My recent work is perhaps best described as "geometric functional analysis,"
as it combines methods from analysis and geometry (with some algebra thrown
in, just for fun). Of particular interest is the subject of real analytic
differential geometry, and analysis on real analytic manifolds, a subject
that is of importance in applications, but about which little is presently
known. I am interested in applying techniques from these areas to
differential equations, geometric mechanics, and geometric control theory.
My past work has been in more traditional topics connected to geometric
mechanics and geometric control theory.
The topics are listed roughly by order of priority in my current research
queue. I foray into all of these areas, but I do have some internal priorities.
Andrew D. Lewis (andrew at mast.queensu.ca)