WILLIAM BECKNER
Ph.D., Princeton University
Dr. Beckner joined the mathematics faculty in 1983. His
teaching and research interests include Fourier analysis,
differential geometry, partial differential equations, and
probability. His work has centered on the proof of
fundamental inequalities in Fourier analysis and the
formulation of sharp limiting Sobolev inequalities with
applications to geometric variational problems. His
current research is directed toward the control of
oscillatory phenomena by renormalization arguments,
geometric analysis of higher-order differential operators
with tensor structure, the conformal symmetry of critical
phenomena and montonicity formulas in two-phase
variational problems for partial differential equations. In
addition, he is interested in symbolic computation and
the development of mathematical software for scientific
work stations.