Christoffel–Darboux kernels and the recovery of densities from moments.

I am a PhD student in mathematics at the Universidad de la República, Uruguay, advised by Mauricio Velasco. Before that I did my BSc and my MSc in mathematics at the same university, advised by Alvaro Rittatore. My area of research is applied algebraic geometry, drawing on real algebraic geometry, approximation theory and polynomial optimization.

A problem that matters in statistics, optimization and machine learning is to recover geometric or statistical information about a measure from finitely many of its moments. Those moments can be estimated from data, or produced by a moment–sums-of-squares hierarchy, which reduces non-convex optimization problems to semidefinite programming. In my doctoral work I study the recovery of densities from moments using the Christoffel–Darboux kernel, a classical tool from approximation theory and orthogonal polynomials that approaches the problem through the truncated moment matrix.

If you would like to get in touch, please do: leandrob@cmat.edu.uy