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.
Februrary 8, 2012
On the rigidity of black holes
Sergiu Klainerman Princeton University
The rigidity conjecture states that all regular, stationary solutions of the Einstein field equations in vacuum are isometric to the Kerr solution. The simple motivation behind this conjecture is that one expects, due to gravitational radiation, that general, dynamic, solutions of the Einstein field equation settle down, asymptotically, into a stationary regime. A well known result of Carter, Robinson and Hawking has settled the conjecture in the class of real analytic spacetimes. The assumption of real analyticity is however very problematic; there is simply no physical or mathematical justification for it. During the last five years I have developed, in collaboration with A. Ionescu and S. Alaxakis, a strategy to dispense of it. In my lecture I will these results and concentrate on some recent results obtained in collaboration with A. Ionescu.
February 25, 2011
Mathematical Strategies for Real Time Filtering of Turbulent Dynamical Systems
Andrew Majda
Courant Institute of Mathematical Sciences -- New York University
An important emerging scientific issue in many practical problems ranging from
climate and weather prediction to biological science involves the real time filtering
and prediction through partial observations of noisy turbulent signals for complex
dynamical systems with many degrees of freedom as well as the statistical accuracy of
various strategies to cope with the .curse of dimensions.. The speaker and his
collaborators, Harlim (North Carolina State University), Gershgorin (CIMS Post doc),
and Grote (University of Basel) have developed a systematic applied mathematics
perspective on all of these issues. One part of these ideas blends classical stability
analysis for PDE's and their finite difference approximations, suitable versions of
Kalman filtering, and stochastic models from turbulence theory to deal with the large
model errors in realistic systems. Many new mathematical phenomena occur. Another
aspect involves the development of test suites of statistically exactly solvable models
and new NEKF algorithms for filtering and prediction for slow-fast system, moist
convection, and turbulent tracers. Here a stringent suite of test models for filtering and
stochastic parameter estimation is developed based on NEKF algorithms in order to
systematically correct both multiplicative and additive bias in an imperfect model. As
briefly described in the talk, there are both significantly increased filtering and
predictive skill through the NEKF stochastic parameter estimation algorithms
provided that these are guided by mathematical theory. The recent paper by Majda et
al (Discrete and Cont. Dyn. Systems, 2010, Vol. 2, 441-486) as well as a forthcoming
introductory graduate text by Majda and Harlim (Cambridge U. Press) provide an
overview of this research.
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.
