报告人：Bastian Harrach教授

报告题目： Introduction to inverse problems for elliptic PDEs （I）-（II）

报告摘要：

This lecture introduces inverse coefficient problems for elliptic partial differential equations through the model example of electrical impedance tomography (EIT), also known as the Calderón problem. We formulate the forward problem variationally, define the Neumann-to-Dirichlet map, and discuss how finite sets of boundary current-voltage measurements lead to matrix-valued data models. We also prove differentiability properties of the parameter-to-measurement map.

报告时间：2026年9月10日9：00~12：00

报告地点：理学楼609

报告题目：Monotonicity and Localized Potentials for Shape Reconstruction （I）-（II）

报告摘要：

This lecture presents monotonicity methods for detecting inclusions in elliptic inverse problems without iterative parameter fitting. The main tools are operator monotonicity and convexity in the Loewner order, together with localized potentials that concentrate energy in prescribed subregions of the domain. We derive rigorous inclusion tests, discuss linearized variants, and explain how the approach accommodates noisy data, finitely many measurements, and inclusions with both positive and negative contrast. 

报告时间：2026年9月10日14：00~17：00

报告地点：理学楼1001

报告题目：Uniqueness and Lipschitz Stability from Finitely Many Measurements （I）-（II）

报告摘要：

This lecture studies the reconstruction of piecewise constant conductivity coefficients from finitely many boundary measurements in electrical impedance tomography. The unknown conductivity is represented by a finite number of parameters associated with a prescribed pixel partition, and suitable a priori lower and upper bounds are assumed.

Using monotonicity, convexity, and localized-potential arguments, we establish that the finite-dimensional inverse problem is uniquely solvable once sufficiently many measurements are available. We then prove a Lipschitz stability estimate, showing that perturbations in the measured data lead to proportionally bounded perturbations in the reconstructed conductivity parameters.

报告时间：2026年9月11日9：00~12：00

报告地点：理学楼1001

报告人简介：Professor Bastian Harrach studied mathematics with a minor in physics at the University of Mainz and received his doctorate in 2006. After postdoc stays in Austria and Mainz, he became associate professor at the TU Munich and the University of Würzburg. In 2013, he was appointed full professor and chair (W3) of Optimization and Inverse Problems at the University of Stuttgart. He followed the call for a W3-professorship for Numerics of Partial Differential Equations at Goethe University Frankfurt in 2015. He rejected a further W3-offer to TU Berlin in 2023 in favor of the competing offer to stay at Goethe University. Since January 1, 2024, he is the Dean of the Department of Computer Science and Mathematics at Goethe University.