HOME    »    PROGRAMS/ACTIVITIES    »    Annual Thematic Program
IMA 2001 Summer Program
Geometric Methods in Inverse Problems and PDE Control
July 16-27, 2001


Organizers:

Christopher B. Croke University of Pennsylvania ccroke@math.upenn.edu
Irena Lasiecka University of Virginia il2v@virginia.edu
Gunther Uhlmann University of Washington gunther@math.washington.edu
Michael Vogelius Rutgers University vogelius@math.rutgers.edu


Description:

An important class of inverse problems involves the determination of coefficients and parameters in a partial differential equation from boundary measurements. These problems arise in many areas such as medical imaging, nondestructive testing, and geophysical prospecting. Control problems in partial differential equations arise from the need to dampen out vibration in a structure using actuators located in accessible regions. As part of this one needs to determine boundary conditions that will lead to a desired state for the solution of the partial differential equation.

The core analytical questions in inverse problems are those of uniqueness and stability, while in control problems the issues are of controllability and stabilizability. In fact, the issues of exact controllability and uniform stabilizability are intimately connected with observability/reconstruction estimates. Instead, the issue of approximate controllability and strong stabilizability are related to unique continuation properties. Thus, the type of estimates/inequalities one seeks in both fields are often closely related. These areas have recently seen the use of differential geometric methods to solve some outstanding questions in those fields. As an example, a combination of unique continuation results with the boundary control method has lead to the solution of the inverse problem of determining a metric of a Riemannian manifold (with boundary) from the dynamic Dirichlet-to-Neumann map associated with the wave equation. [The Dirichlet-to-Neumann map for the wave equation determines the boundary distance function (travel time along geodesics connecting points on the boundary of a Riemannian manifold). A natural question to ask if one can determine the metric from this data alone ; this question is at the center of the boundary rigidity problem studied in Riemannian geometry.] An example from control is the establishment of sufficient conditions for controllability and stabilization, expressed in terms of geometry of the domain. There are also interesting inverse problems for semilinear elliptic partial differential equations where the uniqueness issue is intimately tied with the geometry of the domain. The boundary control method used in inverse problems as well as some deep results in exact controllability are based on the study of propagation of singularities for partial differential equations. The propagation in turn depends on geometric properties of the domain. While there has been some remarkable success, many open problems still remain.

While the importance of differential geometry in the control of PDE and inverse problems has been established, there has never been a concerted effort to bring geometers to interact with experts in these other areas. The workshop goals are to bring together geometers with researchers in inverse problems and control of PDE to facilitate exchange of ideas and encourage collaboration; to make tools of differential geometry known to those working in inverse problems and control, and to open new areas of research in geometry. The workshop will for instance explore the use of inverse problem- and control methods to rigidity problems in geometry.

We are planning a 2-week workshop in which Week 1 will emphasize the Geometric and PDE methods and Week 2 will focus on applications of these techniques to inverse and control problems. Both weeks will begin with overview talks designed to set the stage for the workshop. The presence of several talks of a survey nature will make this workshop an ideal venue for young researcher wanting to get involved in these fields. The format of the workshop will consist in invited talks (both of a survey and of a more specialized nature), two sessions of contributed talks and a panel discussion. The Proceedings of the summer program will be published as an IMA Volume.

Topics that will be covered in this program include:

  1. Boundary Rigidity
  2. Conjugacy of Geodesic Flows
  3. Integral Geometry
  4. Wave propagational inverse problems (Maxwell equations, elasticity, anisotropy)
  5. Propagation of sigularities (Low regularity of coefficient and domain)
  6. Boundary Control methods
  7. Observability/controllability inequalities by differential geometric methods.
  8. Unique continuation
  9. Elliptic inverse problems with rough coefficients

WORKSHOP SCHEDULE
schedule.pdf    schedule.ps   schedule.tex
Week 1: July 16-20 Monday Tuesday
Week 2: July 23-27 Monday Tuesday Wednesday Thursday Friday
WEEK 1 (JULY 16-20)
UNIQUENESS, PROPAGATION OF SINGULARITIES, CARLEMAN ESTIMATES
MONDAY, JULY 16
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee and Registration

Reception Room EE/CS 3-176

9:10 am Willard Miller, Fred Dulles, and Irena Lasiecka Welcome and Introduction
9:30 am Christopher B. Croke
University of Pennsylvania

The Boundary Rigidity and Conjugacy Rigidty Problems

Slides

10:40 am Break Reception Room EE/CS 3-176
11:10 am-12:00 pm Vladimir Sharafutdinov
Sobolev Institute of Mathematics

