10, 11, 17, 18, y 24 de octubre 2018
Aula 1 - Facultad de Matemáticas
Es necesario inscribirse aquí, aunque es gratuito.
Jorge P. Zubelli
National Institute for Pure and Applied Mathematics (IMPA - Brazil)
Mathematical Methods for the Solution of Inverse Problems
Most of the problems that appear in Engineering and the Applied Sciences require the identification of parameters from observed data. This ubiquity lead to a tremendous interest on the field. In fact, the theory of Inverse Problems lies in the cross-roads of many fields including Analysis and Partial Differential Equations, Optimization, Statistics and Numerical Analysis. In this mini-course we shall concentrate on some aspects of Inverse Problems according to the following plan:
- Inverse and Ill-posed problems: The tools of the trade. Singular Value Decomposition. Regularization. Noise modeling. Statistical Inverse Problems.
- Classical Tomography: The Radon transfom. Analytical Results. Numerical Methods. Convergence and Stability of reconstructions.
- Impedance Tomography: Some aspects of the forward problem. The Dirichlet to Neumann map. Calderon’s results. Uniqueness of the solutions and regularization. Optical diffusion tomography and infra-red imaging.
- Inverse Problems in the the applied sciences: Examples from Mathematical Finance and Mathematical Biology.