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

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

## Directions

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

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017

• #### Speaker: () -

When: Wed, September 13, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Samir Khuller (University of Maryland Computer Science ) - https://www.cs.umd.edu/users/samir/

When: Wed, September 20, 2017 - 3:15pm
Where: Kirwan Hall 3206

### View Abstract

Abstract: NP-complete problems abound in every aspect of our daily lives. One approach is to simply deploy heuristics, but for many of these we do not have any idea as to when the heuristic is effective and when it is not. Approximation algorithms have played a major role in the last three decades in developing a foundation for a better understanding of optimization techniques - greedy algorithms, algorithms based on LinearProgramming (LP) relaxations have paved the way for the design of (in some cases) optimal heuristics. Are these the best ones to use in âtypicalâ instances? Maybe, maybe not.

In this talk we will focus on two specific areas - one is in the use of greedy algorithms for a basic graph problem called connected dominating set, and the other is in the development of LP based algorithms for a basic scheduling problem in the context of data center scheduling.
• #### Speaker: (CMNS Dean's Office) -

When: Wed, September 27, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Vladimir Matveev (Friedrich-Schiller-UniversitÃ¤t Jena ) - http://users.minet.uni-jena.de/~matveev/

When: Wed, October 4, 2017 - 3:15pm
Where: Kirwan Hall 3206

### View Abstract

Abstract: We introduce a construction that associates a Riemannian metric $g_F$ (called the
Binet-Legendre metric) to a
given Finsler metric $F$ on a smooth manifold $M$. The transformation
$F \mapsto g_F$ is $C^0$-stable and has good
smoothness properties, in contrast to previously considered
constructions. The Riemannian metric $g_F$ also behaves nicely under
conformal or isometric transformations of the Finsler metric $F$ that
makes it a powerful tool in Finsler geometry. We illustrate that by
solving a number of named problems in Finsler geometry. In particular
we extend a classical result of Wang to all dimensions. We answer a
question of Matsumoto about local conformal mapping between two
Berwaldian spaces and use it to investigation of essentially conformally Berwaldian manifolds.
We describe all possible conformal self maps and all self similarities
on a Finsler manifold, generasing the famous result of Obata to Finslerian manifolds. We also classify all compact conformally flat
Finsler manifolds. We solve a conjecture of Deng and Hou on locally
symmetric Finsler spaces. We prove smoothness of isometries of Holder-continuous Finsler metrics. We construct new easy to calculate''
conformal and metric invariants of finsler manifolds.
The results are based on the papers arXiv:1104.1647, arXiv:1409.5611,
arXiv:1408.6401, arXiv:1506.08935,
arXiv:1406.2924
partially joint with M. Troyanov (EPF Lausanne) and Yu. Nikolayevsky (Melbourne).
• #### Speaker: General Departmental Meeting () -

When: Wed, October 11, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Departmental Meeting () -

When: Wed, October 18, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Departmental Meeting () -

When: Wed, October 25, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Xuhua He (UMD) - http://www.math.umd.edu/~xuhuahe/

When: Wed, November 1, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Pierre-Emmanuel Jabin (UMD) - http://www2.cscamm.umd.edu/~jabin/

When: Wed, November 8, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Simon Levin (Princeton ) -

When: Wed, November 15, 2017 - 3:15pm
Where: Kirwan Hall 3206

### View Abstract

Abstract: TBA
• #### Speaker: Held for Special Lecture (TBA) -

When: Wed, November 29, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Held for Special Lecture () -

When: Wed, December 6, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Daniel Tataru (UC Berkeley) - https://math.berkeley.edu/~tataru/

When: Fri, December 8, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Shrawan Kumar (UNC at Chapel Hill) - http://www.unc.edu/math/Faculty/kumar/

When: Wed, January 24, 2018 - 3:15pm
Where: Kirwan Hall 3206

### View Abstract

Abstract: TBA
• #### Speaker: Claude Le Bris () -

When: Wed, February 7, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Ivan Cheltsov (University of Edinburgh, UK) - http://www.maths.ed.ac.uk/cheltsov/

When: Wed, February 21, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Richard Schwartz (Brown University) - http://www.math.brown.edu/~res/

When: Wed, March 14, 2018 - 3:15pm
Where: Kirwan Hall 3206