Topological problems in low-rank optimization

In low-rank optimization one seeks to minimize functions on manifolds or varieties of low-rank matrices or tensors. This has useful applications in signal and image processing, or in high-dimensional scientific computing. Due to their parametrization by multilinear maps, sets of low-rank matrices and tensors exhibit a rich geometric structure, which sometimes makes it possible to go beyond generic results in the analysis of corresponding nonlinear optimization methods on these sets. This concerns for example necessary first-order optimality conditions or classification of critical points. In this talk we discuss some of these questions.