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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 
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 DirichlettoNeumann map associated with the wave equation. [The DirichlettoNeumann 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 2week 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:
Week 1: July 1620  Monday  Tuesday  
Week 2: July 2327  Monday  Tuesday  Wednesday  Thursday  Friday 
WEEK
1 (JULY 1620) UNIQUENESS, PROPAGATION OF SINGULARITIES, CARLEMAN ESTIMATES 


MONDAY,
JULY 16 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee and Registration 
Reception Room EE/CS 3176 
9:10 am  Willard Miller, Fred Dulles, and Irena Lasiecka  Welcome and Introduction 
9:30 am  Christopher
B. Croke University of Pennsylvania 

10:40 am  Break  Reception Room EE/CS 3176 
11:10 am12:00 pm  Vladimir
Sharafutdinov Sobolev Institute of Mathematics 
Deformation Boundary Rigidity and Other Applications of the Ray Transform to Inverse Problems 
2:002:50 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 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
9:30 am  Michael
E. Taylor University of North Carolina 

10:40 am  Break  Reception Room EE/CS 3176 
11:10 am12:00 pm  Dmitri
Burago Penn State University 
Volume/Distance Estimates, Gaussian Measures of Surfaces, and Ellipticity of Volume Functionals 
2:00 pm  Gerard
Besson CNRS 

2:50 pm  Break  Reception Room EE/CS 3176 
3:204:10 pm  Matthias
M. Eller Georgetown University 
Unique Continuation for Solutions to Systems of Partial Differential Equations with NonAnalytic Coefficients 
WEDNESDAY,
JULY
18 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
9:30 am  Gunther
Uhlmann University of Washington 

10:40 am  Break  Reception Room EE/CS 3176 
11:10 am12:00 pm  Werner
Ballmann Rheinische FriedrichWilhelmsUniversitaet Bonn 
Isospectral Manifolds 
2:00 pm  Stephen
Zelditch Johns Hopkins University 
Inverse Spectral and Resonance Problems for Analytic Plane Domains 
2:50 pm  Break  Reception Room EE/CS 3176 
3:204:10 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 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
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 3176 
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 3176 
Contributed Talks


3:40 pm  Jianguo
Cao University of Notre Dame 
The Spectrum of Noncompact 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 3176 
4:30 pm  Takashi
Takiguchi National Defense Academy of Japan 
A Generalization of Helgason's Support Theorem 
4:505:10 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 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
9:30 am  Michael
Vogelius Rutgers University 
Special Purpose Electromagnetic Tomography 
10:40 am  Break  Reception Room EE/CS 3176 
11:10
am 12:00 pm 
Patrick
Eberlein University of North Carolina 
Nilpotent Groups and the Boundary Geometry of Negatively Curved Manifolds 
2:002:50 pm  Gerhard
Knieper RuhrUniversitaet Bochum 
Asymptotic Geometry of Manifolds of Negative Curvature 
2:50 pm  Break  Reception Room EE/CS 3176 
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 2327) APPLICATIONS TO INVERSE PROBLEMS/CONTROL 

MONDAY,
JULY 23 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
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 3176 
11:0011:50 am 
Fadil
Santosa 
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 3176 
3:204:10 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 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
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 3176 
11:0011:50 am  Shari
Moskow University of Florida 
Identification of Conductivity Imperfections of Small Diameter 
2:00 pm  JeanPierre
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 3176 
Contributed Talks  
3:30 pm  Peter
Gibson Technische Universität Darmstadt 
Discretized Inverse Problems and "Splitting" of Distributions 
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 3176 
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 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
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 3176 
11:0011:50 am  Habib
Ammari CNRS 
Reconstruction of Small Electromagnetic Inhomogeneities 
2:00 pm  James G. Berryman Lawrence Livermore National Laboratory 
TimeReversal Acoustics and MaximumEntropy Imaging 
2:50 pm  Break  Reception Room EE/CS 3176 
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 3176 
Contributed Talks  
4:20 pm  Paolo
Albano University of Bologna 
Observability Estimates for a Parabolichyperbolic Coupled System 
4:40 pm  Seongjai
Kim University of Kentucky 
Smooth Detectors of Linear Phase 
5:005:20 pm  Rakesh University of Delaware 

THURSDAY,
JULY 26 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:15 am  Coffee  Reception Room EE/CS 3176 
9:30 am  Yaroslav
Kurylev Loughborough University 
Geometric Convergence for Manifolds with Boundary and Reconstruction of a Riemannian Manifold 
10:20 am  Break  Reception Room EE/CS 3176 
11:0011:50 am  Leonid
Pestov Sobolev Institute of Mathematics 
On Uniqueness and Solvability of Integral Geometry Problems on a Riemannian Manifold 
2:002:50 pm  Gen
Nakamura Hokkaido University 
Discretization of Dirichlet to Neumann Map and Inverse Boundary Value Problem 
2:50 pm  Coffee  Reception Room EE/CS 3176 
Contributed Talks  
3:30 pm  George
Avalos University of NebraskaLincoln 
Exact Controllabilty of Structural Acoustic Interactions 
3:50 pm  Michael
Galbraith University of Minnesota 
A GeometricOptics Proof of a Theorem on Boundary Control Given a Convex Function 
4:10 pm  Coffee  Reception Room EE/CS 3176 
4:204:40 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 3180 unless otherwise noted. 

Free Day, no workshop events scheduled.  
10:30 am  Coffee  Lind Hall 400 
Week 1: July 1620  Monday  Tuesday  
Week 2: July 2327  Monday  Tuesday  Wednesday  Thursday  Friday 
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 NancyI 
George Avalos  Mathematics  Texas Tech University 
Werner Ballmann  Mathematisches Institut  Rheinische FriedrichWilhelmsUniversitaet 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 MathematikInformatik  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 
ChangWan Kim  Mathematics  Korea Advanced Institute of Science & Technology 
Hyejoo Kim  Statistics  Seoul National University 
JeongHoon 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  RuhrUniversitaet 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  
JeanPierre 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 
JennNan Wang  Mathematics  National Cheng Kung University 
Xiaoming Wang  Mathematics  Iowa State University 
Anna Wienhard  Mathematisches Institut  Rheinische FriedrichWilhelms Universitaet Bonn 
Masahiro Yamamoto  Mathematical Sciences  The University of Tokyo 
Stephen Zelditch  Mathematics  Johns Hopkins University 