Deformation Boundary Rigidity and Other Applications of the Ray Transform to Inverse Problems

pdf    postscript   dvi

2:00-2:50 pm Bruce Kleiner
University of Michigan
Asymptotic Geometry of Negatively Curved Manifolds
4:00 pm IMA Tea/Reception
A variety of appetizers and beverages will be served.
IMA East, 400 Lind Hall
TUESDAY, JULY 17
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Michael E. Taylor
University of North Carolina

The Wave Equation: Analytical Subject and Analytical Tool

Slides

10:40 am Break Reception Room EE/CS 3-176
11:10 am-12:00 pm Dmitri Burago
Penn State University
Volume/Distance Estimates, Gaussian Measures of Surfaces, and Ellipticity of Volume Functionals
2:00 pm Gerard Besson
CNRS

A Margulis Lemma Without Curvature

Slides

2:50 pm Break Reception Room EE/CS 3-176
3:20-4:10 pm Matthias M. Eller
Georgetown University
Unique Continuation for Solutions to Systems of Partial Differential Equations with Non-Analytic Coefficients
WEDNESDAY, JULY 18
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Gunther Uhlmann
University of Washington

Inside-Out: Inverse Boundary Problems

Slides

10:40 am Break Reception Room EE/CS 3-176
11:10 am-12:00 pm Werner Ballmann
Rheinische Friedrich-Wilhelms-Universitaet Bonn

Isospectral Manifolds

isospec.pdf    isospec.ps

2:00 pm Stephen Zelditch
Johns Hopkins University

Inverse Spectral and Resonance Problems for Analytic Plane Domains

Slides

2:50 pm Break Reception Room EE/CS 3-176
3:20-4:10 pm Allan Greenleaf
University of Rochester
Global Uniqueness in the Calderon problem for Conormal Conductivities
THURSDAY, JULY 19
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Roberto Triggiani
University of Virginia
Differential Geometric Methods in the Control of PDEs (Overview)
10:40 am Break Reception Room EE/CS 3-176
11:10 am-
12:00 pm
John Sylvester
University of Washington
Inverse Theory and an Experiment
2:00 pm Robert Gulliver
University of Minnesota
Boundary Control of Wave Equations via Geometry
3:10 pm Break Reception Room EE/CS 3-176
Contributed Talks
3:40 pm Jianguo Cao
University of Notre Dame
The Spectrum of Non-compact Manifolds with Big Ends
4:00 pm Chris Judge
Indiana University
Behavior of the Laplace Spectrum of DegeneratingRiemannian Manifolds
4:20 pm Break Reception Room EE/CS 3-176
4:30 pm Takashi Takiguchi
National Defense Academy of Japan
A Generalization of Helgason's Support Theorem
4:50-5:10 pm Nicolas Valdivia
Wichita State University
Uniqueness in Inverse Obstacle Scattering with General Conductive Boundary Condition
FRIDAY, JULY 20
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Michael Vogelius
Rutgers University
Special Purpose Electromagnetic Tomography
10:40 am Break Reception Room EE/CS 3-176
11:10 am-
12:00 pm
Patrick Eberlein
University of North Carolina
Nilpotent Groups and the Boundary Geometry of Negatively Curved Manifolds
2:00-2:50 pm Gerhard Knieper
Ruhr-Universitaet Bochum
Asymptotic Geometry of Manifolds of Negative Curvature
2:50 pm Break Reception Room EE/CS 3-176
3:20 -4:10 pm Victor Isakov
Wichita State University
Uniqueness of the Continuation, Control and Inverse Problems for the Dynamical Lame System
WEEK 2 (JULY 23-27)
APPLICATIONS TO INVERSE PROBLEMS/CONTROL
MONDAY, JULY 23
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Masahiro Yamamoto
The University of Tokyo
Inverse Problems for Hyperbolic Systems by Carleman Estimates
10:20 am Break Reception Room EE/CS 3-176
11:00-11:50 am

Fadil Santosa
University of Minnesota/IMA

Level Set Methods for Inverse Problems and Optimal Design

Talk:   pdf    postscript

2:00 pm Walter Littman
University of Minnesota
The Scope of the "SUR" Method in Boundary Control
2:50 pm Break Reception Room EE/CS 3-176
3:20-4:10 pm Matti Lassas
University of Helsinki

Inverse Boundary Spectral Problems and Gauge Transformations

Talk:    pdf    postscript    dvi

TUESDAY, JULY 24
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Mikhail Belishev
Steklov Institute of Mathematics
An Invariant Look at Inverse Problems: A Possible Way to Revise the Calderon Problem
10:20 am Break Reception Room EE/CS 3-176
11:00-11:50 am Shari Moskow
University of Florida
Identification of Conductivity Imperfections of Small Diameter
2:00 pm Jean-Pierre Puel
Universite de Versailles St. Quentin
Some Methods for Studying Exact Controllability to Trajectories in Parabolic Evolution Equations and Applications
2:50 pm Break Reception Room EE/CS 3-176
Contributed Talks
3:30 pm Peter Gibson
Technische Universität Darmstadt

