Prof. Matteo Novaga

The aim of this Studium project is to invite an expert in the field of nonlinear partial differential equations and variational methods to contribute in the research projects of the Fédération Denis Poisson involving the study of geometric nonlinear evolution equations arising in either Image Analysis or in Physics ; both applications lead to front propagation problems through, in particular, the so-called "level-sets approach".

Our goal is to work on methods issued from optimization techniques (variational methods) both on the theoretical point of view (spaces and adapted functional frameworks) and on the numerical point of view (design, convergence and implementation of algorithms). Some ill-posed variational problems arise in restoration or segmentation of strongly noisy images (tomography, medical images). Moreover, the current technics of level sets resolution lead to the study of "non-classical" Hamilton Jacobi Equations (for example with non-local terms) and are essentially the same in Image Analysis and in Physics (dislocations' type problems).