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 Library is housed in the department.

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 19, 2013

Topology-Preserving Diffusion of Divergence-Free Vector Fields

Yann Brenier
École Polytechnique

The usual heat equation is not suitable to preserve the topology of divergence-free vector fields, because it destroys their integral line structure. On the contrary, in the fluid mechanics literature, one can find examples of topology-preserving diffusion equations for divergence-free vector fields. They are very degenerate since they admit all stationary solutions to the Euler equations of incompressible fluids as equilibrium points. For them, we provide a suitable concept of ”dissipative solutions”, which shares common features with both P.-L. Lions’ dissipative solutions to the Euler equations and the concept of ”curves of maximal slopes”, à la De Giorgi, recently used by Gigli and collaborators to study the scalar heat equation in very general metric spaces. We show that the initial value problem admits global "dissipative" solutions (at least for two space dimensions) and that they are unique whenever they are smooth.

February 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

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.

April 25, 2008

Surface Waves and Images

Joseph B. Keller
Stanford University

March 30, 2007

Steady Water Waves: Theory and Computation

Walter Strauss
Brown University

September 30, 2005

A New Perspective on Motion by Curvature

Robert V. Kohn
Courant Institute of Mathematical Sciences, New York University

April 15, 2005

Conservation Laws and Some Consequences

Cathleen Synge Morawetz
Courant Institute of Mathematical Sciences, New York University

March 5, 2004

Hyperbolic Conservation Laws with Dissipation

Constantine Dafermos
Brown University, Division of Applied Mathematics

October 8, 2002

Topology and Sobolev Spaces

Haim Brezis
Universite de Paris VI, Insitiut Universitaire de France, and Rutgers University

April 12, 2002

Navier-Stokes and Other Super-critical Equations

Vladmir Sverak
University of Minnesota

April 20, 2001

Shock Wave Theory

Tai-Ping Liu
Academia Sinica, Taiwan & Stanford University

March 31, 2000

Effective Hamiltonians

Lawrence C. Evans
University of California, Berkeley

April 23, 1999

Some remarks on homogenization

Luis Caffarelli
University of Texas, Austin

April 17, 1998

An Example of Diffusion-Induced Blowup of a Parabolic System

Hans Weinberger
University of Minnesota

April 4, 1997

The Zero Dispersion Limit

Peter Lax
Courant Institute

May 9, 1996

Degree Theory Beyond Continuous Maps

Louis Nirenberg
Courant Institute


How to get to the Department of Mathematics by car, by Metro, from airports

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020

  • Department Back to School & Tea

    When: Fri, September 6, 2019 - 3:15pm
  • Faculty Meeting

    When: Wed, September 11, 2019 - 3:30pm
  • Commutative harmonic analysis on noncommutative Lie groups(part of Conference in honor of John Benedetto)

    Speaker: Fulvio Ricci (Scuola Normale Superiore, Pisa) -

    When: Fri, September 20, 2019 - 4:30pm
    Where: Kirwan Hall 3206
  • What's new with Mathematica and Wolfram|Alpha

    Speaker: Andrew Dorsett (Wolfram Research, Inc) -

    When: Wed, September 25, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • 2nd Annual Google Tech Talk

    Speaker: Britt Hedenberg

    When: Wed, September 25, 2019 - 5:30pm
  • STAT Sem. Quantile Regression for Spectral Analysis of Time Series

    Speaker: Ta-Hsin Li (IBM T. J. Watson Research Center) - http://www.research.ibm.com/people/t/thl

    When: Wed, October 2, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • "Noether, Falconer, Mirzakhani, Kovalesky, and Me”

    Speaker: Shelby Wilson (Department of Biology, UMD) - http://biology.umd.edu/shelby-wilson.html

    When: Thu, October 10, 2019 - 3:30pm
    Where: Kirwan Hall 3206
  • Validity of Steady Prandtl Expansion

    Speaker: Yan Guo (Brown University) - http://www.cfm.brown.edu/people/guoy/home.html

    When: Wed, October 16, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • Celestial surfaces

    Speaker: Janos Kollar (Princeton University) - https://web.math.princeton.edu/~kollar/

    When: Wed, October 30, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • Fluid-boundary interactions: transport, stratification and confinement effects

    Speaker: Roberto Camassa (University of North Caroline at Chapel Hill) - https://amath.unc.edu/?people=roberto-camassa

    When: Fri, November 8, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • WIM Alumni Series with Dr. Carolina Franco

    Speaker: Carolina Franco (U.S. Census Bureau) -

    When: Thu, November 14, 2019 - 2:00pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Anthony Romano (US Naval Research Lab, DC) -

    When: Fri, November 15, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • Discretizing Manifolds with Minimal Energy

    Speaker: Ed Saff (Vanderbilt University) - https://my.vanderbilt.edu/edsaff/

    When: Wed, November 20, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • On the Hitchin fibration (first talk, Distriguished Lectures in Algebra and Number Theory)

    Speaker: Bao-Chau Ngo (University of Chicago) - https://www.math.uchicago.edu/~ngo/

    When: Wed, December 4, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • Length and volume in four-dimensional symplectic geometry

    Speaker: Daniel Cristofaro-Gardiner (UCSC) - https://dancg.sites.ucsc.edu/

    When: Fri, December 6, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • (Special Colloquium) (3/2)^n, linear cellular automata, and Apery-like sequences

    Speaker: Hillel Furstenberg (Hebrew University, Israel) -

    When: Thu, December 12, 2019 - 2:00pm
    Where: Kirwan Hall 3206
  • Some Applications of Statistics in Physics: quantized light, scattering, and tomography

    Speaker: Zachary H. Levine (NIST) -

    When: Wed, February 12, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • Why Leadership: Its Appeal & Challenges- Women in Math Alumni Series

    Speaker: Amanda Galante (Johns Hopkins University Applied Physics Laboratory)

    When: Thu, February 20, 2020 - 4:00pm
    Where: Kirwan Hall 1311
  • Prismatic cohomology and applications (Note: Special time)

    Speaker: Bhargav Bhatt (University of Michigan, Ann Arbor) - http://www-personal.umich.edu/~bhattb/

    When: Wed, February 26, 2020 - 3:00pm
    Where: Kirwan Hall 3206
  • Artistic mathematics: truth and beauty

    Speaker: Henry Segerman (Oklahoma State University) - https://math.okstate.edu/people/segerman/

    When: Wed, March 4, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Brian Lawrence (University of Chicago) - http://math.uchicago.edu/~brianrl/

    When: Wed, March 11, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • Solving inverse problems with machine learning (Aziz Lecture)

    Speaker: Lexing Ying (Stanford University) - https://web.stanford.edu/~lexing/

    When: Wed, April 1, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Tim Healey (Cornell University) - https://math.cornell.edu/timothy-j-healey

    When: Wed, April 8, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Spring Dynamics Conference (TBA) -

    When: Thu, April 16, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • Taming Infinities (Aziz Lecture)

    Speaker: Martin Hairer (Imperial College, London, UK) - https://www.imperial.ac.uk/people/m.hairer

    When: Wed, April 22, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Joergen Andersen (Danish Institute for Advanced Study) - https://danish-ias.dk/people/jorgen-ellegaard-andersen/

    When: Wed, April 29, 2020 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Paolo Aluffi (Florida State University) - https://www.math.fsu.edu/~aluffi/

    When: Wed, May 6, 2020 - 3:15pm
    Where: Kirwan Hall 3206