Professor Stephen Buckley
Head of Department
Room: 29 Top Logic
Phone: +353 1 708 3914
Fax: +353 1 708 3913
Email: head@maths.nuim.ie
Research Interests
Steve Buckley is interested in quasiconformal mappings,
potential theory, metric measure spaces, Gromov hyperbolicity, geometric
function theory, and other fields in geometric and harmonic analysis. In
particular, he is interested in various types of Poincaré and Trudinger
inequalities, over Euclidean and non-Euclidean spaces, especially the connection
between such analytic inequalities and geometry.
He is also interested in metric spaces and metric measure spaces, where the
measure is often (but not always) doubling. Related to this, he is attempting to
achieve a better understanding of Gromov hyperbolicity for the quasihyperbolic
and related metrics. He is also interested in CAT(0) and related notions of nonpositive curvature.
Finally, he has also recently been looking at various spaces of analytic
functions. In particular, he has classified the nonlinear superposition
operators between various spaces of Besov and Dirichlet type. This involves the
use of both potential theory (non-standard Trudinger-type inequalities) and
geometric function theory (univalent Besov functions), and so links up with his
other interests.