Analytic Shape Reconstruction of a Planar Conductivity Inclusion

Explore the mathematical intricacies of reconstructing planar conductivity inclusions in this 50-minute virtual seminar presented by the Society for Industrial and Applied Mathematics. Delve into the concept of generalized polarization tensors (GPTs) and their role in describing perturbations in background potential caused by conductivity inclusions. Learn about the unique exterior Riemann mapping for simply connected planar domains and its significance in determining domain shape. Discover explicit expressions for Riemann mapping coefficients in terms of GPTs, derived through matrix factorizations and the application of Faber polynomial polarization tensors. Gain insights from speaker Mikyoung Lim of KAIST as part of the 43rd Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series.