November 7-11, 2022

- Plamen Stefanov (Purdue University)
- Gunther Uhlmann (University of Washington, Seattle and HKUST, Hong Kong)
- Gabriel Paternain (University Cambridge, UK)

The workshop will focus on the recent advances in geometric inverse problems. This includes linear problems of integral geometry type like the geodesic ray transform on functions, tensor fields, classical and generalized Radon transforms and the light ray transform in Lorentzian geometry. Those transforms are of independent interest but also appear often in non-linear inverse problems which are one of the topics of the workshop. Such problems are boundary rigidity, lens rigidity and scattering rigidity, where one wants to recover a Riemannian metric, a matrix field or a connection in a compact or a singular manifold from the boundary distance function, the lens relation or the scattering data (non-abelian X-ray). Related problems include recovery of the geometry from boundary or scattering observations of solutions of hyperbolic or elliptic linear or non-linear PDEs, for example the Einstein, or the Yang-Mills-Higgs equations. Recent advances in inverse spectral problems will be presented as well.

The interest of those problems is motivated also by applications in medical imaging, seismology and cosmology.

- Time Schedule (PDF)

- Jan Bohr (University of Cambridge):

On transport twistor spaces

Slides - Jan Boman (Stockholm University):

Radon transforms supported in hypersurfaces

Slides - Mihajlo Cekic (University of Zurich):

Holonomy and Spectral Inverse Problems

Slides - Yann Chaubet (Cambridge University):

Poincare series counting geodesic arcs - Xi Chen (Fudan University):

Retrieving coupled Yang-Mills-Higgs fields

Slides - Semyon Dyatlov (MIT):

Ruelle zeta at zero for nearly hyperbolic 3-manifolds

Slides - Nikolas Eptaminitakis (Purdue University):

Stability for the X-ray Transform on Asymptotically Hyperbolic Manifolds - Colin Guillarmou (Université Paris Saclay and CNRS):

Local unmarked lens rigidity in negative curvature - Sean Holman (University of Manchester):

Boundary Recovery of Anisotropic Electromagnetic Parameters for the Time-Harmonic Maxwell's Equations

Slides - Katya Krupchyk (University of California Irvine):

Inverse problems for nonlinear elliptic PDE and linearized anisotropic Calderón problem - Marco Mazzucchelli (CNRS and ENS de Lyon):

Surfaces of section for geodesic flows of closed surfaces

Slides - Francois Monard (University of California Santa Cruz):

Mapping properties of X-ray transforms near convex boundaries - Hadrian Quan (University of Washington Seattle):

The Calderon Problem for Fractional Dirac Operators - Jesse Railo (University of Cambridge):

Inverse fractional conductivity problem

Slides - Angkana Rüland (Heidelberg University):

Quantitative unique continuation properties of (nonlocal) discrete elliptic equations

Slides - Mikko Salo (University of Jyväskylä):

Free boundary methods in inverse scattering

Slides - Alexandru Tamasan (University of Central Florida):

On the Range conditions of the X-ray transform of planar symmetric tensors

Slides - Leo Tzou (University of Amsterdam):

A geometric user interface for analytic WF calculus for FIO - Yiran Wang (Emory University):

Some inverse problems in Lorentzian geometry - Jian Zhai (Fudan University):

An inverse boundary value problem for a nonlinear elastic wave equation

Slides - Yang Zhang (University of Washington):

Inverse boundary value problems for quasilinear hyperbolic equations on Lorentzian manifolds - Hanming Zhou (UC Santa Barbara):

Recovery of coefficients in semilinear transport equations - Ting Zhou (Zhejiang University)
- Xuwen Zhu (Northeastern University):

Spectral gaps for large genus hyperbolic surfaces

Slides

Johann Radon Institute for Computational and Applied Mathematics (RICAM)

Austrian Academy of Sciences

Austrian Academy of Sciences

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