My main research area is Banach space theory but, I have some work in real analysis and know some descriptive set theory as it applies to Banach space theory. In particular, I study the geometry of infinite dimensional Banach spaces and bounded linear operators between Banach spaces. Most of my work has focused on constructing Banach spaces with very rigid structure and using methods from descriptive set theory to study operators between Banach spaces.
24. Time Stopping of Tsirelson’s Norm, (with Michael Holt, Noah Duncan), submitted.
23. Extreme points for Combinatorial Banach space, (with Michael Holt, Noah Duncan and James Quigley), submitted.
22. Quantitative Factorization of weakly compact, Rosenthal, and ξ-Banach-Saks operators, (with Ryan Causey), to appear in Mathematica Scandinavica.
21. Classes of operators determined by ordinal indices, (with Ryan Causey, Daniel Freeman and Ben Wallis), J. Functional Analysis, 271 (2016), no. 6, 1691–1746.
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
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.