Explore shape optimization approaches for sharp-interface reconstructions in inverse problems in this virtual seminar talk from the 32nd Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS series. Delve into Antoine Laurain's presentation on recasting inverse problems as shape optimization problems within piecewise constant or piecewise smooth models. Learn about sensitivity analysis of cost functionals using shape optimization techniques and shape derivatives. Discover recent developments, including a shape-Lagrangian approach for point measurements and distributed shape derivatives for geometries with low regularity. Examine numerical results applying distributed shape derivative methods to electrical impedance tomography and full waveform inversion inverse problems.