Avron Douglis (1918-1995) received an AB degree in economics from the
University of Chicago in 1938. After working as an economist for three
years and serving in World War II he began graduate studies in mathematics
at New York University. He received his doctorate in 1949 under the
direction of Richard Courant. He held a one-year post-doctoral appointment
at the California Institute of Technology, and then returned to New York
University as an assistant and then associate professor. In 1956 he
accepted an appointment as associate professor at the University of
Maryland, where he remained for the rest of his career, except for
visiting appointments at the Universities of Minnesota, Oxford, and
Newcastle upon Tyne. He was promoted to full professor in 1958 and became
an emeritus in 1988.
Avron Douglis's research, noted for its depth, precision, and richness,
covered the entire range of the theory of partial differential equations:
linear and nonlinear; elliptic, parabolic, and hyperbolic. The famous
papers he had written with S. Agmon and L. Nirenberg are among the most
frequently cited in all of mathematics.
The Avron Douglis Lectures were established by the family
and friends of Avron Douglis to honor his memory. Each
academic year it brings to Maryland a distinguished expert
to speak on a subject related to partial differential
equations.
The lectures are held at 3:00 p.m. in room 3206 in the Department of Mathematics, unless noted otherwise below.
April 24, 2009 at 4 pm
The global behavior of solutions to critical nonlinear dispersive and wave equations
Carlos E. Kenig
University of Chicago
In this lecture we will describe a method (which I call the concentration-compactness/rigidity
theorem method) which Frank Merle and I have developed to study global well-posedness and
scattering for critical non-linear dispersive and wave equations. Such problems are natural
extensions of non-linear elliptic problems which were studied earlier, for instance in the context
of the Yamabe problem and of harmonic maps. We will illustrate the method with some concrete
examples and also mention other applications of these ideas.
