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Curso “Mathematical Methods for the Solution of Inverse Problems”

Desde el departamento de Estadística, Análisis Matemático y Optimización de Santiago os invitamos al siguiente curso “Mathematical Methods for the Solution of Inverse Problems” que tendrá lugar los días 10, 11, 17, 18 y 24 de octubre de 2018  en el aula 1 de la Facultad de Matemáticas en horario de 16:00 a 18:00 de la tarde. El curso será impartido por el profesor Jorge P. Zubelli (National Institute for Pure and Applied Mathematics (IMPA - Brazil)).

Más información (vincular documento que te adjunto)

El curso es gratuito pero es necesaria la inscripción en el mismo en el siguiente enlace:

https://docs.google.com/forms/d/e/1FAIpQLSfTonKtydlaa3FnM5IAdZEhzkyqVUwq1rXNQmXz-Ic3RXm6Xw/viewform

Resumen:

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:

  1. Inverse and Ill-posed problems: The tools of the trade. Singular Value Decomposition. Regularization. Noise modeling. Statistical Inverse Problems.
  2. Classical Tomography: The Radon transfom. Analytical Results. Numerical Methods. Convergence and Stability of reconstructions.
  3. 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.
  4. Inverse Problems in the the applied sciences: Examples from Mathematical Finance and Mathematical Biology.

Biografía del profesor:

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.