This short course proposal targets Master or Doctoral students as well as
researchers and engineers who could be interested.
It provides them with a first introduction to certain tools of algebraic geometry and in particular the theory of positive polynomials and its dual, the K-moment problem.
This has many important applications not only in polynomial optimization but
also in many other areas (probability, statistics, dynamical systems, ODEs
and PDEs). These tools have already had an impact in several important
applications (e.g. in optimization, signal processing (Super-Resolution),
Optimal Design in statistics, control, computational geometry) and some
Machine Learning applications (computer vision, tensor decomposition &
completion, dictionary learning, mixture of Gaussians). In addition, noncommutative analogues of such tools are becoming of crucial importance in quantum information.
The course will be a 15 hours module, spread out over 4 days.