Discretized Inverse Problems and "Splitting" of Distributions

Slides

3:50 pm Sönke Hansen
Universität Paderborn
Propagation of Polarization in Elastodynamics with Residual Stress and Travel Times
4:10 pm Break Reception Room EE/CS 3-176
4:20 pm Hyeonbae Kang
Seoul National University
Boundary Determination of Anisotropic Conductivity via the Dirichlet to Numann Map
3:30 pm Vladimir V. Kryzhniy
Kuban State University of Technology
Regularizing Algorithm of Numerical Inversion of Laplace Transform usage in Expansion of Exponential Signal Into Partial Fractions
4:00 pm Lizabeth V. Rachele
Tufts University
Uniqueness in Inverse Problems for Elastic Media
WEDNESDAY, JULY 25
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Giovanni Alessandrini
University of Trieste

Size Estimates of Inclusions in an Elastic Body by Boundary Measurements

Talk:   pdf

10:20 am Break Reception Room EE/CS 3-176
11:00-11:50 am Habib Ammari
CNRS
Reconstruction of Small Electromagnetic Inhomogeneities
2:00 pm James G. Berryman
Lawrence Livermore National Laboratory
Time-Reversal Acoustics and Maximum-Entropy Imaging
2:50 pm Break Reception Room EE/CS 3-176
3:20 pm Jin Keun Seo
Yonsei University
A Real Time Algorithm for the Location Search of Discontinuous Conductivities with One Measurement
4:10 pm Break Reception Room EE/CS 3-176
Contributed Talks
4:20 pm Paolo Albano
University of Bologna

Observability Estimates for a Parabolic-hyperbolic Coupled System

http://ejde.math.swt.edu/Volumes/2000/22/abstr.html

http://ejde.math.swt.edu/Volumes/2000/53/abstr.html

4:40 pm Seongjai Kim
University of Kentucky
Smooth Detectors of Linear Phase
5:00--5:20 pm Rakesh
University of Delaware

Inverse Problems for Hyperbolic PDE

Slides

THURSDAY, JULY 26
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Yaroslav Kurylev
Loughborough University

Geometric Convergence for Manifolds with Boundary and Reconstruction of a Riemannian Manifold

Slides

10:20 am Break Reception Room EE/CS 3-176
11:00-11:50 am Leonid Pestov
Sobolev Institute of Mathematics
On Uniqueness and Solvability of Integral Geometry Problems on a Riemannian Manifold
2:00-2:50 pm Gen Nakamura
Hokkaido University

Discretization of Dirichlet to Neumann Map and Inverse Boundary Value Problem

Slides

2:50 pm Coffee Reception Room EE/CS 3-176
Contributed Talks
3:30 pm George Avalos
University of Nebraska-Lincoln
Exact Controllabilty of Structural Acoustic Interactions
3:50 pm Michael Galbraith
University of Minnesota
A Geometric-Optics Proof of a Theorem on Boundary Control Given a Convex Function
4:10 pm Coffee Reception Room EE/CS 3-176
4:20--4:40 pm Judith Vancostenoble
Université Paul Sabatier
Optimality of Energy Estimates for the Wave Equation with Nonlinear Boundary Velocity Feedbacks
6:00 pm Workshop Dinner Bangkok Thai Restaurant
FRIDAY, JULY 27
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Free Day, no workshop events scheduled.
10:30 am Coffee Lind Hall 400

Week 1: July 16-20 Monday Tuesday
Week 2: July 23-27 Monday Tuesday Wednesday Thursday Friday

