Curso “Mathematical Methods for the Solution of Inverse Problems” que terá lugar os días 10, 11, 17, 18 e 24 de outubro de 2018 na aula 1 de la Facultad de Matemáticas da USC en horario de 16:00 a 18:00 da tarde. Impartido polo profesor Jorge P. Zubelli (National Institute for Pure and Applied Mathematics (IMPA - Brazil)).
O curso é gratuito pero é necesario inscribirse na seguinte ligazón: http://goo.gl/hN51PJ
Resumo dos contidos:
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.
Biografía do professor:
Jorge P. Zubelli is Professor of Mathematics at the National Institute for Pure and Applied Mathematics (IMPA - Brazil) and heads the Laboratory for Analysis and Mathematical Modeling in the Physical Sciences (LAMCA - IMPA). He obtained his PhD in Applied Mathematics from the University of California at Berkeley (1989), his MSc from IMPA in 1984, and his Electrical Engineering degree from IME-RJ in 1983 with specialization on Communication Engineering. Since 2002 he has coordinated the Mathematical Methods in Finance Professional Masters program at IMPA. He supervised 10 PhD thesis and over 30 MSc students.