My research interests are in mathematical analysis, mainly in functional analysis and specifically in operator algebras.
My PhD advisor was Professor N. Christopher Phillips.
My research is on operator algebras on `L^p` spaces which "look like `C^{**}`-algebras". Roughly speaking, this consists of developing an analogous theory for such `L^p`-operator algebras that closely relates to the known theory for `C^{**}`-algebras. The interesting part lies in the fact that there is no concept of adjoint operator in a `L^p` -operator algebra and, therefore, the usual tools used to prove results in a `C^{**}`-algebra setting are not always available. This is a relatively new field of study, so not much is known about it. Some of the tools one needs when working on `L^p`-operator algebras are from the classic theory of `C^{**}`-algebras such as `K`-theory, representation theory and crossed products. However, methods from operator spaces and classical Banach space theory are also helpful here.
I am also interested in abstract harmonic analysis. In particular interaction between wavelets and `C^{**}`-algebras and the spectral synthesis problem for the `L^p` group operator algebra of the integers. The toolbox here inculdes topological groups, commutative Banach algebras, `K`-theory, Hilbert `C^{**}`-modules, and frames and bases.
`L^{p}`-modules, `L^{p}`-correspondences, and their `L^{p}`-operator algebras, (2023) preprint (in preparation).
Representations of `C^{**}`-correspondences on pairs of Hilbert spaces, (2022) to appear in Journal of Operator Theory (available at arXiv:2208.14605 [math.OA]).