tomasz Kania and Niels Laustsen), Houston J. Math. 44 (2018), no. 1, 201–208.
24. Time stopping for Tsirelson’s Norm, (with Michael Holt*, Noah Duncan*), Involve 11 (2018), no.5 857–866.
23. Extreme points for Combinatorial Banach space, (with Michael Holt*, Noah Duncan* and James Quigley*) Glasg. Math. J. 61 (2019), no. 2, 487–500.
22. Quantitative Factorization of weakly compact, Rosenthal, and ξ-Banach-Saks operators, (with Ryan M Causey), Math. Scand. 123 (2018). no. 2, 297-319.
21. Classes of operators determined by ordinal indices, (with Ryan M Causey, Daniel Freeman, and Ben Wallis), J. Functional Analysis, 271 (2016), no. 6, 1691–1746.
20. On a generalization of Bourgain’s tree index, (with Ryan M Causey), Houston J. Math. 44 (2018), no. 1, 201–208.
19. On Scottish Book Problem 157, (with Paul Humke and Trevor Richards), Real Analysis Exchange, 41 (2016), no. 2, 331-346.
18. Arbitrarily distortable Banach spaces of higher order, (with Ryan Causey and Pavlos Motakis), Israel J. Math. 214 (2016), no. 2, 553-581.
17. The stabilized set of p’s in Krivine’s theorem can be disconnected, (with Daniel Freeman and Pavlos Motakis), Adv. Math 281 (2015), 553-577.
16. Upper and lower estimates for Schauder frames and atomic decompositions, (with Daniel Freeman and R. Liu) Fund. Math. 231 (2015), 161-188
15. Uniformly factoring weakly compact operators, (with Daniel Freeman) J. Functional Anal. 266 (2014), no. 5, 2921-2943.
14. Operators on 
spaces, (with Lon Mitchell) J. Math. Anal. Appl. 413 (2014), no. 2, 616-621.
13. The strictly singular operators in Tsirelson like reflexive spaces, (with Spiros A. Argyros and Pavlos Motakis) Illinois J. Math. 57 (2013), no. 4, 1173–1217.
12. On spaces admitting no 
or 
spreading model, (with Spiros A. Argyros) Positivity 17 (2013), no. 2, 265-282.
11. An extremely non-homogeneous weak Hilbert space, (with Spiros A. Argyros and Th. Raikoftsalis) Trans. Amer. Math. Soc. 364 (2012), 5015-5033.
10. Ordinal ranks on weakly compact and Rosenthal operators, (with Daniel Freeman) Extracta Math. 26(2) (2011), 173-194
9. A weak Hilbert space with few symmetries, (with Spiros A. Argyros and Th. Raikoftsalis), C.R. Math. Acad. Sci. Paris. 348:1293-1296, 2010.
8. Operators on the spaces of Bourgain and Delbaen, (with Lon Mitchell) Quaestiones Mathematicae 33 (2010), 443–448.
7. On strictly singular operator between separable Banach spaces, (with Pandelis Dodos) Mathematika, 56 (2010), no. 2, 285-304.
6. An ordinal indexing of the space of strictly singular operators, Israel J. of Math., 181 (2011), 47-60.
5. Operators on asymptotic spaces which are not compact perturbation of a multiple of the identity, Illinois J. Math, 52 (2009), no. 2, 515-532.
4. Modifications of Thomae’s function and differentiability, (with James Roberts and Craig Stevenson) Amer. Math. Monthly, 116 (2009), no. 6, 531-535.
3. Descriptive set-theoretic methods applied to strictly singular and strictly cosingular operators, (with George Androulakis) Quaestiones Mathematicae, 31 (2008), 151-161.
2. A hereditarily indecomposable asymptotic 
Banach space, (with George Androulakis) Glasgow Math Journal, 48 (2006) 503-532.
1. Embedding 
into the space of operators on certain Banach spaces, (with George Androulakis, Stephen Dilworth, and Frank Sanacory) Bull. Lond. Math. Soc., 38 (2006) 979-990.