Summer School in Inverse Problems; June 2009; Newark, DE

Luke

DMS-0852454

For the Institute for Mathematics and its Applications (IMA)

and its Participating Institutions (PI), the principal

investigator and his colleagues organize the IMA/PI Summer School

on the Mathematics of Inverse Problems, June 15-July 3. In this

project the investigators include students who are not from the

participating institutions. The program is geared toward

graduate students in the mathematical sciences. The 2009 summer

program on the mathematics of inverse problems covers three

different themes: inverse problems for hyperbolic partial

differential equations, inverse scattering in the frequency

domain, and variational techniques for inverse problems. The

program covers the techniques used to tackle problems at the

cutting edge of mathematical research in each of these areas.

Week-long lectures and problem-solving sessions are presented in

an informal environment by world leaders in each of these areas

-- William Symes (inverse problems for waves), John Sylvester

(inverse scattering), and Jonathan Borwein (variational

analysis). Two of the three lecture series (inverse scattering

and variational techniques) are under contract to appear as

separate chapters in a book to be published by Springer in 2010.

Inverse problems are everywhere, from determining the causes

of global warming, to finding oil and natural gas under the

earth's surface, to diagnosing diseases with medical imaging.

The basic idea of an inverse problem is simple: given an

observation, determine the cause. Unfortunately, most inverse

problems are not easily solved: the model for the observation is

often incomplete or incorrect, and, even if the model is a

perfect match to the truth, it may be impossible to accurately

determine the cause from an observation (the curse of so-called

'ill-posedness'). The last 20 years has seen a dramatic shift in

the mathematics of inverse problems and the capabilities for

solving them, initiated largely by improvements in computing

power and the concurrent evolution of what is often called

'experimental mathematics.' Never before have new theoretical

tools been able to be tested with such immediacy and practical

import. This IMA/PI Summer School on the Mathematics of Inverse

Problems aims at preparing future mathematicians for research in

this growing and increasingly vital field. The schools bring

students together with outstanding researchers in an intensive

setting that is intended to lead students from the more familiar

course-oriented problem solving skills to the frontiers of

mathematical research. Students gain experience not only in

attacking problems on advanced and research-grade topics, but

also in working collaboratively with people from different

backgrounds. The 2009 program has received 51 applications from

a diverse group of individuals, 29 from participating IMA

institutions and 22 from non-IMA institutions. This project

supports students from non-IMA affiliated institutions.