the Ph.D. from Princeton University in 1981. He then spent two years at MIT as an NSF Postdoctoral Fellow,

following which he came to the University of Rochester in 1983 as an assistant professor. He was promoted to

associate professor in 1986, unlimited tenure in 1989 and full professor in 1997. He spent Fall 1987 at the

Mathematical Sciences Research Institute in Berkeley and the 1990-91 academic year at the University of Washington ,

supported by a Sloan Research Fellowship.

Prof. Greenleaf's research interests are in harmonic analysis and
microlocal analysis, with applications to integral geometry

and inverse problems. In recent years, he has been particularly interested
in estimates for oscillatory integral and Fourier integral operators with
degenerate phase functions. These arise in looking at solutions to certain
partial differential equations, and from averaging operators associated
with families of curves or lines in n-space. The latter include X-ray transforms
which provide the mathematical underpinnings of CAT scanning. Recently,
Prof. Greenleaf has also been interested in multiplicative properties of

Fourier integral distributions. Controlling these allows one to obtain
uniqueness and reconstruction in various inverse problems,

such as determining a potential function from the backscattering data
( a subset of the scattering kernel of the associated wave equation)

or from the Cauchy data of the associated time-independent Schrödinger
equation.

More recently, Prof. Greenleaf, together with Matti Lassas of the Helsinki University of Technology, Yaroslav Kurylev of University College, London, and Gunther Uhlmann of the University of Washington, have been using insight gained from the study of inverse problems to give a rigorous foundation and introduce new constructions in the burgeoning field of "cloaking", or invisibility from observation by electromagnetic waves.

Prof. Greenleaf's research is supported in part by National Science Foundation grants.