Research interests: Functional analysis, noncommutative geometry, operator theory, partial differential equations.
I am an analyst specializing in functional analysis and operator theory. I am also interested in the theory of partial differential equations. My current work focuses in spectral theory of Schrödinger and Jacobi operators, spectral theory of a special class of integral operators and noncommutative geometry. All of these areas stem back to mathematical physics and a lot of the work I have focused on has initially started as a mathematical physics problem. In fact, in the noncommutative geometry area, I am interested in Dirac and Dirac-type operators and their analysis classically and the analysis of them noncommutatively. This analysis also involves spectral analysis as well, which can tie into the spectral theory for Schrödinger and Jacobi operators. Moreover the analysis of partial differential equations relates to this theory, so I am also interested in the function space theory of such equations.
Curriculum Vitae: Dr. McBride's CV