This program is primarily for graduate students of IMA Participating
Institutions. The NSF may provide support for a limited
number of students at other US universities.
From Monday, June 15 through Friday, July 3, 2009,
University of Delaware, Newark
will be the host
of the Institute for Mathematics and its Applications (IMA)
Summer Graduate Program in Mathematics.
The course will concentrate on
The Mathematics of Inverse Problems.
Inverse problems is a fast-growing area involving a
broad range of disciplines from the most abstract and pure mathematics to
practical engineering. The 2009 summer program on inverse problems covers
three different types of inverse problems: inverse problems for hyperbolic
PDE's, inverse scattering in the frequency domain, and variational inverse
problems. The program will cover the techniques used to tackle problems at
the cutting edge of mathematical research in each of these areas. This is
a unique and timely synthesis of disciplines that will position future
researchers for the next step in inverse scattering from waves that, we
believe, will combine variational methods with direct qualitative
Week 1, June 15-19:
William Symes/Rakesh, hyperbolic inverse problems.
Symes is Noah Harding Professor in the Department of
Computational and Applied Mathematics at
Rice University and Managing Editor of Inverse
Symes and UD's Rakesh will
focus on inverse problems for hyperbolic PDEs for
one and higher space dimensions. They will consider theoretical
computational issues for inversion from the Dirichlet to
Neumann map as
well as from smaller subsets of this data, including formally
Week 2, June 22-26: John
Colton, inverse scattering problems in the
frequency domain. John
Sylvester of the University of Washington is
one of the world leaders in the theory of inverse scattering in the frequency domain. He and UD's
Colton will give a series of lectures on the mathematical foundations of acoustic
scattering theory together with qualitative methods in inverse scattering theorey.
Supplementary lectures will be given by UD's
Fioralba Cakoni and
Peter Monk on regularization
methods for ill-posed problems and inverse scattering for electromagnetic waves. Numerical
methods in inverse scattering theory will be a common thread in all of the above lectures.
Week 3, June 29-July 3: Jonathan
variational inverse problems.
is Canada Research Chair in IT at Dalhousie and
Laureate Professor of Mathematics in Newcastle Australia. He is
one of 250 of the most highly cited
mathematicians from 1980-1999 (ISIHighlyCited) and the
co-inventor of the Borwein-Preiss
variational principle, among other achievements. Borwein and
will focus on fundamentals of variational
analysis, notions of well-posedness and regularity, and finally
ill-posed problems which are at the frontiers
of analysis. Practical and timely applications to optics and
crystallography will be explored.