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VCU Analysis Seminar

Colloquium Fall 2009

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Research

My broad research area is functional analysis. 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 ridged structures and using methods from descriptive set theory to study operators on Banach spaces.

Spreading models in the duals of Schlumprecht-type spaces, (with F. Sanacory) in preparation.

A weak Hilbert space with few symmetries, (with S.A. Argyros and Th. Raikoftsalis) submitted.

On strictly singular operators between separable Banach spaces, (with P. Dodos) submitted.

An ordinal indexing of the space of strictly singular operators, to appear in the Israel Journal of Mathematics.

Operators on asymptotic l-p spaces which are not compact perturbations of a multiple of the identity,, Illinois Journal of Mathematics, 52 (2009), no. 2, 515-532.

Modification's of Thomae's function and differentiability, (with J. Roberts and C. Stevenson) The American Mathematical Monthly, 116 (2009), no. 6, 531-535. Also see our editors note containing additional citations.

Descriptive set theoretic methods applied to strictly singular and strictly cosingular operators, (with G. Androulakis) Quaestiones Mathematicae, 31(2008), 151-161.

A hereditarily indecomposable asymptotic l-2 Banach space, (with G. Androulakis) Glasgow Mathematical Journal, 48 (2006) 503-532.

Embedding l-infinity into the space of operators on certain Banach spaces, (with G. Androulakis, S.J. Dilworth and F. Sanacory) Bulletin of the London Mathematical Society 38 (2006) 979-990.

Background

I have a BA in pure math from St. Mary's College of Maryland (2002) and a Ph.D from the University of South Carolina (2006) where I studied under George Androulakis. My first academic position was at Amherst College where I was a Visiting Assistant Professor. Since August 2007, I have been an Assistant Professor at VCU. My wife Rachel works at the University of Richmond in communications and together we have son Gabriel, born on pi-day 2005. Good timing.