The Aziz Lectures
Numerical Solution of Differential Equations
The Aziz Lectures are sponsored by Prof. A. Kadir Aziz. The purpose
of the series is to bring distinguished mathematicians to the University of
Maryland, College Park to give survey lectures on the numerical solution of
differential equations.
Prof. Aziz received his Ph.D. from the University of Maryland, College Park in
1957. He was on the faculty of Georgetown University from 1956 to 1967, and
has been on the faculty at the University of Maryland, Baltimore County since
1967. He is presently Professor Emeritus of Mathematics and Statistics at
UMBC. Throughout his career Prof. Aziz has been an active member of the
Numerical Analysis group at College Park.
The Aziz lecture is given at 3pm in the Math Colloquium Room
(MTH 3206).
Usually the speaker gives a related talk in the Applied Math Colloquium
on the previous day (Thursday at 3:30pm).
Aziz Lectures 2007
Nov. 16, 2007
Adaptive Approximation by Greedy Algorithms
Prof. Albert Cohen
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie,
Paris, France
This talk will discuss computational algorithms that deal with the following
general task: given a function f and a dictionary of functions D in a Hilbert
space, extract a linear combination of N functions of D which approximates f at
best. We shall review the convergence properties of existing algorithms. This
work is motivated by applications as various as data compression, adaptive
numerical simulation of PDE's, statistical learning theory.
May 4, 2007
Compressive Sampling
Prof. Emmanuel J. Candes
California Institute of Technology
One of the central tenets of signal processing is the Shannon/Nyquist sampling theory: the number of samples needed to
reconstruct a signal without error is dictated by its
bandwidth-the length of the shortest interval which contains the
support of the spectrum of the signal under study. Very
recently, an alternative sampling or sensing theory has emerged
which goes against this conventional wisdom. This theory allows
the faithful recovery of signals and images from what appear to
be highly incomplete sets of data, i.e. from far fewer data bits
than traditional methods use. Underlying this metholdology is a
concrete protocol for sensing and compressing data
simultaneously.
This talk will present the key mathematical ideas underlying this
new sampling or sensing theory, and will survey some of the most
important results. We will argue that this is a robust
mathematical theory; not only is it possible to recover signals
accurately from just an incomplete set of measurements, but it is
also possible to do so when the measurements are unreliable and
corrupted by noise. We will see that the reconstruction
algorithms are very concrete, stable (in the sense that they
degrade smoothly as the noise level increases) and practical; in
fact, they only involve solving very simple convex optimization
programs.
An interesting aspect of this theory is that it has bearings on
some fields in the applied sciences and engineering such as
statistics, information theory, coding theory, theoretical
computer science, and others as well. If time allows, we will
try to explain these connections via a few selected examples.
Aziz Lectures 2006
December 1, 2006
Imaging in random media
Prof. George C. Papanicolaou
Mathematics Department
Stanford University
I will present an overview of some recently developed methods for imaging with array and
distributed sensors when the environment between the objects to be imaged and the sensors is
complex and only partially known to the imager. This brings in modeling and analysis in random
media, and the need for statistical algorithms that increase the computational complexity of
imaging, which is done by backpropagating local correlations rather than traces
(interferometry). I will illustrate the theory with applications from non-destructive testing
and from other areas.
April 21, 2006
String integration of some MHD equations
Prof. Yann Brenier
Laboratoire Alexandre Dieudonné
Université de Nice-Sophia-Antipolis,
France
We first review the link between strings and some
Magnetohydrodynamics equations. Typical examples are
the Born-Infeld system, the Chaplygin gas equations
and the shallow water MHD model. They arise in Physics
at very different (from subatomic to cosmologic) scales.
These models can be exactly integrated in one space
dimension by solving the 1D wave equation and using the
d'Alembert formula. We show how an elementary "string
integrator" can be used to solve these MHD equations
through dimensional splitting. A good control of the
energy conservation is needed due to the repeated use
of Lagrangian to Eulerian grid projections. Numerical
simulations in 1 and 2 dimensions will be shown.
February 3, 2006
Multiscale Analysis in Micromagnetics
Prof. Felix Otto
Institute for Applied Mathematics
University of Bonn,
Germany
From the point of view of mathematics,
micromagnetics is an ideal playground for a pattern forming system in m
aterials
science: There are abundant experiments on a wealth of visually
attractive phenomena and there is a well-accepted continuum model.
In this talk, I will focus on two specific
experimental pattern for thin film ferromagnetic elements.
One pattern is a ground state, the other pattern is a
metastable state. Starting point for our analysis is the micromagnetic
model
which has three length scales and thus many parameter regimes.
For both pattern, we identify the appropriate paramater regime
and rigorously derive a reduced model via Γ-convergence. We
numerically simulate the reduced model and compare to experimental data.
This is joint work with A. DeSimone, R. V. Kohn, and S. Müller
for the first part and with R. Cantero-Alvarez and J. Steiner
for the second part.
Aziz Lectures 2005
December 9, 2005
Prof. Willi Jäger
Institute for Applied Mathematics
University of Heidelberg,
Germany
Aziz Lectures 2004
November 19, 2004
Prof. Michael Vogelius
Department of Mathematics, Rutgers University
May 7, 2004
Prof. Benoît Perthame
École Normale Supérieure, Paris
Aziz Lectures 2003
November 14, 2003
Prof. Tom Hou
Caltech
March 7, 2003
Prof. Alfio Quarteroni
Politecnico di Milano, Milan, Italy, and
EPFL, Lausanne, Switzerland
Aziz Lectures 2002
Dec. 6, 2002
Prof. John Ball
Department of Mathematics, Oxford
May 3, 2002
Prof. Randolph E. Bank
Department of Mathematics,
University of California at San Diego
Aziz Lectures 2001
Nov. 16, 2001
Prof. Roger Temam
Institute for Scientific Computing and Applied Mathematics, Indiana
University
April 23, 2001
Prof. Franco Brezzi
Istituto di Analisi Numerica
del CNR and Dipartimento di Matematica,
Universita di Pavia, Italy
Aziz Lectures 2000
March 15, 2000
Prof. Vidar Thomée
Dept. of Mathematics,
Chalmers University of Technology and Göteborg University
Aziz Lectures 1999
December 10, 1999
Colliding Black Holes and Gravity Waves: A New Computational
Challenge
Prof. Douglas N. Arnold
Dept. of Mathematics, Pennsylvania
State University
September 24, 1999
A Priori and A Posteriori Error Estimates in Finite Element
Approximation
Prof. Lars B. Wahlbin
Dept. of Mathematics, Cornell
University
February 19, 1999
Mathematical Problems Related to the Reliability of Finite Element
Analysis in Practice: When Can We Trust the Computational Results for
Engineering Decisions
Prof. Ivo Babuska
University of Texas, Austin, Emeritus
Professor at University of Maryland
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