Issue No 10


Euro Summer School
New Analytic and Geometric Methods in Inverse Problems
24 July to 2 August

Euro Conference
Recent Developments in the Wave Field and Diffuse Tomographic Inverse Problems
3–5 August

Organising Committee:
Yaroslav Kurylev (Loughborough),
Brian Sleeman (Leeds) and
Erkki Somersalo (Helsinki)

Supported by:
The European Commission (Framework V), the London Mathematical Society

The Summer School was built around lecture courses on multidimensional inverse problems. There were seven lecture courses, each consisting of 4–5 lectures and 2–3 tutorials. The lecture courses were focussed on recent powerful methods in multidimensional inverse problems based upon an interplay with differential geometry (especially Riemannian and integral geometry) and analysis (in particular spectral theory, harmonic analysis and PDE-control).

Given that most of the participants had a background in analysis and applied mathematics, one of the courses (by Dmitri Burago) was devoted to the new areas of Riemannian geometry relevant to inverse problems. A condensed introduction to the theory of Carleman estimates and PDE-control and their applications to inverse problems was given in the lecture course by Victor Isakov. Analytic techniques of harmonic analysis with respect to the impedance tomography/fixed frequency inverse problems were presented in the talks by Lassi Paivarinta. Further developments in the impedance tomography inverse problems and, in particular, in the inisotropic inverse problems, based upon a combination of methods of the microlocal and harmonic analysis, were given in the lectures by Gunther Uhlmann. Another modern approach to the multidimensional inverse problems aimed at the spectral and dynamic inverse problems was presented in the course by Alexander Katchalov and Matti Lassas. This approach was heavily based on the spectral theory and metric properties of the Riemannian manifolds. The course by Vladimir Sharafudinov gave an extended introduction to modern integral geometry and its relation to inverse problems. Finally, the course by Anders Melin provided a theory of inverse scattering problems based upon the method of intertwining operators. With Faddeev’s Green’s functional being the foundation of this method, this came as a further development of the basic principles described in the courses by Paivarinta and Uhlmann.

The Summer School gave a coherent and complete picture of modern methods in multidimensional inverse problems and provided their common mathematical background in differential geometry and analysis.

The Euro Conference aimed to elaborate upon the ideas introduced at the Summer School through presentations of the most recent achievements obtained in the area (by workers such as Matti Lassas, Gen Nakamura, Atsushsi Katsuda, William Lionheart etc.) In addition, the Conference provided a broader picture of the state of the art in inverse problems (through talks by people such as David Colton, Rainer Kress, Giovanni Alessandrini etc.) The Conference was therefore simultaneously a forum for advanced researchers – where they had the opportunity to present their most recent results and discuss outstanding problems – and a continuation of the Summer School for younger participants, where they had the opportunity to learn about the applications and development of the methods taught at the Summer School.

In addition to the main speakers, there were 14 shorter presentations (20–30 minutes) by younger researchers.

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Abrahamsson, Mikael, Lund University
Alessandrini, Giovanni, University of Trieste
Ayuso, Blanca, Universidad Autonoma de Madrid
Barcelo, Bartolome, Universidad Autonoma de Madrid
Barcelo, Juan Antonio, Universidad Politecnica Madrid
Beltita, Ingrid, Romanian Academy
Bermudo, Sergio, University of Seville
Bingham, Kenrick, Helsinki University of Technology
Burago, Dmitri, The Pennsylvania State University
Chappa, Eduardo, University of Washington
Colton, David, University of Delaware
Coyle, Joe, University of Strathclyde
D’Ambrogi, Barbara, University of Oulu
Dekkers, Sophia, Imperial College London
Di Cristo, Michele, University of Milan
Eller, Matthias, Tennessee Technological University
Favaron, Alberto, University of Milan
Gaburro, Romina, UMIST
Garcia Almeida, Gerardo E, University of Wales, Cardiff
Green, John, University of Sheffield
Holst, Anders, Lund University
Isakov, Victor, Wichita State University
Isozaki, Hiroshi, Osaka University
Kaipio, Jari, University of Kuopio
Katchalov, Alexander, Steklov Mathematical Institute
Katsuda, Atsushsi, Okayama University
Knudsen, Kim, Aalborg University
Korotyaev, Evgeni, University of Potsdam
Kress, Rainer, University of Gottingen
Kurylev, Yaroslav, Loughborough University
Lassas, Matti, Rolf Nevanlinna Institute
Lesnic, Daniel, University of Leeds
Levin, Daniel, University of Oxford
Lionheart, William, UMIST
Liukkonen, Jukka, Helsinki University of Technology
Macia Lang, Fabricio, University Complutense of Madrid
Makio, Hannu, Helsinki University of Technology
Makrakis, George, IACM/FORTH
Mandache, Niculae, University of Loughborough
Marin, Liviu, University of Leeds
McDowall, Stephen, University of Rochester
Melin, Anders, Lund University
Mera, Nicolae, University of Leeds
Moeller, Steen, University of Aalborg
Morassi, Antonino, University of Udine
Nakamura, Gen, Gunma University
Nolan, Clifford, Rensselaer Polytechnic Institute
Ola, Petri, Oulu University
Orispaa, Mikko, University of Oulu
Paivarinta, Lassi, University of Oulu
Piiroinen, Petteri, Sodankylä Geophysical Observatory
Pikkarainen, Hanna, Helsinki University of Technology
Potthast, Roland, Brunel University
Pushnitski, Alexander, Loughborough University
Ruiz, Alberto, Universidad Autonoma de Madrid
Ruzhansky, Michael, University of Edinburgh
Sharafutdinov, Vladimir, Inst of Mathematics, Novosibirsk
Siltanen, Samuli, Instrumentarium Corp. Imaging Division
Sims, Robert, University of Alabama at Birmingham
Sleeman, Brian, University of Leeds
Somersalo, Erkki, Helsinki University of Technology
Stolk, Chris, Utrecht University
Tamasan, Alexandru, Babes-Bolyai University
Tietavainen, Juha-Pekka, Rolf Nevanlinna Institute
Uhlmann, Gunther, University of Washington
Vanska, Simopekka, Rolf Nevanlinna Institute
Voegeler, Matthias, University of Muenster
Wang, Jenn-Nan, National Cheng Kung University
Weder, Ricardo, National University of Mexico
Winkler, Joab, University of Sheffield
Yositomi, Kazushi, Kyushu University

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