LIST OF CONFIRMED PARTICIPANTS

as of 7/17/2001
Name Department Affiliation
Chi Young Ahn Mathematics Brain 21 Korea/Yonsei University
Tuncay Aktosun Mathematics North Dakota State University
Paolo Albano Mathematics University of Bologna
Giovanni Alessandrini Scienze Matematiche University of Trieste
Habib Ammari Center of Applied Mathematics CNRS
Kais Ammari Mathematics University of Nancy-I
George Avalos Mathematics Texas Tech University
Werner Ballmann Mathematisches Institut Rheinische Friedrich-Wilhelms-Universitaet Bonn
Bartolome Barcelo Departamento de Matematicas Universidad Autunoma de Madrid
Mikhail Belishev   Steklov Institute of Mathematics
James G. Berryman   Lawrence Livermore National Laboratory
Gerard Besson Institut Fourier, Laboratoire de Mathematiques CNRS
Russell Brown Mathematics University of Kentucky
Dmitri Burago Mathematics Penn State University
John Cagnol   University Leonard de Vinci
Jianguo Cao Mathematics University of Notre Dame
Yves Capdeboscq Mathematics Rutgers University
Eduardo Chappa Mathematics University of Washington
Christopher B. Croke David Rittenhouse Laboratory University of Pennsylvania
Michael Dobranski Mathematics University of Kentucky
Fred Dulles   Institute for Mathematics & its Applications
Patrick Eberlein Mathematics University of North Carolina
Matthias Eller Mathematics Georgetown University
Michael Galbraith Mathematics University of Minnesota
Peter C. Gibson Applied Mechanics Technische Universitaet Darmstadt
Allan Greenleaf Mathematics University of Rochester
Robert Gulliver Mathematics University of Minnesota
Scott Hansen Mathematics Iowa State University
Soenke Hansen FB 17 Mathematik-Informatik University of Paderborn
Mary Ann Horn Mathematics Vanderbilt University
L. Steven Hous Mathematics Iowa State University
Kai Huang Mathematics Michigan State University
Victor Isakov Mathematics and Statistics Wichita State University
Chris Judge   Indiana University
Hyeonbae Kang Mathematics Seoul National University
Chang-Wan Kim Mathematics Korea Advanced Institute of Science & Technology
Hyejoo Kim Statistics Seoul National University
Jeong-Hoon Kim Mathematics Brain21 Korea/Yonsei University
Jinseog Kim Statistics Seoul National University
Jumi Kim Mathematics Brain 21 Korea/Yonsei University
Seongjai KIm Mathematics University of Kentucky
Bruce Kleiner Mathematics University of Michigan
Gerhard Knieper Fakultaet fuer Mathematik Ruhr-Universitaet Bochum
Kim Knudsen Mathematical Sciences Aalborg University
Vladimer V Kryzhniy Applied Mathematics Kuban State University of Technology
Yaroslav Kurylev Mathematical Sciences Loughborough University
Irena Lasiecka Mathematics University of Virginia
Matti Lassas Rolf Nevanlinna Institute University of Helsinki
Catherine Lebiedzik Mathematics University of Virginia
E. B. Lee Electrical and Computer Engineering University of Minnesota
Debra Lewis Mathematics UC Santa Cruz
Hyeona Lim Mathematics Michigan State University
Mi Kyoung Lim Mathematics Seoul National University
Walter Littman Mathematics University of Minnesota
Patrick Martinez UFR Mathematiques Informatique et Gestion Universite Paul Sabatier
Stephen McDowell Mathematics University of Rochester
Willard Miller   Institute for Mathematics & its Applications
Steen Moeller Mathematical Sciences Aalborg University
Shari Moscow Mathematics University of Florida
Marwan Moubachir Applied Mathematics Laboratoire Central des Ponts et Chaussees
Gen Nakamura Math Graduate Science Hokkaido University
Nilima Nigam Mathematics and Statistics McGill University
Leonid Pestov   Sobolev Institute of Mathematics
Jean-Pierre Puel Laboratoire de Mathematiques Appliquees Universite de Versailles St. Quentin
Lizabeth Rachele Mathematics Tufts University
Rakesh Mathematical Sciences University of Delaware
Jan Marthedal Rasmussen Informatics & Mathematical Modeling Technical University of Denmark
Paul Sacks Mathematics Iowa State University
Jin Keun Seo Mathematics Yonsei University
Vladimir Sharafutdinov   Sobolev Institute of Mathematics
Jaemin Shin Mathematics Brain 21 Korea /Yonsei University
Plamen D. Stefanov Mathematics Purdue University
John Sylvester Mathematics University of Washington
Takashi Takiguchi Mathematics National Defense Academy
Alexandru Tamasan Mathematics University of Washington
Michael Taylor Mathematics University of North Carolina
Roberto Triggiani Mathematics University of Virginia
Gunther Uhlmann Mathematics University of Washington
Nicolas Valdivia Mathematics Wichita State University
Judith Vancostenoble Laboratoire de Mathematiques Emile Picard Universite Paul Sabatier
Michael Vogelius Mathematics Rutgers University
Jenn-Nan Wang Mathematics National Cheng Kung University
Xiaoming Wang Mathematics Iowa State University
Anna Wienhard Mathematisches Institut Rheinische Friedrich-Wilhelms Universitaet Bonn
Masahiro Yamamoto Mathematical Sciences The University of Tokyo
Stephen Zelditch Mathematics Johns Hopkins University
Connect With Us:
Go